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<p>The surface-to-volume ratio (A/V-ratio) is relevant in many areas (e.g. heat regulation of animals, reactivity of substances) and has a&#xa0;significant impact on the progression of the heating curve of the temperature of the lubricating oil in gearboxes. The A/V-ratio is usually the main reason why large gearboxes heat up much more slowly than small gearboxes.</p><p>Even if the rate of change of temperature is also dependent on the specific heat capacity, density and heat transfer coefficient, the A/V-ratio is the decisive reason, because the A/V-ratio differs more between gearboxes of different sizes than the specific heat capacity, density and heat transfer coefficient. The rate of change of temperature varies by more than an order of magnitude due to the size of the gearboxes. Thus, criteria to determine the steady-state temperature based on a&#xa0;rate of temperature change are <i>not</i> generally applicable for gearboxes independent of their size or their A/V-ratio. It is found that the 2 K/h [<CitationRef CitationID="CR1">1</CitationRef>] and 1 K/h [<CitationRef CitationID="CR2">2</CitationRef>] thresholds are <i>not</i> sufficient to determine either the steady-state oil temperature rise, or a&#xa0;shutdown criterion for all tested gearboxes distributed by NORD. Anyhow, for practical reasons it is reasonable to define such a&#xa0;<b>K/h-threshold</b> that is represented by a&#xa0;specific rate of change of temperature. For gearboxes offered by NORD it can be certainly assumed that a&#xa0;smaller threshold than 2 K/h&#xa0;or 1 K/h is applicable to determine the approximate steady-state temperature. It is resource efficient to conduct tests only as long as necessary. In this publication, a&#xa0;generally applicable data-driven (machine learning) algorithm is presented that enables accurate extrapolation with a&#xa0;suitable shutdown criterion to calculate a&#xa0;sufficient amount of runtime to determine the steady-state oil temperature rise independent of the A/V-ratio of a&#xa0;gearbox.</p>

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Resource-efficient determination of the steady-state oil temperature of gearboxes for industrial applications

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Finn Swonke,
  • Nils-Peter Breiholz,
  • Jan Lotz,
  • Reiko Thiele,
  • Bernhard Bouché

摘要

The surface-to-volume ratio (A/V-ratio) is relevant in many areas (e.g. heat regulation of animals, reactivity of substances) and has a significant impact on the progression of the heating curve of the temperature of the lubricating oil in gearboxes. The A/V-ratio is usually the main reason why large gearboxes heat up much more slowly than small gearboxes.

Even if the rate of change of temperature is also dependent on the specific heat capacity, density and heat transfer coefficient, the A/V-ratio is the decisive reason, because the A/V-ratio differs more between gearboxes of different sizes than the specific heat capacity, density and heat transfer coefficient. The rate of change of temperature varies by more than an order of magnitude due to the size of the gearboxes. Thus, criteria to determine the steady-state temperature based on a rate of temperature change are not generally applicable for gearboxes independent of their size or their A/V-ratio. It is found that the 2 K/h [1] and 1 K/h [2] thresholds are not sufficient to determine either the steady-state oil temperature rise, or a shutdown criterion for all tested gearboxes distributed by NORD. Anyhow, for practical reasons it is reasonable to define such a K/h-threshold that is represented by a specific rate of change of temperature. For gearboxes offered by NORD it can be certainly assumed that a smaller threshold than 2 K/h or 1 K/h is applicable to determine the approximate steady-state temperature. It is resource efficient to conduct tests only as long as necessary. In this publication, a generally applicable data-driven (machine learning) algorithm is presented that enables accurate extrapolation with a suitable shutdown criterion to calculate a sufficient amount of runtime to determine the steady-state oil temperature rise independent of the A/V-ratio of a gearbox.