On the Construction of Analytical Cooling Curves from ASTM D6200 Data Using Multi-variable Gradient Descent Method

ASTM D6200 is a standard test method to evaluate cooling characteristics of quench oils. The test produces six discrete numbers representing the cooling characteristics: three temporal scales (time to cool to 600°C, 400°C, and 200°C), two cooling rates (maximum cooling rate and cooling rate at 300°C), and 1 temperature scale (at maximum cooling rate). One of the main purposes of ASTM D6200 is to monitor the oil quality to ensure gears are properly quenched. The current standard only includes specifications for gear quenching oil and its application is limited to physical testing. The intent of this research is to explore the possibility of broadening the support for more quenchants and extending application to virtual engineering. This research includes two parts. The first part is the development of a systematic method to identify the characteristic points of a cooling curve. The second part is the construction of an analytical cooling curve based on the characteristic points. The analytical cooling curve is a mathematical function of temperature versus time that can provide temperature at any given time in the quenching process. In addition, the curve is differentiable to provide the cooling rate information at any given time as well.