Abstract
In this paper, experimental investigation and numerical simulation on heating process of small-sized workpieces in vacuum heat treatment furnace have been conducted. The proportional-integral-derivative (PID) control algorithm was employed for the temperature control of the numerical heat transfer model. Compared with the experimental data, the numerical results were validated. The computational maximum temperature difference of workpieces agreed well with the measured ones. In order to develop a new heating schedule for efficiently and uniformly heating loads, effects of heating rate, preheating rate and preheating temperature on heating performance have been researched. The results show that the maximum temperature difference decreases as the heating rate and preheating rate decrease appropriately. It is also found that decreasing preheating temperature can reduce the temperature difference of first-stage but increase the one of second-stage. Based on the results, an optimum heating process is proposed, through which the temperature difference within the workpiece drops below 50 °C during the whole heating schedule.
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Abbreviations
- T :
-
temperature
- t :
-
time
- C p :
-
specific heat capacity at consist stress
- u:
-
velocity vector
- q:
-
conductive heat flux vector
- n:
-
outward normal vector
- Q 0 :
-
additional heat source
- Q ted :
-
Thermo-elastic damping
- k :
-
thermal conductivity
- P in :
-
heat rate
- V :
-
volume of heating tubes
- K P :
-
proportional coefficient
- K I :
-
integral coefficient
- K D :
-
derivative coefficient
- T set :
-
preset temperature
- I :
-
radiation intensity
- G :
-
total incoming radiative heat flux
- e b :
-
blackbody hemispherical total emissive power
- n :
-
refractive index
- S :
-
propagation direction
- ρ :
-
density
- Ω:
-
solid angle
- Φ:
-
scattering phase function
- α :
-
absorption coefficient
- β :
-
extinction coefficient
- σ s :
-
scattering coefficient
- ε :
-
surface emissivity
- σ :
-
Stefan-Boltzmann’s constant
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Acknowledgements
The support of the State Key laboratory of Rolling and Automation and the financial support from National Key R&D Program of China(NO. 2017YFB0306400)towards this research are acknowledged.
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Li, J., Liu, J., Tian, Y. et al. Experimental and numerical study on optimization of heating process for small-sized workpieces in vacuum heat treatment furnace. Heat Mass Transfer 55, 1419–1426 (2019). https://doi.org/10.1007/s00231-018-2512-2
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DOI: https://doi.org/10.1007/s00231-018-2512-2