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The thermal stress in the quartz ingot, generated by nonlinear temperature gradients during cooling process, and stress-related defects critically degrade its optical performance. Precise control of the cooling process is an emergent task in the production. This paper proposed a transient model to investigate changes of temperature and stress in the ingot during cooling. Also we examined the influences of the heater power profile on the stress evolution. The results show that a step function not only can notably reduce the maximum stress, but also cool down the ingot in a shorter period. The proposed cooling strategies provide a valuable direction for improving quality and productivity of the quartz glass in industry. Introduction Large-size and high-quality quartz glass plays an important role in the production of the optical components in aerospace, nuclear energy and other fields due to its better optical permeability than the normal[1]. Because the cooling rate varies greatly at different locations of a large glass ingot, it results in high thermal stress during cooling, and may cause microscopic fractures[2]. According to modern fracture theory, micro-fractures can be extended horizontally and vertically[3].It is common to expose the quartz glass to high temperature for a prolonged time to release the stress. Only by cooperating with interdisciplinary technology can accelerate its solution, and eventually overcome it. Studies of the synthesis or cooling processes of ceramics, crystals and non-quartz glass in similar furnaces or similar cooling process have been performed. Kingery et al. investigated factors affecting thermal resistance of ceramic materials[4]. Fang et al. investigated thermal stress of single crystal during the growing process[5] and of multicrystalline silicon during directional solidification[6]. Wang et al. organized the power allocation during the cooling process of sapphire[7]. Ma et al. optimized the induction-heated pulling-down furnace[8], and the melting process of the porous silica ingot[9]. Xiao et al. optimized thermal stress of the laser glass by controlling the point, line, and surface of the ingot[10]. Shepard et al. proposed a new method to measure the internal stress of glass and validated it[11]. Fan et al. conducted a simulation study on different thicknesses of toughened glass and found a better tempered glass with a thickness of less than 3 mm[12]. There are also some studies analyzing effect of internal energy of quartz glass on cracks through a microscopic view[13]. However, most of the research focused on a small temperature range in the entire process, or was not specifically designed for quartz glass. There is no research on the entire cooling process in quartz glass industry. In this paper, a transient model is proposed with heat transfers and thermal stress for the cooling of the quartz glass. A detailed stress evolution during the cooling is obtained for different heater power profiles. The maximum stress of the glass ingot is chosen as an evaluation of the stress level. The main purpose is to find a way how to reduce the stress in the cooling. According to the transient maximum stress profiles, the ramp-down rate of the heater power can be optimized to reduce the cooling stress and enhance the productivity by accelerating the cooling process.

Optimizing the Cooling Process of the Quartz Glass in an Electric Furnace