Computational Modeling of Die Swell of Extruded Glass Preforms at High Viscosity

Abstract

Computational simulations of glass extrusion are performed to quantify the effects of material behavior and slip at the die/ glass interface on the die swell. Experimental data for three glass types are used to guide the computational study, which considers glass material to be viscous with and without shear thinning and viscoelastic using the Maxwell upper-convected model. The study starts with assuming no-slip at the glass/die interface to see if material behavior alone can explain the die swell results, and then considers slip using the Navier model where interface shear is directly proportional to the relative slip speed at the interface. Consistent with the possibility of slip and intended high viscosity applications, viscosity ranging from 10 7.4 -10 8.8 PaÁs was used. Based on optimization of the various input parameters required to achieve the measured die swell and ram force values, the study concludes that interface slip occurred as only extreme values of the shear thinning parameters provided an alternative.

Computational Modeling of Hole Distortion in Extruded Microstructured Optical Fiber Glass Preforms

“…Furthermore, the level of friction is assumed to be the same at all surfaces where glass contacts the die outer and the die insert with the feed holes and the pins. To better understand the magnitude of the normalized friction coefficient, in the die swell study by Trabelssi et al [22] normalized friction coefficients in the range of 2.5 < log(k×m/) < 3.5 were obtained for three different glass types contacting a stainless steel die for the same viscosity range of interest as the current study. Furthermore, in the extrusion study by Trabelssi, et al [22], a no-friction response occurred for approximately log(k×m/) < -1 while no-slip occurred around log(k×m/) > 8, which gives an active range of the normalized friction parameter as -1 < log(k×m/) < 8.…”

“…Compared to extrusion of a solid rod [22], the die includes an insert consisting of a disk with feed holes and protruding pins [25]. Referring to Figure 1, the insert forms two chambers.…”

“…Following the die swell study by Trabelssi, et al [22], inertia and gravity can be neglected due to the high viscosity (> 10 7 Pa·s) and low ram speed (< 0.5 mm/min for a billet diameter of about 30 mm) that are required to achieve the desired optical quality. A key assumption made in the current study is that steady state has been achieved, which neglects the transient phase as the glass flows through the feed holes and merges in the welding chamber.…”

“…While the viscosity level helps to simplify the problem in the above mentioned ways, it also makes interface slip more likely; thus it cannot be neglected. Following Trabelssi et al [22] and Trabelssi and Joseph [20], the linear form of the Navier friction model is used to describe the interface behavior between the glass and the die. In this model the interface friction,  wall , is related to the relative sliding speed between the die and the glass, u wall , by…”

“…Furthermore, in the manufacture of precision lenses and MOFs a relatively high viscosity in the range of 10 7 -10 9 Pa•s must be used. Therefore, interface slip between the glass and die/mold surface occurs [19][20][21][22][23], which has been shown to affect size and shape [22,24] of the resulting component.…”