Final Shape of Precision Molded Optics: Part I—Computational Approach, Material Definitions and the Effect of Lens Shape

Abstract

Coupled thermomechanical finite element models were developed in ABAQUS to simulate the precision glass lens molding process, including the stages of heating, soaking, pressing, cooling and release. The aim of the models was the prediction of the deviation of the final lens profile from that of the mold, which was accomplished to within one-half of a micron. The molding glass was modeled as viscoelastic in shear and volume using an n-term, prony series; temperature dependence of the material behavior was taken into account using the assumption of thermal rheological simplicity (TRS); structural relaxation as described by the Tool-Narayanaswamy-Moynihan (TNM)-model was used to account for temperature history dependent expansion and contraction, and the molds were modeled as elastic taking into account both mechanical and thermal strain. In Part I of this two-part series, the computational approach and material definitions are presented. Furthermore, in preparation for the sensitivity analysis presented in Part II, this study includes both a bi-convex lens and a steep meniscus lens, which reveals a fundamental difference in how the deviation evolves for these different lens geometries. This study, therefore, motivates the inclusion of both lens types in the validations and sensitivity analysis of Part II. It is shown that the deviation of the steep meniscus lens is more sensitive to the mechanical behavior of the glass, due to the strain response of the newly formed lens that occurs when the pressing force is removed.

Precision glass molding: Toward an optimal fabrication of optical lenses

“…The large deviations near the center and the edge of the lens are due to the cooling-induced shrinkage and edge effect, respectively [40]. For a precision lens, the allowed center thickness change is about 25 mm [41], and the maximum deviation of overall surface shape should be within several micrometers or smaller [77,78]. Thus, the above numerical analysis [40] has demonstrated that mold compensation is essential; otherwise the lenses by PGM are not usable.…”

“…Recently, a method was proposed for identifying the shear relaxation modulus and the structural relaxation function via measuring the time variation of the glass plate thickness [80]. The CTE variation was often modeled by the ToolNarayanaswamy-Moynihan (TNM) model [77,78], the parameterization of which needs structure relaxation tests and thermal expansion tests. It is clearly complicated to establish a constitutive model using these methods.…”

“…Based on the shoving model [83], the temperature-dependent viscosity of optical glass can then be directly linked to its shear modulus, and the CTE of glass can be predicted through modulus based on a phenomenological TNM model [77,78], in which the parameters needed in TNM model can be determined by the modulus changes along with the temperature in the impulse excitation method. The above constitutive model with the measured/derived parameters has been verified and programmed into ABAQUS as a user material (UMAT) [40].…”

“…To obtain sophisticated solutions and useful guidelines for process optimization, the finite element (FE) method has been widely used to reveal the mechanism of geometry deviation and residual stresses [77,78]. This involves an accurate constitutive description of optical glass, the instantaneous property change of optical glass during the heating-cooling cycle in PGM, and lens distortion characterization.…”

“…Some used measured thermo-viscoelastic properties of the materials (BK-7 and TaF-3 [75]), obtained the viscoelastic property of glass by using the relaxation data from a cylinder compression test with the assumption of incompressibility [76], or treated glass as an elasto-viscoplastic material to account for the strain rate effect [79]. In most of these works the temperature-dependent rheology was modeled by the classical phenomenological Vogel-Fulcher-Tammann equation [37] or the thermos-rheological simple assumption [75,77], in which the parameters need to be obtained by curve fittings to a series of viscosity tests. Recently, a method was proposed for identifying the shear relaxation modulus and the structural relaxation function via measuring the time variation of the glass plate thickness [80].…”