Fused silica aspherical cylindrical microlens arrays (ACMAs) are widely used in high-power lasers, mask aligners, large ground-to-air telescopes, and other optical systems that require high precision or operate in extreme environments because of their special geometric characteristics and excellent optical performance. Precision glass molding technology is the first choice for processing optical glass components with high precision, high efficiency, and low cost, compared with traditional array processing methods, such as ultra-precision machining, etching, and laser processing. However, it is difficult to monitor the glass molding process. Hence, finite element simulation is an effective means by which to study the molding process. However, the accuracy of finite element simulation is closely related to the thermo-mechanical and thermo-viscoelastic characteristics of glass. In particular, the thermo-viscoelastic parameters have the most important influence on the accuracy of molding simulation. In this study, we investigate the high-temperature viscoelastic properties of fused silica and establish a corresponding viscoelastic constitutive model. Then, a simulation study of fused silica ACMA precision molding is carried out, and the effects of the process parameters on the maximum stress of the lens are analyzed to provide a reference for fused silica ACMA experiments.

In this study, the minimum uniaxial creep test (MUCT) of fused silica is carried out, and the creep displacement of a fused silica cylinder is obtained. Based on the generalized Maxwell model and Williams-Landel-Ferry (WLF) equation fitting, the viscoelastic constitutive model and time-temperature equivalent model of fused silica are established. To accurately predict the stress state during the fused silica ACMA molding process, it is necessary to ensure the accuracy of the viscoelastic parameters. Therefore, the obtained viscoelastic parameters of fused silica by MUCT are simulated via the finite element method. Finally, the fused silica ACMA molding is simulated. The large deformation of glass during the molding stage is an important source of stress, and the holding stage can quickly reduce the stress, compared with the annealing stage, owing to the higher temperature. Hence, the effects of several process parameters (molding temperature, molding speed, molding pressure, friction coefficient, holding pressure, and holding time) in the molding and holding stages on the maximum stress of the lens are analyzed to obtain the optimized process parameters.

According to the MUCT results of fused silica, the viscoelastic constitutive model of fused silica based on the generalized Maxwell model is obtained. It is found that fused silica exhibits significant stress relaxation behavior above the transition temperature and that its shear modulus decreases to about 0.1% in short time [Fig. 5(b)]; the higher the temperature, the faster the relaxation rate. Moreover, based on the WLF equation, the time-temperature equivalent model of fused silica is obtained, and the prediction of the shear modulus of fused silica at different temperatures is achieved. The simulation results of MUCT are also consistent with the experimental results, which shows the accuracy of the viscoelastic parameters. The simulation study of fused silica ACMA molding shows that higher molding temperature can reduce the maximum stress of the lens [Fig. 9(b)] because of the higher relaxation rate and better fluidity of glass. A greater molding speed can cause a greater maximum stress value of the lens (Fig. 10) owing to the swifter deformation of glass, which leads to the inability of the stress to immediately relax. Friction can cause shear stress in the lens and change the stress state of the lens, and the appropriate friction coefficient can effectively reduce the maximum stress of the lens (Fig. 11). The maximum stress of the lens after constant pressure molding is smaller than that after constant molding rate molding [Fig. 12(b)]. Therefore, constant pressure molding is better than constant molding rate molding during fused silica ACMA molding. The maximum stress of the lens can be effectively reduced by applying the holding pressure after molding [Fig. 13(b)], but the mold presents “springback”, and the lower holding pressure cannot eliminate this phenomenon. Choosing the proper holding pressure and holding time can eliminate the mold “springback” when reducing the maximum stress. After the molding and holding stages, the maximum stress of the lens is 0.9693 MPa.

In this study, the high-precision stress state simulation of fused silica ACMA molding is investigated. Based on the MUCT and generalized Maxwell model, the viscoelastic constitutive model of fused silica is established. Fitting the WLF equation based on the relationship among the shear modulus values of fused silica at different temperatures, the time-temperature equivalent model of fused silica is established. The simulation results of MUCT show that the obtained viscoelastic constitutive model has high accuracy. A finite element simulation is conducted on the fused silica ACMA molding by inputting the obtained viscoelastic parameters of fused silica. The effects of different process parameters during the molding and holding stages on the maximum stress of the lens are analyzed. Moreover, on the premise of a downward displacement of 1.5 mm, the optimized process parameters are obtained. That is, the constant pressure mode is selected, the molding temperature is set to 1400 ℃, the friction coefficient is set to 0.3, the holding pressure is set to 400 N, and the holding time is set to 100 s. After the molding and holding stages, the maximum stress of the fused silica ACMA is 0.9693 MPa, which provides a reference for fused silica ACMA molding experiments.