Birefringence measurement for validation of simulation of precision glass molding process

During fabrication of glass lens by precision glass molding (PGM), residual stresses are setup which adversely affect the optical performance of lens. Residual stresses can be obtained by measuring the residual birefringence. Numerical simulation is used in the industry to optimize the manufacturing process. Material properties of glass, contact conductance and friction coefficient at the glass-mold interface are important parameters needed for simulations. In literature, these values are usually assumed without enough experimental justifications. Here, the viscoelastic thermo-rheological simple (TRS) behavior of glass are experimentally characterized by four-point bending test. Contact conductance and friction coefficient at P-SK57™ glass and Pt-Ir coated WC mold interface are experimentally measured. A plano-convex lens of P-SK57™ glass is fabricated by PGM for two different cooling rates and whole field birefringence of the finished lens is measured by digital photoelasticity. The fabrication process is simulated using finite element method. The simulation is validated, for different stages of PGM process, by comparing the load acting on the mold and displacement of the molds. At the end of the process, the birefringence distribution is compared with the experimental data. A novel plotting scheme is developed for computing birefringence from FE simulation for any shape of lens. This article is protected by copyright. All rights reserved.

[1]  K Ramesh,et al.  Digital photoelasticity – A comprehensive review , 2011 .

[2]  Lijuan Su,et al.  Investigation of the effect of coefficient of thermal expansion on prediction of refractive index of thermally formed glass lenses using FEM simulation , 2011 .

[3]  M. Arai,et al.  Characterization of the Thermo-Viscoelastic Property of Glass and Numerical Simulation of the Press Molding of Glass Lens , 2009 .

[4]  Hans Nørgaard Hansen,et al.  Thermal modelling of the multi-stage heating system with variable boundary conditions in the wafer based precision glass moulding process , 2012 .

[5]  P. Mahajan,et al.  Optimized Design of Optical Surface of the Mold in Precision Glass Molding Using the Deviation Approach , 2015 .

[6]  Anurag Jain,et al.  Compression Molding of Aspherical Glass Lenses–A Combined Experimental and Numerical Analysis , 2005 .

[7]  Fritz Klocke,et al.  A hybrid polymer–glass achromatic microlens array fabricated by compression molding , 2011 .

[9]  M. A. Burke,et al.  Finite‐Element Calculation of Stresses in Glass Parts Undergoing Viscous Relaxation , 1987 .

[10]  Kathleen Richardson,et al.  Final Shape of Precision Molded Optics: Part I—Computational Approach, Material Definitions and the Effect of Lens Shape , 2012 .

[11]  Fritz Klocke,et al.  Nonisothermal glass molding for the cost-efficient production of precision freeform optics , 2016 .

[12]  Ulrich Fotheringham,et al.  Thermal and Structural Property Characterization of Commercially Moldable Glasses , 2010 .

[13]  R. Landel,et al.  The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids , 1955 .

[14]  A. Yi,et al.  Annealing of Compression Molded Aspherical Glass Lenses , 2014 .

[15]  J. C. Tucker,et al.  Dependence of the Fictive Temperature of Glass on Cooling Rate , 1976 .

[16]  Kathleen Richardson,et al.  Final Shape of Precision Molded Optics: Part II—Validation and Sensitivity to Material Properties and Process Parameters , 2012 .

[17]  Fritz Klocke,et al.  Numerical Simulation and Experimental Study of Residual Stresses in Compression Molding of Precision Glass Optical Components , 2008 .

[18]  Fritz Klocke,et al.  Efficient mold manufacturing for precision glass molding , 2009 .

[19]  P. R. D. Karthick Babu,et al.  Development of photoelastic fringe plotting scheme from 3D FE results , 2006 .

[20]  Fritz Klocke,et al.  An integrated solution for mold shape modification in precision glass molding to compensate refractive index change and geometric deviation , 2014 .

[21]  Jérôme Molimard,et al.  Exact and efficient interpolation using finite elements shape functions , 2009 .

[22]  Anurag Jain,et al.  Finite Element Modeling of Structural Relaxation During Annealing of a Precision-Molded Glass Lens , 2006 .

[23]  R. Balendra,et al.  A new method of measuring thermal contact conductance , 2004 .

[24]  A. Q. Tool,et al.  RELATION BETWEEN INELASTIC DEFORMABILITY AND THERMAL EXPANSION OF GLASS IN ITS ANNEALING RANGE , 1946 .

[25]  Thomas F. Soules,et al.  An Efficient and Stable Algorithm for Calculating Fictive Temperatures , 2006 .

[26]  Lianguan Shen,et al.  Quantitatively measurement and analysis of residual stresses in molded aspherical glass lenses , 2014 .

[27]  Liangchi Zhang,et al.  Numerical optimization platform for precision glass molding by the simplex algorithm. , 2017, Applied optics.

[28]  J. D. Musgraves,et al.  Thermo-mechanical characterization of glass at high temperature using the cylinder compression test. Part I: Viscoelasticity, friction, and PPV , 2013 .

[29]  Hans Nørgaard Hansen,et al.  Evaluation of the viscoelastic behaviour and glass/mould interface friction coefficient in the wafer based precision glass moulding , 2014 .

[30]  S. Vengadesan,et al.  Numerical Modeling of Cooling Stage of Glass Molding Process Assisted by CFD and Measurement of Residual Birefringence , 2016 .

[31]  O. S. Narayanaswamy A Model of Structural Relaxation in Glass , 1971 .

[32]  Mathieu Sellier,et al.  An iterative algorithm for optimal mould design in high-precision compression moulding , 2007 .

[33]  Sung-Han Rhim,et al.  Prediction of birefringence distribution for optical glass lens , 2007 .

[34]  Tsunemoto Kuriyagawa,et al.  Modeling high-temperature glass molding process by coupling heat transfer and viscous deformation analysis , 2009 .

[35]  G. Scherer,et al.  Viscoelastic‐Elastic Composites: I, General Theory , 1982 .

[36]  H. Aben,et al.  Photoelasticity of Glass , 1993 .

[37]  G. Scherer,et al.  Viscoelastic-Elastic Composites: II, Sandwich Seal , 1982 .