Open Access
Add to BibSonomy
Abstract
Chalcogenide glass lenses have been widely applied in infrared optical systems for their outstanding optical performance. It is a tendency for complex optical glass elements to be mass-produced with precision glass molding (PGM) technology, of course including chalcogenide glass aspheric lenses. But there is a problem that sometimes the surface profiles of the molded lenses are unstable which leads to a low pass-yield. Precision glass molding experiments and finite elements simulations are carried out to study the reasons for the mentioned problem in this paper. The results reveal that the laying error of the ball chalcogenide glass preform does not have a significant effect on the surface profile of the molded lens. However, in mass production the control of the temperature after forming stage in the PGM process is very important for obtaining the molded lenses with very similar surface profiles. The research results could help relevant researchers design the PGM processing parameters to overcome some errors in the mass production and manufacture precision glass molding machines. The increase in the yield of complex optical glass elements fabricated by PGM technology will further promote the application of such elements in various fields.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
To broaden the applications of the imaging optical systems, thermal imaging technology is used to assist the visible light imaging technology. These imaging optical systems have already been applied in some high-tech industrial fields, such as automotive, medical, security, and measurement [1]. Among infrared materials, chalcogenide glasses have low dispersion, low cost, high optical uniformity, and excellent properties in achromatism [2–4]. The application of aspherical lenses can reduce optical aberrations, internal reflection, and lens count [5]. Therefore, the usage requirement of chalcogenide glass aspherical lenses is enormous and pressing.
Chalcogenide glasses are non-crystalline materials and have lower glass transition temperatures than oxide glasses. Therefore, complex chalcogenide glass elements can be fabricated with PGM technology, which has high forming accuracy, high efficiency, short manufacturing cycle, low cost, and reusable tooling [6,7]. Compared with traditional manufacturing techniques such as grinding, polishing, etching, and laser processing, PGM technology offers the advantages of low pollution, net shaping, and mass manufacturability [8].
PGM technology is a complex strong thermo-mechanical molding technology. The forming quality of the molded lenses is affected by a variety of processing parameters and processing conditions [7]. Some researchers have studied the effect of PGM processing parameters on molded lenses. Since some experimental phenomena can not be directly observed and some physical quantities can not be gained from the sensor monitoring results of the precision molding machine, the finite element method (FEM) is adopted to cover the shortage [7]. Son et al. studied the effect of molding temperature on the transferability of the diffractive structure and the difference in the transferability between the inner and outer diffraction ring when PGM chalcogenide glass diffractive optical elements [1]. Zhou et al. explained why the curve deviation decreased with the increase of the holding force, and verified the curve deviation is not sensitive to the selection of demolding temperature with FEM [9]. Jiang et al. proposed an improved simulation model to predict the form deviation of the molded lenses by combining the simulation with the commercial simulation platform ABAQUS and the optical path difference resulting conducted by applying a ray-tracing method. The research results proved that the accuracy of the prediction of the form deviation highly depends on the structure relaxation behavior during PGM [10]. Our research team developed a residual stress prediction model for aspheric lenses, which proved to be effective through PGM experiments and FEM [11]. We also established a heat transfer model in the heating stage of the PGM process and used the FEM to verify the established model [12]. Zhou et al. analyzed the refractive index changes of As2S3 at different cooling rates with the FEM based on the Tool-Narayanaswamy-Moynihan model for structural relaxation behavior [13]. When PGM chalcogenide glasses lenses with antireflective surfaces, Vu et al. carried out a multiscale simulation modeling by which the form accuracy of the molded glass lenses was predicted at the macroscale while the replication of the antireflective structure was visualized at nanoscale simulation [14].
Although PGM technology has developed for many years, there are still typical forming defects in the molding process, namely cracks, form deviation, and so on [7]. Particularly in mass production, the form deviations of the molded lenses are unstable leading to plenty of the molded lenses do not meet the usage conditions. The reasons for this unstable state should be discussed. This paper aims to investigate the effect of the PGM process on the surface profiles of molded lenses. That is, the same processing parameters are set in the PGM experiments, and the existing differences in the actual PGM processes are analyzed to indicate what factor is the main reason that causes the surface profiles of the molded lenses unstable. In this study, a group of PGM chalcogenide glass aspherical lens experiments are carried out. The viscoelastic parameters of the chalcogenide glass used in the experiments are deduced by relevant theory and other glass viscoelastic parameters. Then three-dimensional simulations with finite element analysis software MSC.Marc are adopted to study the influence mechanism of related parameters on the stress and strain of the chalcogenide glasses. The research results reveal the effect of the laying error of the ball chalcogenide glass preform and processing parameters on the form deviation of the molded lens. Finally, a group of cylindrical glass compression experiments are carried out and verify the research results. The research results could help improve the stability of the surface profiles of the molded lenses.
2. Materials and methods
PGM machines can be classified into fixed die and inline die by the tooling configuration. The cross-section schematic diagram of a typical inline tooling configuration is shown in Fig. 1. The tooling consists of a stack of top mold core, bottom mold core, outer sleeve, and inner ring [15].
When the designed lens geometry is bi-convex, equal meniscus, positive meniscus, negative meniscus, or bi-concave, the glass preform type could choose ball preform [16]. It is important to place the glass preform on the center of the bottom mold core surface before the PGM experiment starts. Because the surface of the glass preform and the forming surfaces of the mold cores are optical surfaces with low surface roughness, the friction parameter between the glass preform and the mold core is close to 0 at room temperature. When the centering tool is not used, the ball glass preform will spontaneously go to the center of the bottom mold core surface under the influence of gravity. When the ball glass preform is placed on the bottom mold core, the preform swings under gravity for tens of seconds until it stops. If the top mold core is inserted into the outer sleeve while the ball preform is still moving or the ball preform is motionless but the operating platform has a slight slope, the axis of rotational symmetry of the preform may not coincide with the mold core which is the laying error, as shown in Fig. 2. The influence of the laying error of the glass preform on the molded lens will be discussed below.
Fig. 2. Assembly diagram when (a) there is no laying error and (b) there is a laying error for glass preforms.
A group of four PGM chalcogenide glass aspherical lens experiments are carried out. The glass material is chalcogenide glass As40Se60 (GG6) from GRINM Guojing Advanced Materials Co., Ltd. The mold material is J05 grade tungsten carbide (WC) from Fujidie Co. The schematic diagram of the designed chalcogenide glass aspherical lens whose shape is meniscus is shown in Fig. 3. Surface 2 of the designed lens is a sphere surface with a radius of 72.5 mm, while surface 1 is a rotationally symmetric aspheric surface that is described by Eq. (1).
The processing parameters of the four experiments are set the same and listed in Table 1. The experiment process is divided into four stages, including heating, forming, annealing, and cooling stages [17,18]. The experiment process is divided by temperature step for it is in every stage. The 1st and 2nd steps are heating stage, the 3rd and 4th steps are forming stage, the 5th step is annealing stage, the 6th step is cooling stage.
Table 1. The precision glass molding processing parameters in the experiments
The “STEP” parameter in the heating and cooling stages about heating/cooling rate means that the temperature setting numeric value is changed in steps. Based on Ref. [16], a 10 mm diameter chalcogenide glass As40Se60 ball preform can be uniformly heated after 300s. Thus, in addition to the heating time of the first temperature step, the time 300s for the second temperature step is enough to make the temperature of the glass preform uniform in this paper. When taking a PGM experiment on a single station PGM machine, usually tens of seconds are set to relax the applied load [19]. The sampling period in the experiments was set as 3000 s. One thousand data items were collected within the sampling period. That is, the sampling cycle is sampling period/1000 items, which is three seconds. In the second pressing step of the experiments in this paper, 102 seconds are set to adequately relax the stress of the glass while 34 group data will be obtained in this step for every PGM experiment.
In the forming stage, the lower shaft is driven upward. The setting position parameter is the position of the lower shaft. The position is set as 83.596 mm at the end of the forming stage, where the glass material can not fill the mold cavity. In this condition, when there is no laying error for the glass preform, the molded lens should not have a vertical face on the side, as shown in Fig. 5(a). Otherwise, when there is a laying error for the glass preform, part of the molded lens will have a vertical face on the side, as shown in Fig. 5(b). The photographs of the convex and concave surfaces of one molded typical lens are shown in Fig. 6, which is roughly the same as the other three molded lenses.
Fig. 5. Photographs of molded lenses (a) without vertical face and (b) with vertical face on the side.
Table 2 shows the experiment results of the molded lenses whether have a vertical face on the side in the four precision glass molding experiments. The convex surface form deviation curves of the four molded lenses measured by Talysurf PGI 1240 are shown in Fig. 7. Form is a deviation away from the intended nominal shape of the surface, ignoring variations due to texture [20]. The surface roughness results of the glass specimens are not exhibited in this paper.
Table 2. The appearance of the vertical face on the side of the molded lens in the four experiments
2.1 Heating stage
The heat generators for the PGM machine used in this paper are infrared lamps. The tooling configuration shown in Fig. 1 leads to that infrared lamps can not directly radiate on the surface of the chalcogenide glass preform. In addition, chalcogenide glasses are designed to transmit infrared radiation, and little if any heat is generated directly within the chalcogenide glass from the lamps [16]. In the heating stage, the button for filling the forming cavity with nitrogen is turned on. Therefore, the heat transfer that the chalcogenide glass preform directly participates in consists of conduction and convection.
GMP-415 machine is equipped with PID controllers that regulate lamp output to both minimize their maximum operating cycle and ensure that temperatures do not significantly exceed their set point. The value of the temperature comes from sensors. The important characteristics of sensors include reusability, reproducibility, stability, sensitivity, robustness, reliability, etc. [21]. The applications of optical fiber sensors include temperature detection, strain detection, liquid level sensing, bending torsion measurement, and so on [22]. Polymer optical fibers have some advantages compared to silica fibers, such as a lower Young’s modulus, a higher thermo-optic coefficient, and a larger elongation before breakage which are exploited in a large variety of applications in the sensing field [23]. Because the PGM process includes a temperature change at hundreds of degrees Celsius and the tooling in the PGM process is not motionless, the form of thermal monitoring for the used PGM machine uses thermocouples. The inline tooling in this paper is not fixed in the PGM machine, the end of the thermocouple is inserted into the WC part which is fixed with the die plate, as shown in Fig. 4. Thermocouples consist of a pair of metal wires made of dissimilar materials that are joined at one end to read a voltage drop on the other end. The amount of voltage difference is temperature-dependent [16]. In the processes of the precision glass molding experiments, the monitor data of some physical parameters are saved in the compact flash card which is inserted in the machine. By reading the contents of the compact flash card, the temperature curves of the upper and lower die plates over the time of 1st temperature step are plotted in Fig. 8.
Fig. 8. The temperature waveforms of the upper and lower die plates over the time of the 1st temperature step of the four experiments.
In the four experiments, the upper die plate temperatures change with time and are basically the same, and so do the lower die plate. At the end of the 1st temperature step, the temperature of the upper die plate is about 220 °C, and the temperature of the lower die plate is about 223 °C. According to Table 1, there are 300s to allow the glass preform temperature to achieve uniformity. Based on the tooling configuration, the glass preform temperature at the end of the heating stage is close to the monitor temperature of the lower die plate. Therefore, the temperature of the glass preform is assumed to be 223 °C after the heating stage.
2.2 Forming stage
The forming stage consists of two steps. The first step of the forming stage which corresponds to the 3rd temperature step, aims to press the chalcogenide glass to a specified state by moving the lower shaft to the specified position. The second step of the forming stage which corresponds to the 4th temperature step, aims to hold the toolings still for 102s.
For the first step, the displacement waveforms of the lower die plate in the four experiments over time are shown in Fig. 9. According to the enlarged view, the moving speed of the lower die plate in the four experiments is No.3 > No.2 > No.1 >No.4. The position of the lower die plate is related to the deformation of the chalcogenide glass preform.
Fig. 9. The waveforms of the displacement of the lower mold over time in the forming stage of the four experiments.
2.3 Annealing stage
In the annealing stage, the upper die plate is in contact with the top mold core, while the lower die plate is in contact with the bottom mold core. Since WC has good heat transfer performance, the temperature detected by the upper thermocouple is considered the upper mold temperature, while the temperature monitored by the lower thermocouple is considered the lower mold temperature. At the end of the annealing stage, the upper and lower die plates are both cooled to 180°C. The curves of the temperatures over time in the four experiments are shown in Fig. 10. It can be seen that the temperatures of the molds rise for some time before they begin to fall. The maximum temperatures during the annealing stage are different in the four experiments.
Fig. 10. The curves of the temperatures over the time of the upper mold and the lower mold before reaching 180°C in the four experiments.
2.4 Cooling stage
In the cooling stage, the toolings are in tight contact with the lower die plate, while the toolings are far away from the upper die plate. Thus, the detected lower die plate temperatures are assumed as the mold cores temperatures. The temperature curves of the upper and lower molds over time in the cooling stage of the four experiments are shown in Fig. 11.
Fig. 11. The temperature curves of the (a) upper and (b) lower molds over time in the cooling stage of the four experiments.
3. Viscoelasticity of chalcogenide glass
The FEM is adopted to analyze the instability of the surface profiles of precision molding chalcogenide glass aspherical lenses in mass production in this paper. Achieving accurate simulation in the glass lens molding process is largely dependent on the mechanical and thermal properties of the glass material. In particular, thermo-viscoelastic parameters are very important for improving simulation precision [8]. There are three equations to describe viscosities of glass over a broad temperature range, namely the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) equation, the Avramov–Milchev (AM) equation, and the Vogel-Fulcher-Tammann–Hesse (VFT) equation. MYEGA equation is a relatively new theory that has no viscosity singularity at temperatures above 0 K and is suitable for extrapolation of the viscosity data to the high-temperature region. Relevant studies show that the MYEGA equation is suitable for describing experimentally obtained viscosity data of chalcogenide glass [24,25]. MYEGA equation is expressed as Eq. (2).
The structure of vitreous As2S3 and As2Se3 is described as a layered two-dimensional network mainly consisting of structural units [AsS3/2] and [AsSe3/2] in the shape of a trigonal pyramid. Inside the layers, the atoms (structural units) are connected with strong covalent bonds while there are only van der Waals bonds between the layers [26]. As2S3 and As2Se3 both show an ‘intermediate’ behavior from the kinetic fragility point of view [25]. Since As2Se3 glass and As2S3 glass have such similarities and viscoelastic parameters of glass are related to the viscosity of glass, the viscoelastic parameters of As2Se3 glass can be calculated based on the viscoelastic parameters of As2S3 glass [18]. In Ref. [25], the experimental viscosity data of both two chalcogenide glasses are well-fitted by the MYEGA equation. The important parameters calculated from the viscosity data for As2S3 and As2Se3 are listed in Table 3. According to Eq. (2) and Table 3, the viscosity of As2Se3 at 223°C is about 7.6873 dPa·s.
Table 3. Overview of important parameters calculated from the viscosity data for As2S3 and As2Se3 [25]
To obtain the mathematical relationship between As2Se3 temperature and As2S3 temperature when they are at the same viscosity, firstly calculate the viscosities of As2Se3 when the temperatures are from 150°C to 250°C based on Eq. (1), Table 3 and Fahrenheit to Celsius formula. Secondly, the corresponding temperatures of As2S3 are calculated when the viscosities of As2S3 are the same as the just calculated viscosities of As2Se3. IBM SPSS Statistics software was used for regression analysis of different temperatures corresponding to the same viscosity of glasses As2Se3 and As2S3. The two groups of data have a linear relation as expressed in Eq. (4), while R-squared is 0.999987.
where T1 and T2 are the temperatures of As2S3 and As2Se3, respectively, a is 0.89424, b is 17.0794. According to Eq. (2) and Table 3, As2S3 has a viscosity of 14.84318801 at 428 K (220°C), and As2Se3 has the same viscosity at 417 K (213.87°C). According to Eq. (4), when the temperature of As2S3 is 220°C, the temperature of As2Se3 is 213.81°C to make the viscosities of the two glasses the same. The difference value of 0.06°C points that Eq. (4) is a good expression to describe the temperature relationship between the two glasses when they have the same viscosity.For viscoelastic materials, the stress relaxation behavior at different temperatures can be shifted along the logarithmic time without shape change on the reference master curve [13]. This is the so-called Thermo-Rheological Simplicity (TRS) behavior. The empirical Williams-Landel-Ferry (WLF) equation Eq. (5) is used to characterize the shift factor aT(T).
where Tref is the reference temperature, and C1 and C2 are constants adjusted to fit the shift factor. The shift factor can be calculated from the creep compliance curves or shear relaxation modulus curves along the logarithmic time axis. Supposing that ${T_{ref\_A{s_2}{S_3}}}$ is the reference temperature of As2S3, ${T_{ref\_A{s_2}S{e_3}}}{C_{2\_A{s_2}{S_3}}}$ is the reference temperature of As2Se3, ${C_{1\_A{s_2}{S_3}}}$ andare the constants in Eq. (5) for As2S3, ${C_{1\_A{s_2}S{e_3}}}$ and ${C_{2\_A{s_2}S{e_3}}}$ are the constants in Eq. (5) for As2Se3. For As2S3, when the reference temperature ${T_{ref\_A{s_2}{S_3}}}$ is chosen as 220°C, ${C_{1\_A{s_2}{S_3}}}$ is 5.487 and ${C_{2\_A{s_2}{S_3}}}$ is 49.798 [13]. Supposing that the viscosity of As2S3 at the temperature ${T_{ref\_A{s_2}{S_3}}}$ is the same as the viscosity of As2Se3 at the temperature ${T_{ref\_A{s_2}S{e_3}}}$, the viscosity of As2S3 at the temperature T1 is the same as the viscosity of As2Se3 at the temperature T2. The shift factor when the temperature of the glass As2S3 changes from ${T_{ref\_A{s_2}{S_3}}}$ to T1 is the same as when the temperature of the glass As2Se3 changes from ${T_{ref\_A{s_2}S{e_3}}}$ to T2. Then Eqs. (6)–(9) can be gained.Therefore, ${C_{1\_A{s_2}{S_3}}}$ is 5.487, ${C_{2\_A{s_2}S{e_3}}}$ is 44.531, ${T_{ref\_A{s_2}S{e_3}}}$ is 213.8°C.
The shear modulus G(t) of As2S3 can be represented by the Prony series as expressed below:
Table 4. Shear stress relaxation modulus of As2Se3 at reference temperature 213.8°C
4. Results and discussions
According to Table 2, there are laying errors for the chalcogenide glass preforms in the 1st and 3rd experiments, while there are no laying errors for the chalcogenide glass preforms in the 2nd and 4th experiments. However, the surface profiles of the molded lenses in the 1st and 2nd experiments are very similar. Thus, the laying error of the ball chalcogenide glass preform does not have a significant effect on the surface profile of the molded lens. In normal experiments, the glass preform should be placed on the center of the mold core. Thus, the difference in the 2nd and 4th experiment processes will be discussed. The transition temperature of As40Se60 is 187°C [27]. According to Fig. 11, the temperature differences between the four experiments in the cooling stage are too small to affect the surface profile of the molded lens. Therefore, the forming stage and the annealing stage will be discussed below.
Since glass preform deformation in the forming stage can not be seen and some physical parameters can not be detected by the sensors, the finite element method is used to analyze the existing problem. The diagram of the three-dimensional geometrical model consisting of the molds and the glass preform is established in the finite element analysis software MSC.Marc is shown in Fig. 12. The mechanical and thermal properties of the chalcogenide glass and the molds are listed in Table 5 [12,13,18,28].
Table 5. Mechanical and thermal properties of the chalcogenide glass and molds
4.1 Forming stage
In the forming stage of the PGM process, the toolings and the glass preform are held up by the lower die plate and move upward. When the top mold core contacts the upper die plate, the glass preform begins to be deformed by pressure. The forming stages in the 2nd and 4th experiments will be simulated with MSC.Marc software. Therefore, when establishing the simulation models, a displacement constraint of 0 is applied to the upper-end face of the upper die plate. At the same time, the displacement values varying time shown in Fig. 9 are applied to the lower end face of the lower die plate respectively in two simulation models. Based on the saved data in the compact flash card, when the chalcogenide glass preform deforms 6.981 mm under the molding pressure to the designed center thickness, the time in the 2nd experiment is 477s, while it is 564s in the 4th experiment. In addition, to simulate the second step of the forming stage, 102s is respectively added to the operating time in the two simulations while the positions of the molds are the same as those at the end of the first step of the forming stage. In the established simulation models, the increment step is set every 3s.
The cloud maps of the equivalent von Mises stress of the chalcogenide glasses in the 2nd and 4th experiments, when the lower shaft moves to the designed position, are shown in Fig. 13. It can be seen that the difference mainly exists in the half-part of the glass close to concave surface. In 2nd experiment, the values of the equivalent von Mises stress in a large scale of the upper half part of the chalcogenide glass are bigger than 6.3004 MPa and smaller than 7.242 MPa, while the values are bigger than 5.851 MPa and smaller than 6.592 MPa in 4th experiment. The difference in the equivalent von Mises stress is big in the two experiments.
Fig. 13. The cloud maps of the equivalent von Mises stress of the chalcogenide glasses in the (a) 2nd and (b) 4th experiments at the end of the first step of the forming stage.
There is 102s stress relaxation time for the glass before entering the PGM annealing stage. Since the increment step is set every 3s, the cloud maps of the equivalent von Mises stress of the chalcogenide glasses in 2nd and 4th experiments at the end of the second step of the forming stage are shown in Fig. 14. The difference of the equivalent von Mises stress in the glass in the two experiments are not obvious as that in Fig. 13. The max equivalent von Mises stress is 5.988 MPa in the 2nd experiment, while it is 5.930 MPa in the 4th experiment. Therefore, the setting of relaxation time effectively reduces the adverse influence of machine error on the molded glass lens.
Fig. 14. The cloud maps of the equivalent von Mises stress of the chalcogenide glasses in the (a) 2nd and (b) 4th experiments at the end of the second step of the forming stage.
4.2 Annealing stage
The heat transfer in the PGM annealing stage includes convection and conduction. The initial condition is the value of 223°C applied to all the nodes in the established model geometry. In the contact relations, the value of the “distance close to contact” is set to the value of 0.001 for all two contact geometries to realize the heat conduction while it will not introduce a big simulation error. The contact heat transfer coefficient is set as 2400W/m2 °C [18]. The boundary condition in thermal analysis is added to the elements’ faces that can contact with N2. The gas temperature is set as 30°C. The effectiveness of heat transfer by convection is measured by a property known as the heat film coefficient. The value of the heat film coefficient mainly depends upon the physical properties of the fluid and how turbulent the flow is. The typical value for heat film coefficients for gasses forced convection is 11-114 W/m2°C [29]. The convection heat transfer coefficient is set as 20 W/m2°C in the boundary condition of the simulation model. The convection heat transfer coefficient is set as 0.02 W/m2°C. In the established simulation models, the increment step is set every 10s.
When the die plates are approximately cooled to 180 °C, the temperature distribution cloud maps of the cross-section of the molds and the chalcogenide glass, and the only glass are shown in Fig. 15. To distinguish the parts for convenience, the grids are visible in Fig. 15. It can be seen that when the die plate is cooled to 180°C, the time is about 100s. According to Fig. 10, the die plate temperature first rises and then gradually decreases. For the four PGM experiments, in the annealing stage, the time from the die plate temperature decrease to the temperature 180°C is about 100s. Therefore, the established simulation model is credible.
Fig. 15. Temperature distribution cloud maps of the cross-section of (a) the molds and glass and (b) the only glass at the 10th incremental step.
The temperature distribution cloud maps of the cross-section of the molds and the glass in the 11th incremental step and 25th incremental step are shown in Fig. 16. It can be seen that the temperature of the top mold core and lower die plate first is cooled down. When the mold temperature is high, the glass temperature is corresponding high. When the experiment process enters the annealing stage, the external pressure is repealed. But the glass will be under the gravity of the top mold core. Since the glass temperature rises, the viscosity of the glass becomes smaller. Then, the glass gets further deformation. The form deviation of the molded lens may be due to the machine error in the annealing stage.
Fig. 16. Temperature distribution cloud maps of the cross-section of the molds and glass in the (a) 11th incremental step and 25th incremental step.
Based on Fig. 15 and Fig. 16, the temperature difference between the molds is far smaller than the glass. Thus, three finite element simulations are carried out while the boundary conditions are applied to the molds. Assuming the temperature of the molds is uniform, the data of the monitoring temperature varying the time in No. 1, No. 3, and No. 4 PGM experiments are the temperature of the molds. The cloud maps of the equivalent of total strain and the equivalent of the thermal strain of the cross-section of the glass in the No. 1 experiment are shown in Fig. 17. The max equivalent of strain without thermal strain is about 0.792e-3 (2.073e-3 subtract 1.281e-3) in the edge position of the glass. It can be seen that the strain other than the strain produced by thermal shrinkage is not negligible. The cloud map of the major principal value of total strain of the cross-section of the glass in the No.1 experiment is shown in Fig. 18. The max major principal of total strain is on the edge position of the lens and has a significant impact on the lens profile in the normal direction of the surface, which is related to the form deviation of the molded lens.
Fig. 17. Cloud maps of (a) equivalent of total strain and (b) equivalent of the thermal strain of the cross-section of the glass in the annealing stage of the No.1 experiment.
Fig. 18. Cloud map of the major principal value of total strain of the cross-section of the glass in the annealing stage of the No. 1 experiment.
The cloud maps of the equivalent of total strain and the equivalent of the thermal strain of the cross-section of the glass in the No. 3 experiment are shown in Fig. 19. The max equivalent of strain without thermal strain is about 0.353e-3 (1.723e-3 subtract 1.37e-3) in the edge position of the glass. Therefore, there is an obvious difference in the equivalent of the total strain of the molded lens in No. 1 and No. 3 experiments, when without thermal strain it still is much different. Therefore, the abnormal temperature of the annealing stage has a serious effect on the surface profile of the molded lens.
Fig. 19. Cloud maps of (a) equivalent of total strain and (b) equivalent of the thermal strain of the cross-section of the glass in the annealing stage of the No. 3 experiment.
5. Confirmatory experiments
The surface profile is related to the surface sag in the diameter direction of the lens. Thus, the effect of the processing parameters on the surface profile of the lens can be simplified as the effect of the processing parameters on the surface sag of the lens. When the glass specimens are cylinders whose end faces are flat surfaces, the surface sag of the glass is the height of the glass. A group of cylindrical glass compression experiments at three different temperatures are carried out. The glass specimen materials are the same as those in Section 2. The designed temperatures of the three experiments are 225°C, 230°C, and 235°C, respectively. The experiment processes in the three experiments are the same. Firstly, the glass is heated to the designed temperature. Secondly, the glass keeps the designed temperature for 999s. Thirdly, the lower shaft moves upward to a fixed position, so that the glass is deformed. Fourth, the lower shaft is motionless for 120s. Based on section 4.1, the stress of the lens will be close to 0 when this stage finishes. Finally, the glass is cooled at an approximately constant cooling rate of 0.1°C/s, as shown in Fig. 20. The photograph of the glass specimens after precision molding experiments is shown in Fig. 21. The heights of the three glass specimens before and after the experiments are shown in Table 6. It can be seen that the temperature at the beginning of the annealing stage has a non-negligible effect on the molded lens.
Fig. 21. Photographs of the (a) top view and front view of the glass specimens after precision molding experiments.
Table 6. The original and final heights of the glass specimens
According to Fig. 10, the annealing rates of the four experiments are similar. Since the curves of the No. 1 and No. 2 experiments in section 2 are close, the surface profiles of the molded lenses are most close. Moreover, the difference in the temperature curves between the No. 2 and No. 3 experiments is larger than that between the No. 2 and No. 4 experiments, correspondingly the difference in the surface profile of the molded lenses between the No. 2 and No. 3 experiments is larger than that between No. 2 and No. 4 experiments. Therefore, in mass production, the control of the temperature after forming stage in the PGM process is very important.
6. Conclusions
Aiming at the instability of the surface profiles of precision molding chalcogenide glass aspherical lenses in mass production, a group of PGM experiments are carried out. Based on the appearances of the molded lenses, the effect of the laying error of the ball glass preform on the form deviation is first analyzed. Then, the actual processing parameters are compared, and find out that the main differences lie in the forming and annealing stages in the PGM experiments. To further find the main reason for the mentioned problem, some finite element simulations are carried out to visualize physical quantities that are not visible during the experiment based on the viscoelasticity of chalcogenide glass. Finally, confirmatory experiments are carried out and verify the results of the previous analysis. The primary findings are as follows:
- (1) The laying error of the ball glass preform does not have an obvious effect on the surface profile of the molded lens in mass-production with PGM technology.
- (2) In the forming stage, the setting of a specific relaxation time for the deformed glass can improve the stability of the surface profiles of the molded lenses mass fabricated by PGM technology when there are machine errors.
- (3) The temperature control in the annealing stage of the PGM process has an important effect on the surface profile of the molded lens. Therefore, in subsequent mass production studies, it is very important to achieve good temperature repeatability during the annealing stage.
Funding
Natural Science Foundation of Jilin Province (20220101124JC); Jilin Scientific and Technological Development Program (20210201034GX).
Acknowledgments
This work was supported by the 111 Project of China (D21009). The authors thank Prof. Changxi Xue for his academic advice and GRINM Guojing Advanced Materials Co., Ltd for providing the chalcogenide glasses.
Disclosures
The authors declare that there are no conflicts of interest related to the work in this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. B.-R. Son, J.-K. Kim, Y.-S. Choi, and C. Park, “Transferability of Diffractive Structure in the Compression Molding of Chalcogenide Glass,” Micromachines 14(2), 273 (2023). [CrossRef]
2. F. Zhang, Q. Yang, H. Bian, M. J. Li, X. Hou, and F. Chen, “Fabrication of chalcogenide glass based hexagonal gapless microlens arrays via combining femtosecond laser assist chemical etching and precision glass molding processes,” Materials 13(16), 3490 (2020). [CrossRef]
3. F. Zhang, Q. Yang, H. Bian, S. K. Wang, M. J. Li, X. Hou, and F. Chen, “Fabrication of a chalcogenide glass microlens array for infrared laser beam homogenization,” Materials 14(20), 5952 (2021). [CrossRef]
4. Y. Liu, Y. Xing, H. Fu, C. Li, C. Yang, B. Cao, and C. Xue, “Deformation analysis of the glass preform in the progress of precision glass molding for fabricating chalcogenide glass diffractive optics with the finite element method,” Micromachines 12(12), 1543 (2021). [CrossRef]
5. A. Jain and A. Y. Yi, “Numerical simulation of compression molding of aspherical glass lenses,” AIP Conf. Proc. 712, 239–244 (2004). [CrossRef]
6. L. Zhang, W. Zhou, N. J. Naples, and A. Y. Yi, “Investigation of index change in compression molding of As40Se50S10 chalcogenide glass,” Appl. Opt. 57(15), 4245–4252 (2018). [CrossRef]
7. W. Yang, Z. Zhang, W. Y. Ming, L. Yin, and G. J. Zhang, “Study on shape deviation and crack of ultra-thin glass molding process for curved surface,” Ceram. Int. 48(5), 6767–6779 (2022). [CrossRef]
8. A. T. Vu, R. d. l. A. Avila Hernandez, T. Grunwald, and T. Bergs, “Modeling nonequilibrium thermoviscoelastic material behaviors of glass in nonisothermal glass molding,” J. Am. Ceram. Soc. 105, 6799–6815 (2022). [CrossRef]
9. J. Zhou, M. Li, Y. Hu, T. Shi, Y. Ji, and L. Shen, “Numerical evaluation on the curve deviation of the molded glass lens,” J. Manuf. Sci. E. 136(5), 051004 (2014). [CrossRef]
10. C. Jiang, C. M. Tovar, J.-H. Staasmeyer, M. Friedrichs, T. Grunwald, and T. Bergs, “Simulation of the refractive index variation and validation of the form deviation in precisely molded chalcogenide glass lenses (IRG 26) considering the stress and structure relaxation,” Materials 15(19), 6756 (2022). [CrossRef]
11. H. Fu, C. Xue, Y. Liu, B. Cao, C. Lang, and C. Yang, “Prediction model of residual stress during precision glass molding of optical lenses,” Appl. Opt. 61(5), 1194–1202 (2022). [CrossRef]
12. Y. Liu, Y. Xing, C. Yang, C. Li, and C. Xue, “Simulation of heat transfer in the progress of precision glass molding with a finite element method for chalcogenide glass,” Appl. Opt. 58(27), 7311–7318 (2019). [CrossRef]
13. J. Zhou, J. Yu, L. J. Lee, L. Shen, and A. Yi, “Stress relaxation and refractive index change of As2S3 in compression molding,” Int. J. Appl. Glass. Sci. 8(3), 255–265 (2017). [CrossRef]
14. A. T. Vu, C. Rojacher, T. Grunwald, and T. Bergs, “Molded anti-reflective structures of chalcogenide glasses for infrared optics by precision glass molding,” Proc. SPIE 11175, 67 (2019). [CrossRef]
15. A. Symmons and M. Schaub, Field Guide to Molded Optics (SPIE, 2016).
16. J. J. Nelson, Precision lens molding of glass: a process perspective (Springer, 2020).
17. T. Zhou, J. Yan, J. Masuda, and T. Kuriyagawa, “Investigation on the viscoelasticity of optical glass in ultraprecision lens molding process,” J. Mater. Process. Technol. 209(9), 4484–4489 (2009). [CrossRef]
18. Y. Liu, Y. Xing, C. Li, C. Yang, and C. Xue, “Analysis of lens fracture in precision glass molding with the finite element method,” Appl. Opt. 60(26), 8022–8030 (2021). [CrossRef]
19. J. Zhou, C. Y. Zhu, L. H. Li, M. C. Ng, and K. Liu, “Temperature and rate dependent debonding behaviors of precision glass molding interface,” J. Am. Ceram. Soc. 104(1), 243–255 (2021). [CrossRef]
20. Taylor Hobson, “Form Talysurf PGI 1240 Aspherics Measurement System,” https://img1.17img.cn/17img/old/literature/C16151.pdf..
21. R. Singh, Z. Wang, C. Marques, R. Min, B. Zhang, and S. Kumar, “Alanine aminotransferase detection using TIT assisted four tapered fiber structure-based LSPR sensor: From healthcare to marine life,” Biosens. Bioelectron. 236, 115424 (2023). [CrossRef]
22. R. He, C. Teng, S. Kumar, C. Marques, and R. Min, “Polymer Optical Fiber Liquid Level Sensor: A Review,” IEEE Sens. J. 22(2), 1081–1091 (2022). [CrossRef]
23. R. Min, B. Ortega, and C. Marques, “Fabrication of tunable chirped mPOF Bragg gratings using a uniform phase mask,” Opt. Express 26(4), 4411–4420 (2018). [CrossRef]
24. P. Koštál, J. Barták, T. Wieduwilt, M. A. Schmidt, and J. Málek, “Viscosity and fragility of selected glass-forming chalcogenides,” J. Non-Cryst. Solids 575, 121205 (2022). [CrossRef]
25. P. Koštál, J. Shánělová, and J. Málek, “Viscosity of chalcogenide glass-formers,” Int. Mater. Rev. 65(2), 63–101 (2020). [CrossRef]
26. J. L. Adam, X. H. Zhang, V. S. Shiryaev, et al., Chalcogenide glasses (Woodhead, 2014).
27. GRINM Guojing Advanced Materials Co., Ltd., “chalcogenide glass,” http://www.guojing-tech.com/.
28. A. Jain, G. C. Firestone, and A. Y. Yi, “Viscosity Measurement by Cylindrical Compression for Numerical Modeling of Precision Lens Molding Process,” J. Am. Ceram. Soc. 88(9), 2409–2414 (2005). [CrossRef]
29. M. Lewis, Food Process Engineering Principles and Data (Woodhead, 2023), Chap. 19.
