Thermal forming is a technique for forming glass foils precisely into a desired shape. It is widely used in the automotive industry. It can also be used for shaping X-ray mirror substrates for space missions, as in our case. This paper presents the initial results of methods used for automatic data processing of in-situ measurements of the thermal shaping process and a comparison of measured and simulatated values. It also briefly describes improvements of the overall experimental setup currently being made in order to obtain better and more precise results

Havlíková, R.

Landováa, M.

Maršíková, V.

Míka, M.

Pína, L.

Švéda, L.

English

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

Acta Polytechnica Vol. 51 No. 6/2011Thermal Forming of Glass — Experiment vs. SimulationL. Sveda, M. Landova´, M. Mı´ka, L. P´ına, R. Havl´ıkova´, V. Marsˇ´ıkova´AbstractThermal forming is a technique for forming glass foils precisely into a desired shape. It is widely used in the automotiveindustry. It can also be used for shaping X-ray mirror substrates for space missions, as in our case. This paper presentsthe initial results of methods used for automatic data processing of in-situ measurements of the thermal shaping processand a comparison of measured and simulatated values. It also brieﬂy describes improvements of the overall experimentalsetup currently being made in order to obtain better and more precise results.Keywords: X-ray mirrors, Comsol Multiphysics, simulations, thermal forming, gravity forming, in-situ measurements,data processing.1 Thermal forming processfor lightweight opticsThermal forming is a technique for shaping light-weight precise space X-ray mirrors that has beenunder development for several years. Teams work-ing on the topic include the NASA team led byDr. Zhang [7] working on the former CON-X project,an Italian group [8], and the Czech group consist-ing of people from CTU, ICT, the Astronomical In-stitute and Rigaku company, working on the formerXEUS/IXO/Athena mission [9].The principle of the technique is rather straight-forward. A precise form (a mandrel) is prepared.A glass sheet is then placed atop the mandrel (orbetween two mandrels) and a temperature proﬁle isapplied. Since glass behaves like a viscous liquidabove certain temperatures, forming can occur andthe shape remains even after the sample cools down.The method described in this paper is very similarto the method outlined above, except that no man-drel is used. The glass sheets are held only on theiredges, and shaping at high temperatures takes placeonly due to gravity [6]. The principle is demonstratedin Figure 1. A similar method is used for manufactur-ing car front windows, however with a lower precisionrequirement.2 MetrologyThe shape of the formed glass sheet was measured bytwo principally diﬀerent methods and provided com-plementary information about the forming process.In order to acquire information about the dy-namics of the forming process, a noncontact opticalmethod was used. A scheme of the setup is shown inFigure 1. The sample remains in its position insidethe furnace while it is observed via a camera with anobjective. Figure 2 shows a typical image obtainedby the camera. The typical period between two con-secutive images was 5–10 minutes. A set of imageswith timestamps was obtained, and was further pro-cessed in order to obtain valid data.Fig. 1: Schematic view of the experiment. The glass wasplaced atop the support only by its edges. The tem-perature was increased and gravity performed the actualforming. The maximal bending as a function of time andtemperature was then measured and compared with thesimulationsFig. 2: Example of image processing of the in-situ opticalmeasurement. The original image (upper, false colors) isprocessed in order to obtain reference points (second im-age), the reference line and the vertical line for glass posi-tion measurement is found (third, overlaid on the originalimage, false colors) and the position of the glass is ﬁnallyfound in this vertical line (fourth)72Acta Polytechnica Vol. 51 No. 6/2011Several Matlab scripts were written in order toprocess the images automatically, if possible, or semi-automatically. The most important information fordeveloping the forming process that can be obtainedfrom measurements of this kind is the dynamics of theprocess. Thus, the total bend of the sample at eachtime was measured. The algorithm ﬁrst located twoﬁxed reference points within each image. This is be-cause the images can be shifted and inclined relativeto each other, as the doors needed to be opened eachtime in order to take the image. Then the center ofthe sample was found, where the maximal bend wasexpected. The relative position of the center withrespect to the reference points — the total bend —was identiﬁed. This was done either automatically,when the lighting conditions were optimal, or semi-automatically with some help from the user. Finally,the values were calibrated in order to obtain valuesin mm and not in pixels. A single step of the scriptis shown in Figure 2.The other semiautomatic script was also written,and was able to process the image in order to deter-mine the sample proﬁle. It was used to detect theshape change of the sample between the end of theforming process and the end of the cooling process.As the method used standard commercial equip-ment only (camera, lenses, tripod, etc.) and thedoors had to be opened each time, the precision ofthe method is low, typically 0.1—0.5 mm. It cantherefore be used successfully only for a study of theprocess dynamics. The Taylor Hobson PGI PLUScontact proﬁlometer was used to obtain more accu-rate data for shape ﬁtting. This device is able tomeasure proﬁles up to 120 mm in length, samplingdown to 0.25 micron and with vertical resolution atthe nanometer scale.Three lines were measured on each sample at eachof the orthogonal directions, two close to the edgesand one close to the center of the sample. The datafrom the device was initially processed by the TaylorHobson software, and was further exported and pro-cessed in Matlab as well. The proﬁles were rotatedin order to make them horizontal and concentric, asit is impossible to position the sample perfectly onthe table. Varioius curves were then ﬁtted onto thedata, including polynomials of the order 2 and 4, acircle and a catenary curve.3 SimulationsComputer simulation of the forming process is a com-plex task [1–4]. Generally, a combination of a ther-mal model and a mechanical model has to be ap-plied. The thermal model should contain spatial andtemporal temperature proﬁles, as well as the ther-mal interaction of the furnace and the form with thesample. This can be either measured or simulated.Mechanically, it can be modelled as a simple beammade of a viscoelastic material, where several borderconditions need to be met. The gravitational forceis easily applied as a volume force. The dynamicviscosity of the material as a function of the tem-perature at a given location has to be known. Theproper sample/support interaction must be entered.Either a rigid system or a system where some move-ments with deﬁned friction are allowed, etc. Surfacetension can be included.The simulation performed here used the ComsolMultiphysics software with the CFD module [5], butwith several simpliﬁcations. The temperature of thesample was assumed to be homogeneous and identi-cal to the temperature of the furnace. This seems tobe unrealistic, but it is a good starting point. Morework needs to be done to justify and modify thiscondition. Rigid borders were applied, no slip, nosqueezing of the glass, and the sample lay freely onthe support. Uncertainty in border deﬁnition is ex-pected to produce diﬀerences in the bending speedof the order of 20 % [2]. Most of the forming timewas spent above the transform temperature, thus aviscous Newton liquid model was used with the dy-namic viscosity given by the curve in Figure 3. Theoutput of the Comsol Multiphysics simulations wasonly a velocity ﬁeld as a function of time. The datawas thus imported to Matlab and integrated in orderto obtain the actual proﬁle.Fig. 3: Dynamic viscosity as a function of the temper-ature used in the simulation in the form of the Vogel-Fulcher Tammann equation [6]4 Processing experimentaldataThe experiments were performed with glass sam-ples made from Desag D263 glass. Two diﬀerentsample sizes were used: 75 × 25 × 0.75 mm3 and100 × 100 × 0.4 mm3. The forming process, tem-peratures, measurements and ﬁts by diﬀerent curvesas well as a description of the equipment used in the73Acta Polytechnica Vol. 51 No. 6/2011experiment are described in greater detail in [6]. Theaverage forming speed as a function of the formingtemperature for one of the samples is shown in Fi-gure 4, together with the simulated data.Fig. 4: Average forming speed for a sample 100 × 100 ×0.4 mm3 in size as a function of temperature. The mea-sured values are compared with the simulationAll the forming experiments were measured in-situ, and the results were processed by the noncon-tact method. The resulting data was then combinedinto the form of a uniﬁed plot where the change inshape (the bending) is a function of the forming timeand the temperature (see Figure 5).Fig. 5: Measured bending as a function of time and form-ing temperature for 100× 100× 0.4 mm3 samplesA simulation of all the experiments was performedand the data was processed in the same way as theexperimental data in order to provide a comparison(see Figure 6). The overall shape and values are con-sistent, although not perfectly matching yet, see Fi-gure 4, which compares the average shaping speed asa function of temperature.Detailed contact proﬁlometer measurements showthat, due to short openings of the doors in order tomake in-situ images for noncontact measurements,there are temperature gradients that result in inho-mogeneous forming. It can be seen that the shape isdiﬀerent at the edge closer to the doors. Further, wehave no actual information about the temperaturesand the temperature gradients in the glass, whichis very important for the simulation. It is expectedthat, together with the poorly deﬁned support, thisleads to most of diﬀerences between the simulationand the experiment. Inaccurate noncontact measure-ment is not important for average forming speed de-tection, as least square ﬁtting is used.Fig. 6: Simulated data based on the experiments fromFigure 5. More data points are used for interpolating thecolored surface5 Expected improvementsSeveral key points were identiﬁed during the ex-periments described above, which aﬀect the mea-surements and the forming process itself, and arecurrently being upgraded. The shaping process isstrongly aﬀected by opening of the doors for mak-ing images, thus a sapphire window in the doors willbe used. In addition, poorly deﬁned support will bereplaced by stable and perfectly deﬁned mechanicalsupport. Independent temperature measurements in-side the furnace for greater precision will be per-formed. In order to be able to increase the preci-sion of the optical measurements, a camera at a ﬁxedpoint relative to the furnace will be used. It will beequipped with a telecentric lens. The lighting will beadjusted to enable automatic data processing for allimages.6 ConclusionsA general method for in-situ measurements of a ther-mal free fall glass forming process has been demon-strated, including automatic data processing. Thedata was used for improvements to a forming methodsuitable for space X-ray telescopes, and as an input74Acta Polytechnica Vol. 51 No. 6/2011for computer simulations of the process. The simu-lation and the experiments are consistent, but morework needs to be done. Key points which need to bemodiﬁed and corrected in future experiments havebeen identiﬁed, and experimental upgrades are cur-rently underway.AcknowledgementWe acknowledge support from the Grant Agency ofthe Academy of Sciences of the Czech Republic, Ma-terial and X-ray Optical Properties of Formed SiliconMonocrystals project, grant number IAAX01220701.References[1] Stary´, M.: Gravitacˇn´ı tvarova´n´ı skla I. – Labo-ratorn´ı meˇren´ı, Skla´rˇ a keramik, 59, 7–9, 2009,p. 150–154.[2] Stary´, M.: Gravitacˇn´ı tvarova´n´ı skla II. – Num-ericka´ simulace, Skla´rˇ a keramik, 59, 10–12, 2009,p. 213–217.[3] Chen, Y.: Thermal forming process for precisionfreeform optical mirrors and micro glass optics,PhD thesis, The Ohio State University, 2010.[4] Stokes, Y. M.: Very Viscous Flows Driven ByGravity, PhD thesis, University of Adelaide, 1998.[5] http://www.comsol.com/[6] Landova´, M.: Thermal forming of glass and Sifoils for X-ray space telescopes, thesis, Instituteof Chemical Technology Prague, 2011.[7] Zhang, W. W.: Lightweight and high angular res-olution X-ray optics for astronomy, Proceedingsof the SPIE, 8 076, 2011, p. 807 602.[8] Prosperio, L., et al.: Thermal shaping of thinglass substrates for segmented grazing incidenceactive optics, Proceedings of the SPIE, 7 803,2010, p. 78030K.[9] Hudec, R., et al:, Advanced X-ray optics withSi wafers and slumped glass, Proceedings of theSPIE, 7 437, 2009, p. 74370S.Libor SvedaLadislav PínaRadka HavlíkováCTU in PragueFNSPEBřehova 7, 115 19 Prague 1, Czech RepublicMartina LandováMartin MíkaICT PragueTechnická 5, 166 28 Prague 6-DejviceCzech RepublicVeronika MaršíkováRigaku Innovative Technologies Europe, s. r. o.Novodvorská 994, 142 21 Prague 4, Czech Republic75

Thermal Forming of Glass — Experiment vs. Simulation

Abstract

Similar works

Full text

Available Versions

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

Directory of Open Access Journals