Experimental Characterization Providing Enhanced Opto-Thermo-Mechanical Modeling

Alexandra Mazzolia, Philippe Saint-Georgesb, Anne Orbana, Jean-Sébastien Ruessc, Jérôme Loicqa, Sarah

Marcottea, Christian Barbiera, Yvan Stockmana, Marc Georgesa, Cedric Thizya, Philippe Nachtergaeleb, Stéphane Paquayb, Pascal De Vincenzob

a Centre Spatial de Liège, Av. Du Pré-Aily, 4031 Angleur, Belgium ;

b Open Engineering, Rue des Chasseurs-Ardennais 8, 4031 Angleur, Belgium ; c GDTech, Rue des Chasseurs-Ardennais 8, 4031 Angleur, Belgium

ABSTRACT A model is valid only if it represents the actual world. This paper presents several applications developed at CSL to improve or confirm multi-physic modeling, the difficulties of which being the coupling between several physical parameters, mechanics, thermals, optics, ... The objectives of these applications are to improve, develop analytical modeling guidelines and confirm the models Generally, the validation processes are carried out on simple test cases. The paper will demonstrate that simple test cases are not necessarily easy to measure, and that correlation with the model is not straightforward. Typical study cases presented are: - Heating of a spherical lens fixed in an aluminium barrel, with the presence of temperature gradients impacting the geometrical deformation of the lens and leading to refractive index gradients. - Samples with glued and bolted connections/junctions that can be encountered in stable structures on spacecraft (Silicon Carbide (SiC) and Titanium (TA6V)). These are measured by a holographic method. - The third system is a YAG laser rod heated by means of a dedicated oven. In the first test bench, the impact of thermo-elastic distortions on the optical performances has been measured using a Fizeau interferometer and compared to OOFELIE::Multiphysics' simulation results. The correlation between experimental and numerical data is discussed. For the second the thermo-mechanical correlations are performed, while for the last test bench preliminary testing results are presented. 1. INTRODUCTION Taking benefit of more and more powerful computers, it became possible to manage complex numerical modeling considering the coupling between different physical parameters. The goal is to predict with a higher accuracy and a better fidelity the behavior of a complex system. To fulfill these goals two worlds need to be faced. On one side integrated software solution which is able to efficiently process large scale models involving strongly coupled multiphysics interactions. This solution is based on the current simulation modules OOFELIE Multiphysics, SAMCEF Field and FINE

Suite. On the other side standard or developed metrology tools able to access the degree of accuracy and understanding of the actual set-up. Comparing these two worlds offers reliability improvement of the models. In this paper three simple study cases are addressed: - An opto-thermo-mechanical case with the heating and deformation of a lens inside a mount, - A thermo-mechanical case with the study of samples glued and bolted connections/junctions that can be encountered in stable structures on spacecraft (Silicon Carbide (SiC) and Titanium (TA6V)). These are measured by a holographic method. - An opto-thermal case consisting of a YAG laser rod heated by means of a dedicated oven, In this case polarization is considered additionally to wave front measurements. 2. OOFELIE MULTIPHYSICS OOFELIE::Multiphysics is a finite element simulation software dedicated to strongly coupled multiphysical problems [1]. It combines several physical fields such as mechanics, thermic, vibro-acoustics, pyro-piezoelectricity, electromagnetism, Peltier effect, electro-kinetics, fluid structure interaction and optics. OOFELIE::Multiphysics is well adapted for innovative design of complex devices such as sensors, actuators and MEMS. It also offers a unique automated link to the optical design software ZEMAX and the modeling of thermo-optic and elasto-optic effects. The multiphysical simulations linked to ZEMAX enable the design of complex optical devices by taking into account the environmental solicitations. Typical applications are high precision cameras, telescopes, satellite optics, active/adaptive optics. The automated in-memory communication with ZEMAX is based on the DDE protocol on Windows (Dynamic Data Exchange). The computed optical surface deformations and refractive index gradients are automatically exported to ZEMAX. This process makes the design more quick and efficient without the risk of loss of data integrity. Linked to the optical model in ZEMAX, the structural model in OOFELIE combines optical elements such as mirrors and lenses with mechanical or electro-mechanical components. High precision designs are performed thanks to the data exchange between

OOFELIE and ZEMAX. The various parameters defining the optical surfaces are retrieved by OOFELIE. High reliability of the meshed structural model is ensured by a sag correction process which is performed before the finite element analysis. Then the deformation of each optical surface is computed in its local coordinates accounting for the effect of transverse nodal displacements. 3. SPHERICAL LENS TEST CASE

3.1 Set-up description To be confident in the correlation method, very simple test cases are studied. The first one consists in a 50 mm diameter biconvex F/4 spherical lens made of BK7. Its mount is in black anodized aluminum and includes a retainer ring that securely holds the lens in place. The lens in its mount is on a five axes system to allow an alignment of the lens in front of the interferometer. The interferometric system allows to evaluate the optical performances of the system by measuring the wavefront (WF) variation. The stress is induced on the system by two heaters glued on the mount. Thermocouples are placed on the mount to monitor the temperature during the test (See Figure 1).

Figure 1. Distribution of heaters and thermocouples on the

lens mount Correlation between the center of the lens and the mount is first performed with a thermocouple glued at the centre of the lens. For each measurement after stabilization of the temperature on the thermocouples WF are acquired. The degradation of the optical performances of the lens is obtained by comparing the wavefront error (WFE) of the beam at warm temperature with the WFE at ambient temperature. A view of the test bench is shown in Figure 2.

Figure 2. Spherical lens test bench.

3.2 Test results analysis Figure 3 shows measured WFE. The first one corresponds to a measurement at ambient temperature, the second one to a 58.4°C temperature measured at the center of the lens. The third image is the difference between both WFE. As expected the dominant aberration is focus and its impact on the lens properties is a modification of its focal length according to the formula

∆f = 2 . 4F2 .⋅WFE . λ (1) where F is the f-number i.e. the focal length divided by the entrance pupil diameter, WFE is the part of the WFE corresponding to the focus and λ is the wavelength.

Figure 3. Measured WFE at T=20.5°C and 57.2°C at lens

center and remainder from their subtraction. Nevertheless, taking only this defocus term into account doesn’t allow to fit the experimental results. Indeed it is required to consider the focal length modification due to a temperature change in the lens.

Figure 4. Measured and calculated variations of focal length. Figure 4 shows a comparison between the measured and calculated variations of focal length. They are both

positive and correspond to an increase of the lens focal length. The closest results to the measurements are the one obtained from the sum of the two calculated defoci. It confirms that the refractive index gradient has an important impact on the focal length modification.

3.3 Modelisation and simulations Now that the simple test bench has demonstrated an expected and clear behaviour, the next step consists in modelling the set-up and to evaluate the reliability of the model. Appropriate contacts between the lens, the barrel and the maintaining ring are defined. The contacts between the lens and the barrel and between the lens and the ring are limited to wires. Since the heating of the lens may lead to a loss of these contacts (partial or total), two simulations are considered. The first model involves thermo-mechanical wire to surface contacts. It does not permit any slide motion of the lens in its mount. The second model uses thermal wire to surface contacts. It lets the lens free in order to simulate the case of contact loss between the lens and its mount, while insuring the thermal load. One may expect that the right configuration is between these two extreme behaviors. The measured temperatures are applied on the periphery of the mount in order to simulate the applied heating. Convective fluxes between the lens and ambient air are also taken into account. Both models lead to the same temperature field. The simulated temperatures inside the lens are in good accordance with the experimental values. Even if the temperature gradient is the same for both models, the deformations of the lens and its mount are quite different for the simulation 1 (thermo-mechanical wire to surface contacts) compared with the simulation 2 (thermal wire to surface contacts). In the second model, the lens is free to deform as if no mount was present. The comparison between the two cases is shown in Figure 16.

Figure 5. Comparison between the two studied model deformations (simulation 1 on left, simulation 2 on right).

The thermally induced degradation of optical performances is evaluated from the deformation of the two optical surfaces of the lens and the refractive index change. These data are computed by OOFELIE and automatically exported to ZEMAX at the end of the

computation. Figure 17 illustrates the simulation results, compared with the experimental values. This comparison is based on the focus aberration, i.e. the Z2,0

Zernike standard coefficient, computed by ZEMAX. Again, the results of the two simulations are given. The second model leads to a better accordance with experimental measures. The above results are obtained by ray-tracing in the optical software ZEMAX. Both surface deformation and refractive index gradient (GRIN) are exported to ZEMAX. A user defined surface is used for exporting the surface deformation and the GRIN simultaneously. The surface deformation is fitted by Zernike standard polynomials and the GRIN is approximated by a quadratic polynomial interpolation.

Figure 6. Comparison of simulated and measured focus

aberration. 4. SAMPLES GLUED AND BOLTED CONNECTIONS/JUNCTIONS TEST CASE The baseline is to start from very simple configuration with a well know characteristics of the sample (dimension, assembly procedure, blank traceability) to allow good model correlation. Advanced measurement techniques are required to characterize and determine the different main contributors to the final end to end performance and to perform accurate correlation. In this test case, material characteristics are assumed to be well known: SiC/SiC and SiC/TA6V glued and bolted samples have been studied.

Figure 7. Globally glued samples geometry (left) Bolted

samples geometry (right) The advanced measurement techniques used is a four axis holographic technique.

4.1 Test description The holographic camera (HC) developed by CSL [1], has been used to measure the thermo-elastic distortions. It is composed of a compact optical head and an electronic rack containing the 5W Nd-YAG laser operating at 532 nm. Relative displacements ranging from 20 nm to 20 µm can be measured in one shot over a whole field and contactless. A first step consists in recording the hologram of the object under test, the reference state. Then, a stimulation (thermal or mechanical) is applied to the object. Finally the hologram is readout; the interference pattern resulting from the superposition of the wave front diffracted by the hologram (reference state of the object) and the one coming directly from the object (deformed state of the object) is recorded on a CCD camera. The phase image obtained is unwrapped to obtain the continuous relative displacement. Nevertheless, the relative displacements are measured out-of-plane because of the object illumination and observation geometry. For this study, a two-illuminations configuration has been implemented [3], as shown in Fig. 4

Figure 8. Two-illuminations configuration of the HC.

Two holograms are simultaneously recorded in the camera. In this configuration, the relative out-of-plane and in-plane (in one direction) displacements are measured. The uncertainty for both measurements is 40 nm. In this configuration only two acquisitions can be performed from the same reference, compared to the four with one illumination. To obtain the correct relative displacements, one has to know the absolute in-plane or out-of-plane displacement of one point in the field of view of the HC, or the relative in-plane or out-of-plane displacement between two points. A scaling is then applied to the data. For this study this additional processing is possible since the CTE of SiC is well known. The in-plane relative displacement between two points on the samples can therefore be calculated. The samples are located in a vacuum chamber and lie on an Invar bench mounted on three Invar blades screwed to the bottom flange of the chamber. The temperature

variations of the samples are obtained by circulating, with a chiller, a mix of glycol and water in a shroud located underneath the Invar bench. The temperature range achievable with this chiller is from - 28°C to 60°C. Thermocouples are available in the chamber to monitor the temperature on the samples. The support of the HC is an assembly of columns to make it as stable and rigid as possible. The whole setup is placed on an optical table (Figure 9).

Figure 9. Test set-up.

4.2 Test results and test correlation

FEM predictions lead to quite good correlations with the test data, with most of the time less than 10% of discrepancies in both the out of plane and in-plane response, if the correct joint of glue thickness and/or applied temperature field and/or interface modeling are taken into account in the model. Figure 10 presents out of plane measured data for a bolted configuration. These have been correlated (by EADS (F) Ref [3]) to model prediction also shown in Figure 10.

Figure 10. Out of plane measurement (left) and model

prediction (right).

A correct interface modeling is mandatory to capture the correct test behavior: this was particularly the case for the SiC-SiC bolted assembly, where the presence of disk-washer sliding was put into lights by the FEM

predictions, which was afterward corroborated by a precise inspection of the test procedure. More details concerning these analyses can be found in [3] 5. YAG BAR TEST CASE A preliminary test bed was developed. It consisted in a YAG bar of 50 mm length with a square section of 12x12 mm². It was heated in a dedicated oven up to 200°C. Polarimetric and wave front measurement have been carried out with this simple set-up. See ref [4]. From those results it appears that the birefringence measurements along the beam traveling through the center of the YAG bar is not enough to give accurate measurement. Also the simulations of thermal effects such as the thermal strain-induced birefringence are not observed in accordance with the OOFELIE model. A dedicate set-up was build up to get a more accurate mapping of the birefringence inside the bar due to a change of temperature (see Figure 11).

Figure 11. Polarimetric test set up. Both polarisation components are analysed in two separated arms. Each arms are composed with a photodiode and a camera analyzing the

pupil. Preliminary results are presented. A spread collimated beam is used to cover the whole pupil of the YAG bar. YAG bar is first placed between two crossed polarizer. The transmitted beam is analyzed by a CCD-camera. Picture of transmitted beam is analyzed with temperature in transient case. In the example below, heating target was set at 50°C. The following picture shows the transmitted beam in function of the mean temperature on the YAG bar.

25°C 28°C 31°C

34°C 37°C 40°C

43° C 46° C 50°C Figure 12. Transmitted beam versus the YAG bar

mean temperature. The first and the last picture show approximately the same scheme; those correspond to the steady state at 25°C and 50°C respectively. Contrariwise, the other pictures are related to the transient case when temperature gradient occurs inside the medium. Because temperature gradient induces thermal stress inside the medium additional birefringence appears. The future development of the bench will quantify birefringence by TE&TM phase shift measurement. The pupil will be analysed in both polarisation components with synchronised cameras. 6. CONCLUSION Trough these 3 simple test cases, it has been demonstrated that a lot of care need to be taken to correctly understand the test configuration and that accurate correlation is not straightforward. It indicates that models are really useful for accurate design and analysis but will not replace a real testing. The comparisons between test and model help to understand the physics of the set up and to correct the model and to take into account the test results inside a more complex system. The correlation between the simulation results obtained by OOFELIE Multiphysics with experimentations showed good agreement between the experimental and simulated WFE degradation. Nevertheless two simulation models were considered. The first one involves thermo-mechanical wire to surface contacts. It does not permit any slide motion of the lens in its mount. The second model used thermal wire to surface contacts. It lets the lens free in order to simulate the case of contact loss between the lens and its mount, while insuring the thermal load. The model which gave the best match with the experiment is the second one, but the reality is nevertheless in between. For the glued and bolted connections/junctions, the test indicates a good correlation with FEM predictions. Nevertheless to achieve this good correlation, a correct interface modelling is mandatory.

Concerning the YAG bar the simulations of thermal lensing were not compliant with the measurements. Effects such as the thermal strain-induced birefringence, a better definition of the thermal loads and the consideration of radiative exchanges between the oven and the bar will be introduced in the model. To achieve a good experimental understanding a dedicate set-up was build up providing a more accurate mapping of the birefringence inside the bar due to a change of temperature. ACKNOWLEDGMENT The present work has been conducted in the context of the Multi-Φ project, funded by the Marshall Plan of the Walloon Region (Belgium), which is acknowledged by the authors. 7. REFERENCES [1] I. Klapka, A. Cardona, "An object Oriented

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[3] F. Eliot, C. Thizy, A. Shannon, Y. Stockman, D. Logut, “Thermo-elastci distortion measurements by holographic interferometry and correlation with finite element models for SiC connections/junctions on spacecraft” IAC-10-C2.2.6 2009.

[4] Alexandra Mazzoli, Philippe Saint-Georges, Anne Orban, Jean-Sébastien Ruess, Jérôme Loicq, Christian Barbier, Yvan Stockman, Marc Georgesa, Philippe Nachtergaele, Stéphane Paquay, Pascal De Vincenzo, “Experimental validation of opto-thermo-elastic modeling in OOFELIE Multiphysics” SPIE Marseilles 2011.