Compensation of residual stress induced shape errors in precision structures

Transcription

1 Compensation of residual stress induced shape errors in precision structures Horst Baier, Stephan Rapp 1 Institute of Lightweight Structures, TU München, Boltzmannstr. 15, Garching (Germany), baier@tum.de 1 :now at Kayser Threde,Perchtingerstr. 5, München (Germany),Stephan.rapp@kayser-threde.com ABSTRACT Shape adjustment or compensation of manufacturing errors for high precision space structures via proper attachment and programming of shape memory materials and especially memory polymers is presented. The overall process, polymer characterisation, the determination of size and positioning of polymeric shape memory actuators are shown together with two benchmark applications. Results together with good analysis-test correlation demonstrate the feasibility of the approach 1. INTRODUCTION AND OVERVIEW Many satellite structures and especially those of high precision satellite payloads and instruments not only have to have sufficient stiffness and strength but also high shape accuracy, which often is the overall design driver. For example, high performance optical benches or high precision mirrors and reflectors require minimum deviations from their ideal nominal shapes. Shape deviations may be caused by manufacturing errors e.g. due to residual curing stresses especially of fiber composites parts, and may be also further induced during operation in orbit by thermal and microdynamic loads. The compensation and control of errors induced by external loads is one of the core activities for large earth bound optical telescopes, which makes telescopes for optical astronomy in space close to obsolete. Related activities for space instruments are still more in the technology and study phase. A space application for shape controlled mirrors is foreseen for the James Webb telescope planned for infrared wavelength as described e.g. in [1]. Reasons for the slow progress of this technology for space applications result from increased complexity due to the need of sensing, controlling and especially actuating devices including power electronics and support structures which results into hardly avoidable mass penalties. So in most relevant space applications the effort is more given to minimize spurious loads by proper thermal and microdynamics control. On the other side, such measures do not reduce manufacturing errors which might contribute to a significant part to the overall error budget. So in this paper the focus will be on possible approaches to compensate such shape errors on ground, see also figure 1. Deviations due to warpage might occur in especially nonsymmetric fiber composite plates and shells, while spring-in effects are often due to material concentration and non-homogenous curing at joints and edges such as in rectangular cross-sections e.g. of wave guides. Fig. 1 : Typical shape errors in CFRP manufacturing

2 The basic idea of the approach to compensate manufacturing errors on ground is to attach smart shape memory materials onto structural parts (in nonfunctional areas) such that the induced stresses resulting from a (single) shape change of these materials better adjust the actual shape to the reuired one. In the following, the basic overall process is outlined first, followed by a discussion especially of shape memory polymers (SMP) and determination of relevant properties. Analysis and testing of a structural benchmark example demonstrates the feasibility of this approach and a good correlation between analysis and test results. For this technique possible limits have to be taken into consideration as well, such as possible stress relaxation of SMP in higher temperatures, the discussion of which is concluded by an outlook on further steps. It should be also mentioned that in addition to shape manufacturing error or possible shape control in space, investigations are also underway for drastically shape morphing during space operation to adjust for modified mission requirements [3]. 2. OVERALL APPROACH FOR MANUFACT. ERROR COMPENSATION The overall approach of compensation residual stress effects on structural shape accuracy is outlined in figure 2. Starting with the required shape specified for proper operational performance and the measured shape of the actual manufactures structure, a finite element model of this structure is used to determine proper size, positioning and programming level (induced free strain) of the compensating SMP. For this step properly determined material properties of the SMPs are required. After their actual programming, the SMP patches are attached (usually glued) to the structure and triggered by (moderate) temperature to get back to its original shape thus inducing compensating actuation forces into the structure. The resulting adjusted shape should then be (significantly) closer to the required one, which can be verified by a further shape measurement step. From this overview it becomes obvious that this process also works with other type of smart materials such as shape memory alloys. Such types of materials only need to be switched nominally only once and perhaps twice in case of some reiteration of this programming process is undertaken. Fig. 2: The overall process for shape correction

3 3. SHAPE MEMORY MATERIALS AND POLYMERS AS SHAPE CORRECTION ACTUATORS Since there is usually the need to use the shape error compensation actuation only once on ground, actuation materials and their triggering mechanisms can be quite straightforward. A natural choice are shape memory materials, which when triggered usually under (moderate) heat change their shape. If such materials are attached to a constraining structure, this then causes actuation forces. The most popular shape memory material is the shape memory alloy (SMA) such as the nickel-titanium alloy Nitinol, however, some ceramics and polymers also show this effect. The shape change mechanisms for SMAs are phase changes of the material. Though the resulting strain is in the order of 5 to 10 % only, actuation forces are relatively high due to the relatively high Young s modulus in the order of 50 to 70 GPa. Mass density is in the order of that of steel. On the other side, mass density of SMPs is low and they may experience memory strains in the order of 100%, but modulus is at least one order of magnitude lower. In order to limit the discussion, focus here will be on shape memory polymers (SMPs). SMPs usually show a single one-way-effect, which can be described by a cycle illustrated in figure 3. mechanically deformed. Cooling down the material in this mechanically constrained state, the deformation freezes in. This process is called programming and ends up with the programmed, temporary shape. Heating up the material above the transition temperature again, the shape recovery starts and the material returns to its original, permanent shape. The physical background for this macroscopic behavior is the use of polymer network chains as molecular switches. The secondary cross-links in shape memory polymers show a temperature dependent behavior, which enables the shape memory effect. Thermomechanical characterization and different (potential) applications are summarized by Leng and Du [4]. Proper determination of relevant material properties is one key for reliable modeling and application, which is briefly addressed in the following. 4. ACTUATION PROPERTIES OF SHAPE MEMORY PATCH ACTUATORS The behavior of shape memory polymers can be described by a thermo-mechanical cycle. Depending on the mechanical constraints, this cycle is different. The picture series in figure 3 shows an unconstrained cycle. Loaded cycles and the resulting energy output are shown by Rapp and Baier []. Here the focus is on the fully constrained, or blocked, recovery cycle. In operation the actuator patches are never fully blocked, and small recovery strains occur due to a limited stiffness of the structure. However, these small strains shall be neglected and a blocking recovery stress can be used. During this process the memory effect and the thermal expansion are superimposed, which might lead to compression stresses or buckling of samples at the beginning of the recovery. Ending up with the blocking block (Equation 10), the recovery is completed. Cooling the sample to room temperature (RT = 21 o C) leads to an increase of the tensile stress due to additional thermal act (Equation 11) then is used for the patch actuation force. (1) with F block being the blocking force and A is the cross sectional area. Figure 3 Illustration of the thermo-mechanical shape memory cylce of a sample, heated with integrated heating wires SMPs can be manufactured with more or less conventional curing processes in arbitrary shape. Heating the material above its transition temperature T Trans, the Young's modulus E drops down and it can be (2) where T is the coefficient of thermal expansion, E(T) is a temperature-dependent Young s modulus and T is the temperature change. While the blocking stress is only based on the shape memory effect and the programming history, the actuation stress how it occurs for patch actuators shows a significant additional term

4 based on a thermal stress. This also results into different behavior for tension and compression actuation. 5. REMARKS ON FINITE ELEMENT MODELLING AND ON ACTUATOR SIZING/POSITIONING SIMULATIONS Finite element modelling is used to determine number, positioning and size of the actuation patches. The actuation patches have to be added in the usually available model for the structure with proper material properties. Though the material behavior strictly is nonlinear and maybe also viscoelastic, assumptions for linearization and independency of time have proven to be valid in a first instance (see also conclusion chapter) With the assumption of a linear elastic material behavior, which is adequate for the small recovery strains in the blocked configuration and the simulation of the full recovery level, a linear relationship between act (3) where E eff is the effective Young s modulus for the modelling of the SMP, C M is the shape memory and is the actuation strain. Such a linear relationship between a stimulus and a strain is well known for the thermal expansion: (4) In addition to these modelling aspects, the consideration of the interface between polymer patches and structure may play a role as well, see also [6]. 6. APPLICATION AND EXPERIMENTAL VERIFICATION To verify the feasibility of this patch actuation and shape adjustment process, supposedly planar but actually slightly curved CFRP shells are used with the dimensions of 180 mm 180 mm 1 mm and an asymmetric [0/90] layup of Sigratex Prepreg CE uni-directional (UD) plys.(figure 4). These asymmetric and thin structures are used to generate significant shape errors due to curing stresses. Deviation measurements by dot projection photogrammetry showed maximum out-of-pane deformations after manufacturing are between 9.5 mm and 10.7 mm for t four samples used. The actuator patches are applied to the structural surface and the introduced curvature reduction of the shell is measured. Proper positioning and size of the SMP actuators under constraints on mass and number of patches are determined by finite element models and optimization algorithms. During manufacturing and testing also the relevance of the bonding material and the need for low thickness of the glue became obvious: This analogy can be used in the finite element method for the modeling of actuation properties If a fully constrained condition is assumed for the patch, an effective Young s modulus E eff can be calculated from the actuation stress, determined from the property characteristics and the free recovery strain: Figure 4: Initial and adjusted shape errors for plate specimen

5 Four different types of actuators with different geometry and different positions on the structure have been used. Typical results of shape adjustment or improvement shown in figure 5. Fig. 5: (a) Summary of deformation reduction results; (b) shape contour of sample before and after SMP patch actuation It can be seen that a considerable improvement in shape accuracy could be achieved. Moreover, correlation to simulation results derived from finite element models including SMP actuation is also quite satisfactory.on the other side, possible creep of the SMP and with that a reduction of actuation forces might be a problem possibly to be overcome by the inclusion of fillers and nano-particles. A further application for SMPs are high precision waveguides. Figure 6(a) shows a cross section of a hybrid CFRP-copper waveguide. The orthogonality and flatness of the waveguide walls are very sensitive geometric values regarding the electrical performance. However, during manufacturing, warpage effects lead to acute angles. To reduce these distortions SMP actuator patches can be applied to the outer surfaces. The resulting recovery energy compensates residual stresses and improves the shape. Afinite element simulation was conducted to demonstrate the shape readjustment. Figure 6(b) shows the resulting scaled thermal deformation of the waveguide cross section for a curing temperature of 100 C. Figure 14(c) illustrates the location of the patch actuators. Furthermore the figure shows Figure 6: CFRP-copper hybrid waveguide: (a) photograph of cross section; (b) contour showing shape errors due to curing; (c) SMP actuator patch locations and contour of readjusted shape; quantitative data on the lower part

6 7. CONCLUSION AND OUTLOOK The approach basically has shown to be valid to adjust the shape of precision structures by compensation the spurious effects e.g. of residual stress due to curing by introducing compensating actuation forces or stresses. Nevertheless, some open points still have to be addressed. One of the most relevant and critical aspect is possible relaxation of actuation stresses due to viscoelastic behavior of SMP especially at higher temperatures. This problem is reduced for thermally controlled high precision instruments and structures, and can be further reduced e.g. by doting SMP with nano particles. As shown in figure 7 for a polymer doted with two different types of nano-alumina, Young s modulus can be significantly increased. Moreover, thermal conductivity is improved which helps in the triggering phase in the shape adjustment process. Volume fractions of such nanomaterials higher than about 5% have shown to be less beneficial due to their less proper dispersion and increased clustering, giving rise to local yield points. Figure 7: Effect on material stiffness of a polymer doted with unmodified and modified nano-particles showing significant stiffness increase against non treated polymer References [1] Nella, J., Etchinson, P. et.al., (2009), Next generation space telescope (NGST) observatory architecture and performance, Proceedings AIAA Structures, Structural Dynamics and Materials Conf., 2009 [2] Yu,Zhi-Qianga, [2] You, Shu-L., Yang, Zhen-Guo., and Baier, H., Effect of Surface Functional Modification of Nano-Alumina Particles on Thermal and Mechanical Properties of EpoxyNanocomposites, Advanced Composite Materials , (2011) [3] Datashvili, L. and Baier, H., (2011), Flexible fiber composites for space structures, in: George Chang (ed.), in: Fiber Composite Structures, Nova Science Publishers, Inc., USA, to appear Nov [4] Leng, J., Du, S., [Shape Memory Polymers and Multifunctional Composites], CRC Press, (2010) [5] Rapp, S., Baier, H., Shape memory polymer actuator patches for shape adjustment of fiber composite parts, Proc. 19th AIAA/ASME/AHS Adaptive Structures Conference, Denver, USA, (2011) [6] Rapp, S., Baier, H., Determination of recovery energy densities of shape memory polymers via closed loop, force controlled recovery cycling, Smart Materials and Structures Vol. 19 (2010)