Design and Test of a Micro-displacement Actuator Based on Giant Magnetostrictive Material

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1 Design and Test of a Micro-displacement Actuator Based on Giant Magnetostrictive Material Liang Shao *a,c,d, Dehua Yang a,c, Bintang Yang b, Kunxin Chen a,c a National Astronomical Observatories/Nanjing Institute of Astronomical Optics & technology, Chinese Academy of Sciences, Nanjing , China; b The state key lab of mechanical system and vibration, Jiao Tong Univ., Shanghai , China c Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing , China; d Graduate School of the Chinese Academy of Sciences, Beijing100039, China; ABSTRACT To meet the performance requirements of co-focusing and co-phasing of segmented mirror active optics (SMAO) in modern astronomical telescope, micro-displacement actuators with nanometer resolution and millimeter stroke are necessary. The design and test of a micro-displacement actuator based on giant magnetostrictive material is present in this paper. The actuator s main components, such as giant magnetostrictive drive core, displacement pantograph mechanism and output guide mechanism, are discussed in detailed. The giant magnetostrictive drive mechanism generally may offer nanometer resolution and micron stroke. A displacement/stroke pantograph mechanism is designed with absolutely sealed flexible hydraulic structure (ASFHS) to enlarge the stroke. In addition, a secondary giant magnetostrictive drive mechanism is integrated to serve final resolution of final displacement output. In view of flexure exhibiting excellent mechanical properties free of friction, clearance and lubrication, a flexure guide mechanism with the capacity of excellent lateral load is designed to fulfill linear displacement output steadily. The sub-systems like the giant magnetostrictive drive core and displacement pantograph mechanism have been tested before integration of the whole actuator. The final test of the actuator is carried out with dual frequency laser interferometer at lab. Besides, to meet technical requirements of future extremely large telescope, further development issues mainly related to application practice of the actuator is discussed at the end. Keywords: Micro-displacement actuator, giant magnetostrictive material, displacement/stroke pantograph mechanism, astronomical telescope, nanometer resolution. 1. INTRODUCTION The increasing aperture of modern giant optical astronomical telescope is much beyond the advancement of modern manufacturing capability. The dilemma of the needed large aperture of telescope in modern astronomy against the limitation of manufacturing process is resolved since the emergency of the SMAO, which has already been widely implemented in large aperture infrared/optical astronomical telescopes. A number of segmented sub-mirrors, whose apertures are 1~2 m level and whose shape is usually hexagonal, are adjusted by control system of active optics technology to be substituted for large single aperture mirror [1][2]. Since SMAO has been successfully pioneered in the twin Keck telescopes, most existing large aperture infrared/optical astronomical telescopes adopted SMAO technology, such as GTC, HET, SALT, LAMOST, etc. A series of large telescopes under construction and/or to be constructed are also adopted SMAO, for instance, E-ELT, TMT, NGST, CFGT and so on. Fig.1 [3] shows the schematic control loop of SMAO and primary light path of Keck telescope. As shown in Fig.2 [3], the primary mirror of Keck is segmented with 36 hexagonal segments of 1.8 meters from corner to corner each. * lshao@niaot.ac.cn; phone: ; fax: ; Second International Conference on Smart Materials and Nanotechnology in Engineering, edited by Jinsong Leng, Anand K. Asundi, Wolfgang Ecke, Proc. of SPIE Vol. 7493, 74933U 2009 SPIE CCC code: X/09/$18 doi: / Proc. of SPIE Vol U-1

2 Fig.1 Light path and control loop of Keck Telescope Fig.2 Layout of segments, actuators and sensors Micro-displacement actuator is the key mechanism in SMAO. To meet the performance requirements of co-focusing and co-phasing in SMAO, as key drive device, a micro-displacement actuator with nanometer resolution and millimeter stroke is necessary. In SMAO, each segmented cell, which is regarded as rigid body, needs three degrees of freedom, as shown in Fig.3 [3], tip/tilt two rotations out of the mirror plane, and piston translation along the normal of the mirror plane. They are normally realized with three independent axial supports laid in an equilateral triangle. Prototype of the segmented mirror and its axial support system of the reflecting Schmidt corrector in LAMOST is shown in Fig.4. [4] Fig.3 Schematic configuration of a segment mirror system Fig.4. Prototype of sub-mirror system of LMAOST 2. BRIEF DESCRIPTION OF THE DESIGN As the key device of SMAO, micro-displacement actuator needs high performances with long stroke of a few millimeters and fine resolution of few nanometers. For traditional mechanism, long stroke is always in contradiction with high resolution. Setbacks like friction, backlash, and elastic deformation confine the resolution of traditional transfer motion mechanism to fractions of a micron. To achieve performances with long stroke and fine resolution, new drive core and motion transmission mechanism are introduced. Design of the micro-displacement actuator in this paper takes advantage of a dual-level drive structure. The giant magnetostrictive mechanism is used as drive core in each drive level. Displacement/stroke pantograph mechanism is designed with ASFHS to amplify the stroke of the first stage of the actuator, which is the coarse level to realize required stoke. A secondary giant magnetostrictive drive mechanism is integrated to serve final displacement output, Proc. of SPIE Vol U-2

3 which is the fine level to output required resolution. Flexure exhibiting excellent mechanical properties free of friction, clearance and lubrication can realize precise displacement output at nanometer level. A flexure guide mechanism with good capacity of lateral load is designed to fulfill steady linear displacement output. The functional block diagram of the overall design scheme of the actuator is shown in Fig.5. Fig.5 Principle schematic diagram of a segment mirror system 3. PRINCIPLE OF GIANT MAGNETOSTRICTIVE MECHANISM Most of existing large telescope of 8-10 m class using SMAO, such as the Keck, HET and SALT, use micro-displacement actuators based on mechanical reducer and AC/DC motor. The Keck has developed a hydraulic reducer type micro-displacement actuator, while the other projects mostly take advantage of the market-available products. The US Diamond Co. and German PI Co. provide mechanical-reducer based actuator with AC/DC motor. The former is adopted by HET, and latter by SALT. The LAMOST project in China also ordered PI motorized actuators. New material such as piezoelectric ceramic and magnetostrictive material has been developed. PI Co. exploits actuators based on piezoelectric ceramic that express excellent resolution performance. However, tiny stroke, high tension and high thermal value limit their application in astronomical telescope. PI CO. is also developing micro-displacement actuator based on magnetostrictive material, but has not yet supplied market-available products, which are to be used in astronomical telescopes, up to now [5]. Fig.6 Schematic diagram of actuator structure Fig.7 Prototype f actuator structure Giant magnetostrictive material (GMM) is of increasing interest for the design of efficient actuators with relatively small size but large driving force and precise displacement, based upon its properties, such as large magnetostriction, microsecond response, high output force and high coupling factor, etc. GMM has been successfully employed in designing novel actuators. For instance, with Terfenol-D (commercially available GMM, Etrema Inc. USA), an actuator sizing φ mm may generate 5000 N blocked force and 1600N dynamic driving force. Accordingly, GMM actuator with its unique property implies promising usage in active optics. Thanks to its solid-state driving principle, GMM actuator usually enabled to be simple structure may implement direct actuation that inherently can avoid such drawbacks as lagging, backlash and insufficient positioning precision as well, those occurred in traditional ways for acting optical systems. By far, a new GMM actuator that can move 4 nanometers resolution has been successfully realized in the previous research [6]. The actuator, Fig.6 and Fig.7, consists of an active rod which is preloaded Proc. of SPIE Vol U-3

4 symmetrically in a rigid housing and surrounded by a coil fed by a current. The magnetization of the Terfenol-D produces a magnetostrictive strain in the rod, for generating displacement which may be amplified to a large -stroke by ASFHS in our design. 4. DESIGN AND TEST OF THE ABSOLUTELY SEALED FLEXIBLE HYDRAULIC MECHANISM Displacement/stroke pantograph mechanism in micro-displacement actuators usually adopts lever and/or hydraulic cylinder mechanism. Compared with traditional lever, flexible lever can attain the same pantograph effect free of friction, clearance and lubrication, except for enough stroke. Pantograph mechanism based on hydraulic cylinder structure has been successfully applied in Keck telescope. To traditional hydraulic cylinder structure, friction and leakage course low resolution. Different from traditional hydraulic cylinder mechanism, sealed type of hydraulic mechanism based on flexible cylinder can be free of friction and leakage, as takes advantage of the property of specially designed and sealed metal cylinder exhibiting axial flexibility and radial rigidity. Thanks to its axial flexibility, such hydraulic cylinder mechanism can achieve stroke of a few millimeters which is good enough compared to traditional hydraulic cylinder, however without friction and leakage. Thanks to its radial rigidity, radial expansion of such hydraulic cylinder is nearly kept constant under static axial load. In fact, in SMAO, load on its micro-displacement actuators can be regarded as approximately constant with tiny variation during operation. Using dual frequency laser interferometer, the schematic diagram of test platform is shown in Fig.8, and the laboratory test platform is built as shown in Fig.9. Resolution test results of the sealed hydraulic cylinder mechanism are shown in Fig.10 and listed Table.1. Fig.8 Schematic diagram of measurement system Fig.9. Laboratory test platform Proc. of SPIE Vol U-4

5 Fig.10 Resolution test result of ASFHS Table.1 Data analysis of pantograph ratio PI actuator step (nm) Displacement output of Standard deviation Pantograph ratio hydraulic cylinder(nm) (nm) Theoretically, the resolution of ASFHS is infinitesimal. while the actual resolution is 39.0 nm in this test, as is shown in Fig.10, due to the contaminated data,especially, when the step is less than 30.0 nm. Environmental disturbances are main reasons why resolution is limited ~39 nm. Thermal effect is dominant to cause stereo mutation of the hydraulic fluid sealed in the cylinder, and further to influence finer resolution measurements. Thus, to figure out the actual resolution of the hydraulic cylinder mechanism, obviously,compensation for the thermal disturbance is necessary. Temperature variation tendency at lab is extrapolated by the data monitored during some time of a couple of minutes [7]. The algorithm simply employs least-squares procedure. After compensation, resolution test results of the sealed hydraulic cylinder mechanism are shown in Fig.11 and Table.2. The acutual finest resolution is down to 28.6 nm in the test. Proc. of SPIE Vol U-5

6 Fig.11 Resolution test results after thermal compensation Table 2 Data analysis of pantograph ratio after temperature compensation PI actuator step (nm) Displacement output of Standard deviation (nm) Pantograph ratio hydraulic cylinder structure (nm) Fig.12 Backlash measurement Fig.13 Analysis for axial stiffness of a single cylinder Fig.14 Analysis of the sealed hydraulic mechanism Fig.15 Axial stiffness measurement Proc. of SPIE Vol U-6

7 It is seen that the ratio is much vulnerable under thermal disturbance,as is much clearer at finer displacement steps. At this sense, the actual resolution measured at greater steps is more convincing. The same experiment setup is employed for backlash test. The known backlash of PI actuator is used as standard input in the test. The difference between the test result and the known backlash of PI actuator, which is to be divided by the tested pantograph ratio, is the actual backlash of the hydraulic cylinder mechanism. Refer to Fig. 12, the forward backlash is μm, and the backward μm, both are less than 3 μm which is the typical performance of market-available products, say, PI actuator used in LAMOST. Theoretically, perfectly sealed flexible hydraulic cylinder structure would be free of backlash. The tiny relict of air bubble in hydraulic fluid and the complexity of the measurement system may be the most possible reasons attributing to the above measurement errors. For SMAO, its axial support stiffness of each segmented mirror is of great importance, from control point of view. Before test with dual frequency interferometer, we performed theoretical axial stiffness analysis of the hydraulic cylinder. Refer to Fig. 13 and Fig. 14, the hydraulic mechanism is simplified as a single cylinder and as full working state, respectively. Complete differential method is employed to analyze radial deformation of the sealed flexible cylinder under axial load F. Firstly, a single flexible cylinder is analyzed (refer to Fig. 13). The cylinder is simplified as a regular section that would expand in radial direction when pressed axially. Let V be the volume of the single flexible cylinder, which is full of hydraulic fluid, H the axial length, D the effective diameter, and R the effective radius. Thus, we have the flowing calculations for a single cylinder: V 1 2 = π D H (1) Δ V = πdh Δ D+ πd Δ H = 0 (2) 2 4 2H Δ H = Δ D (3) D Where, F is the axial pressure. Interior pressure, P, is simply expressed as follows: F 4F P = 2 1 = 2 π D π D (4) 4 In addition, the tensile force, T, and the circumferential line length, L, in the cylinder wall are then calculated as follows: T 2FH = RHP= (5) π D T T Δ L= ε L= L= L EA EtH (6) L= π D, Δ L= π Δ D (7) Where, ε is strain, E is Young s modulus. Thus, we can obtain the axial stiffness k: Proc. of SPIE Vol U-7

8 F π DEt k = = ΔH 4H (8) Based on the above analysis for a single flexible cylinder, refer to Equation (1) - (3) and Fig. 14, the axial stiffness of a sealed hydraulic cylinder mechanism can be calculated as follows V = πd1h1+ πd2h2 (9) 4 4 Δ V = 2DH Δ D + 2D H Δ D + D Δ H = 0 (10) Finally, referred to Equation (5) - (8), (9), (10), we have the system stiffness, K, of the flexible hydraulic mechanism. F π DE 3 K = = = N / mm Δ H 4( D H / t + D H / t ) (11) The Same setup for resolution test is used to measure the stiffness of ASFHS by applying a series of unit weight. The measurement is shown in Fig.15, where the calculated stiffness is N/mm. Compared with the forgoing stiffness computed by complete differential method, based on Equation (11), the tested result is 19.16% less, as proves that the simplification and complete differential method are reasonable and effective. This stiffness serves roughly 100 Hz under a mass of 20 Kg, which well satisfies the requirement for a typical segment mirror system. 5. DESIGN AND ANALYSIS OF FLEXURE GUIDE MECHANISM To flexible guide mechanism, excellent axial flexibility and radial inflexibility are necessary. Stabilization of axial load output is dependent on axial flexibility, while linearity of axial displacement is dependent on radial rigidity. Taking advantage of axial flexibility and radial rigidity of high elastic diaphragm, a flexible guide mechanism based on dual parallel diaphragms is conceived. Fig. 16 shows the schematic diagram of the flexible guide mechanism. In order to avoid buckling of the diaphragm, especially when thrust is large, the diaphragm is symmetrically cut in vane shape. Moreover, in order to achieve stroke of a few millimeters, the ends of the vane-shaped diaphragm are bended 90 degree, as shown in Fig.17. Fig.16 Schematic diagram of flexible guide mechanism Fig.17 CAD drawing of bended diaphragm To confirm the excellent axial flexibility and radial rigidity of the flexible guide mechanism, FEA analysis has been performed and related contours are shown in Fig.18. Proc. of SPIE Vol U-8

9 (a) (b) (c) (d) (e) (f) Fig.18 FEA analysis of flexible guide mechanism. (a) axial reaction under 1 mm axial displacement (b) deformation of diaphragm under 1 mm axial displacement (c) deformation under radial unit force in X direction (d) deformation under radial unit force in Y direction (e) deformation under radial unit force in X direction and 1 mm axial displacement (f) deformation under radial unit force in Y direction and 1 mm axial displacement The axial reaction force is 26.4 N when the displacement output is 1 mm, which is acceptable for the stroke performance in actual application. To radial stiffness, thanks to the orthonormality of the structure, only two radial stiffness in X direction, K x, and in Y, K y, are analyzed by FEA, thus, the stiffness in any radial direction, K R, can be directly calculated by composing method with trigonometric function, which is referred to Equation (12) as bellow. K = K cosα + K sinα (12) R x y Proc. of SPIE Vol U-9

10 The minimum radial rigidity is N/mm under 1 mm axial displacement, which meets the requirement of segmented mirror active optics. 6. PRELIMINARY TEST OF THE ACTUATOR PROTOTYPE Preliminary test of prototype has been carried out at lab of School of Mechanical Engineering, Shanghai Jiao Tong University. Schematic test setup is shown in Fig.19 and the actuator prototype is shown in Fig.20. Resolution of prototype is offered by the single giant magnetostrictive drive cell at the finer displacement output stage that has been expounded in section 2. The tested stroke of a single giant magnetostrictive drive cell achieves ~0.3 mm (refer to Fig. 19), and the total output of actuator is ~0.6 mm (refer to Fig. 20). In this test, we see that there is obvious difference between the actual amplification of stroke and the nominal pantograph ratio of the hydraulic cylinder mechanism that has been described in section 4. The causes may manifest two aspects; firstly, there are too many joints/connections in the prototype system. Manufacturing tolerance and flexures are needed to adjust carefully during assembly. The axial adjustment is accomplished with undesirable shims that may bring about micron gap and fade system stiffness. Secondly, the flexible metal hydraulic cylinder of the smaller radius is sensitive to greater axial load, which may result deviation of the axial displacement output. Measurements are to be taken into consideration to improve the performance of the full actuator system, moreover, further optimization work is to be done to achieve larger stroke up to ~ 2 mm. Fig.19 Principle of measurement setup Fig.21 Stroke of a single cell Fig.20 Prototype under measurement Fig.22 Stroke measurement of the prototype actuator Proc. of SPIE Vol U-10

11 7. CONCLUSION In the performance measurements and result analyses of the micro-displacement actuator based on GMM, we discussed the measurement method and principle of data analysis, the test results confirmed that giant magnetostrictive drive cell and related mechanical components work well. Specifically, the following conclusions are drawn. 1. Giant magnetostrictive drive cell works well and nanometer resolution has been successfully realized in the previous research. Enlarged by the absolutely sealed hydraulic mechanism, millimeter stroke of final displacement output is accomplished by the prototype actuator so far. 2. As to the absolutely sealed hydraulic mechanism, free of friction and leakage, its resolution of displacement output achieves 30 nanometer, and exhibits good axial stiffness of N/mm, which meet the typical requirement of SMAO. 3. Excellent axial flexibility and radial rigidity are employed by the flexible guide mechanism which satisfies the required stroke performance in actual application. Flexible guide mechanism is well free of friction, clearance and lubrication. 4. In preliminary test of integrated prototype of the actuator, the maximum stroke of the prototype actuator achieves 0.6 mm, which will be improved to triple by future optimization. By preliminary design and test of the first prototype, feasibility of micro-displacement actuator based on GMM has been confirmed. Nevertheless, in detail design, there are still many works to be done. Hopefully, the final measurement of the actuator is to be carried out at micro-displacement measurement lab of Nanjing Institute of Astronomical Optics & technology, where the more precise measurement environment may be offered. ACKNOWLEDGEMENT The authors would like to thank Mr. Yajun Zhang and Mrs. Aihua Li, from NIAOT, and Mr. Pengyou Xu, from Shanghai Jiaotong University, for their help during the measurement. The research is partially supported by NSFC (Grant No ), Shanghai Pujiang Program (No. 08PJ ), and SRF for ROCS, SEM. The authors are grateful to their great supports. REFERENCES 1. Cui X Q, Li Y P, Ni X Y, et al. The active support system of LAMOST reflecting Schmidt plate, Large Groundbased Telescopes. Proc. of SPIE, 2003, Vol. 4837: Shao L. Mechanism Design and Research of Micro-displacement Actuator Based on Giant Magnetostrictive Cell. Master thesis, Graduate school of CAS, Yang B T, Yang D H, Meng G, et al. Application study on giant-magnetostrictive actuator for driving segmented mirrors of very large astronomical telescope. International Conference on Smart Materials and Nanotechnology in Engineering. Proc. of SPIE, 2007, 64230Z. 4. Yang D H, Qi Y J. Measurement of the Actuation Transmitting Mechanism of the Segment Prototype of the LAMOST Telescope, Optomechanics Proc. of SPIE, 2005, Vol. 5877: 58770V. 5. Shao L, Yang D H, Chen K X, Yang B T. Review of Mechanical Structure of Micro-displacement Actuator for Optical Astronomical Telescope. Progress in Astronomy. 27(1): 70-79, Yang B T, Bonis M, Tao H, et al. A magnetostrictive mini actuator for long-stroke positioning with nanometer resolution. Journal of Micromechanics and Microengineering, 16: , Yang D H, Qi Y J, Zhu Z D, et al. Design and Test of the active micro motion mechanism for optical mirror segment. Optics and Precision Engineering, 13 (2): , Proc. of SPIE Vol U-11