international journal of conceptions on mechanical and civil...

International Journal of Conceptions on Mechanical and Civil Engineering Vol. 1, Issue. 1, Dec’ 2013; ISSN: 2357 – 2760

58 | 1 3 3

Design optimization & realization of µ motion mechanisms for on board correction of segmented

mirrors Vikas Sinha and Vijay Chaudhary

Dept. of Mechanical Engineering, CSPIT, Changa,

Anand, India. [email protected]

Hemant Arora, A R Srinivas and D Subramanyam Scientist,

SAC, ISRO, Ahmedabad, India.

Abstract— The need for micro mechanism in space application is on rise. As more and more planetary mission are planned for future, the requirements of having very large aperture mirrors for very high ground resolution are growing tremendously. Large mirrors in space are limited by the size of launch fairing diameter for the launch vehicle and its corresponding bearing on the cost/ time and complexity of the complete development activity. The advent of deployable mirrors has paved the way for such limitations. Here the main disadvantage is the onboard (while in space) correction of the deployed arms of mirrors. Feedback based micro manipulators are needed to get very good optical surface and optical numbers. These are met by careful design and realization of high precise micro manipulators. This paper focuses on the work carried out in the design, optimization and development of such micro manipulators for tipping, tilting and piston movements using a novel multidimensional flexure to take care of the several degrees of freedom of the correction required onboard. These design options have been optimized, evaluated using FEM techniques and validated using experimentation. Results measured are confirming the requirement needed for space based deployment of segments.

Keywords- flexure, actuation, piezo, micromotion

I. INTRODUCTION With increase in demand for higher resolution images of

earth, it has become inevitable to have a large aperture mirrors for better visualization of distant object. Nowadays, Space optics is more opted for these missions over the terrestrial one to eliminate the effect cause by atmospheric disturbance. But launching such a large aperture mirror in space is itself a big challenge considering constrains like shape and volume of the launch bay and mass of the mirror. Such constrains can be handled by segmenting the mirror. These segments of a full diameter mirror can be folded and deployed through a mechanism, which can eliminate the constraint of space limitations in a launch vehicle. Segmentation gives the inherent flexibility to mirror mechanism making it difficult to achieve optical quality surfaces. It introduces the complexity depending mainly on segment numbers and gaps. This requires feedback and active shape controller such as piezos, motors etc. for aligning each segment with one another. [1]

This paper focuses on Design and Development of Flexure as a micro manipulator for proper alignment of mirrors segments, using Amplified Piezo Actuators (APAs) as primary actuators. Piezo are usually identified as PZT, A ceramic of Lead Zirconate titanate. The problem of non-linearly and hysteresis with the Piezo actuator can be solved by providing a feedback control system. Here flexures are used as a novel concept, using its inherent compliance of a material for deformation to transfer the force/ motion of piezo to the segment smoothly for output displacement and also to handle the additional stresses developed in the piezo. The flexure must be able to take the load of the segment and also to transfer the motion in nanometer resolution within micrometer range.

II. DESIGN OF FLEXURE BASED HINGES FOR MICRO MOTION

The tipping, tilting and piston movement of the segment give it all the six DOFs for its movement. Two position actuators are insufficient as it gives only tip and piston movement while the four actuators are redundancy, as it is more than sufficient. Hence, for optimization, the segment is equipped by three position actuators allowing the segment all six DOFs. Fig. 1 shows the assembly of segment with its position actuators connected to fixed triangular base. The base is connected to the deployable arm of the mirror.

Fig. 1: Geometry Model of a Mirror Segment Assembly


59 | 1 3 3

Fig. 2: Segment at (a) normal (b) piston (c) Tipped (d) Tilted position

APAs itself are pre-stressed structure; directly connecting with segment will cause premature failure due to excess stress under repetitive working cycle. This leads to use of hinges between piezos and segment and base to reduce the stresses between them. Since the motion required is in micron range, Flexure can do this job very well, without introducing any further joints in the system.

In the last 50 years, many flexible joints (Flexures) have been researched and developed, mostly designed by considering the two varieties: notch-type joints and leaf springs. Notch type flexible joints (fillet joints), Fig. 3 (a, b), were first analyzed by Paros and Weisberg in 1965 and since then, studied by many researchers and designers [2]. Today, these are widely used for high-precision, small-displacement mechanisms. These joints have also been applied by Howell and Midha to develop the field of pseudo-rigid-body compliant mechanisms [3]. Leaf springs are most generic flexible translational joint, composed of sets of parallel flexible beams (Fig. 3 (c)) providing high-precision motion stages. Leaf spring joints are widely used in medical instrumentation and MEMS devices.

a) Planer notch joint b) spherical notch joint c) leaf spring

Fig. 3: Basic Flexible joint components

As the Segment has to move in all six DOFs, the flexure should be able to bend in all direction. It is difficult to design tri-axial flexure due to limitation of space constraint and decrease in fundamental frequency with the geometry. Hence, this paper only presents the design and experiment using uni-axial and bi-axial flexures.

The geometry of the flexure is a very important parameter deciding the stress and mode frequency of the flexure. Various shapes and structures of the flexure were design using CAD software. [4][5][6] Fig. 4 show one of the flexure designed for this particular application. One end of the flexure is connected to the segment or fixed base, while the other end bolted to the piezo.

Fig. 4: Modified I Bar Section (Double)

III. FEM SIMULATION OF FLEXURE DESIGN CAE tools were used for Finite Element Analysis in

simulating the actual environment with the given boundary condition and measure the deflection on segment and stresses developed in flexure due to piezo actuation.[7] Figure 1 shows the assembly of single petal where three piezos, each sandwiched between two flexures are attached to fixed support to the one end and to the petal at another end.

Boundary Conditions: Segment and triangular base, Piezo, Flexure are specified as Aluminum, Invar and SS respectively. Two piezos are actuated simultaneously by giving forced displacement at each arm of the piezo. Triangular base was kept as a fixed support.

Meshing of model is done by FEA software using tetrahedron element. Fig. 5 shows 3DSolid mesh model of the piezo and I bar flexure assembly.

Fig. 5: FE Meshed Model of Flexure and piezo assembly

Modal analysis was carried out by implementing boundary conditions mentioned above so that the assembly remains above the random frequency generated. The resultant displacement distribution profile for the fundamental mode frequency is as shown in Fig. 6.


60 | 1 3 3

Fig. 6: Displacement profile for fundamental Mode frequency of Segment

Assembly

Structural analysis carried out by giving the boundary condition as stated earlier to study the displacement and stress generated in the assembly during piezo actuation. Resultant Deformation profile is shown in the Fig. 7 while actuating two piezo simultaneously. Deformation over the Actuated and non actuated piezo is shown in Fig. 8, while stress profile for these is shown in Fig. 9.

Fig. 7: Deformation profile for Segment Assembly

Fig. 8: Deformation profile of (a) Non Actuated Piezo and Flexure (b)

Actuated Piezo and Flexure

Fig. 9: Stress profile of (a) Non Actuated Piezo and Flexure (b) Actuated

Piezo and Flexure

Similar test being carried out by optimizing various flexures by varying its dimensions and simulation were carried out. Results of best configuration are displayed on Table I.

Out of these Uniaxial and Bi-axial flexure were selected fabrication owing to their advantages in the ease of fabrication and assembly with the segmented mirror. Though P.I of modified I-bar section was maximum, the same cannot be preferred due to its difficulty in assembly with the segmented mirror.

TABLE I. RESULTS FOR VARIOUS FLEXURES FOR DIFFERENT PARAMETERS

Type Of Flexure

Fundamental Frequency (Hz)

Max. Stress (MPa)

P. I. ( Hz/ MPA)

Range [Max Disp.(+) – Min Disp.(-)] (μm)

Total Displacement At Actuated Piezo (μm)

Total Displacement At Non Actuated Piezo (μm)

without flexure

220.15

147.18

1.495 70.95/ 23.72

36.92 -0.278

Z-section

(3mm single)

42.25 78.38 0.539 103.8/ 34.43

52.738 1.245

Z-section

(2mm Double)

60.125

80.142

0.75 103.76/ 34.29

52.76 -0.577

Modified S Shaped

Sigma

71.93 95.76 0.751 105/ 39.94 53.3 1.06

Z Shaped

Sigma

67.249

92.48 0.727 105.62/ 36.46

53.15 0.812

Modified

I Bar Section

(Double)

106.68

95.51 1.117 103.38/ 34.07

51.69 0.642

Hinge Type

123.71

92.89 1.332 103.12/ 33.87

52.1 -0.592

Free Hand

61.167

96.52 0.634 106.22/ 36.56

53.27 1.026

180 Zs

72.915

91.51 0.797 105.06/ 35.32

53.003 -0.571

Uniaxial Flexure

96.004

90.50 1.061 106.95/ 37.65

51.19 1.702

Biaxial Flexure

47.38 91.77 0.516 106.37/ 36.88

53.611 0.569


61 | 1 3 3

IV. EXPERIMENTATION Experiments were carried out for the hinge joint and for

Uniaxial and biaxial flexure. Fig.10. shows a assembly of Piezo with a Bi-axial Flexure. They were assembled to the mirror according to given boundary condition. Dial Gauges were used to measure the displacement by putting it directly over the petal where flexures are joined. Voltage was supplied to the piezos through function generator and amplified through amplifier and accordingly displacements were measured due to its actuation. Repeated cycles were taken to confirm the deflection on segment. (Fig 11)

Fig. 10: Flexures assembled on both side of the Piezo APA60S

Fig. 11: Assembly test

A. Voltage Displacement Characteristic for Hinge Joint: Fig 12 shows the image of the Hinge Joint. The rotational

movement is caused by turning of the roller screw. It was screwed with two APA200M and one APA100M which are of pulling type causing the deformation in downward direction during actuation.

Fig. 12: Hinge Joint

Fig. 13: Voltage-Displacement graph for the APA200M actuated Piezo.

Fig. 14: Voltage-Displacement graph for the APA200M and APA100M

actuated Piezos.

First, one piezo was actuated and the displacement produced by it were recorded. Again, two piezos were actuated simultaneously and measurements were recorded. Graphs for both measurements are shown in Fig 13 and 14.

B. Voltage Displacement Characteristic for Uniaxial and Biaxial Flexure: In this particular experiment displacements caused by the

flexures were recorded. Fig 15 shows graph of Uniaxial and bi-axial flexure connected to APA60S.

Fig. 15: Uniaxial Flexure and Biaxial Flexure

On actuating the single APA60S, following characterization was shown by Uniaxial and biaxial flexure as given in Fig 16 and 17 respectively.

Fig. 16: Voltage-Displacement graph for Uniaxial flexure by single actuated

Piezo.

Fig. 17: Voltage-Displacement graph for Biaxial flexure by single actuated

Piezo.

-50

0

50

100

150

0 50 100Dis

plac

emen

t (μm

)

Voltage (V)

APA200M 1APA200M 2

-20

0

20

40

60

0 50 100

Dis

plac

emen

t (μm

)

Voltage (V)

APA60S 1

-200

204060

0 50 100

Dis

plac

emen

t (μm

)

Voltage (V)

APA60S 1

APA60S 2

APA60S 3


62 | 1 3 3

When two piezo is actuated simultaneously, the following trend was shown by Uniaxial and Biaxial flexure as shown in Fig 18 and 19 respectively.

Fig. 18: Voltage-Displacement graph for the Uniaxial Fleure for two actuated

Piezo.

Fig. 19: Voltage-Displacement graph for Biaxial Flexure for two actuated Piezo.

V. RESULTS AND DISCUSSION

TABLE II. RESULT FOR DEFLECTION OF PETAL DUE TO ACTUATAION OF PIEZO

Deflection on petal at actuated piezo

(μm)

Deflection on petal at non actuated piezo (μm)

Type Simulation Experimental

Simulation Experimental

Hinge joint (APA100S) n (APA200S)

65.47 66 3.14 6

113.37 137 3.14 6

Uniaxial flexure

(APA60S)

51.19 52 1.36 2

Biaxial flexure

(APA60S)

53.611 52 1.12 4

Table shows the results of Hinge joint, Un-iaxial and Bi-

axial flexure. The flexures show a comparable result between simulation and experimentation. This is due to its compliant nature. There variation between the results of simulation and experiment for hinge joint is due to friction and slippage between roller screw and its support.

VI. CONCLUSION The need of micro mechanism for fine adjustment of the

deployed segment aboard a spacecraft is established. Flexure based designs as a solution for the micro control of tip/ tilt/ piston action of proposed segment is prepared. Various design

for 1D and 2D flexure are prepared as viable solution for the problem defined. The proposed designs of the flexure are option using FE tools for better stiffness (first mode of natural frequency) and lowest von-mises stress.

A performance index has been introduced to compare the behavior of the design options. The best P.I. achievable and viable was for a Uniaxial Flexure (0.847). The optimized design of the flexure is validated by experimental evaluation of flexure with the actuated segments. The measured results and the simulated one are in closed conformance with each other. Minor changes in the measured and simulated results are attributed to the facts such as (a) measured experimental accuracy, (b) position accuracy of the measurement system (c) repeatability of the measured accuracy and position accuracy above. However the inaccuracies in the measurement are eliminated by ruggedizing the experimental setup. Repeated measurement gave close matching. Fig. 20 shows such repetitiveness for the two cycles of the experimentation.

Fig. 20: Voltage-Displacement graph for the single actuated Piezo showing

the repeatability

It can be concluded that the proposed flexure design met the requirements/objectives of the micromanipulation. These design are now adapted for mirror segments of upcoming developmental activities of space optical payloads.

REFERENCES [1] K. Shah, V. Chaudhary, H. Arora, A. R. Srinivas, “Design Optimization

of Mirror Segment for Primary Segmented Mirror”, Journal of Mechanical Engineering Vol. 9 No.1, pp 29-34, 2011

[2] J. M. Paros, L. Weisbord, “How to Design Flexure Hinges”, Machine Design, pp. 151-156, 1965

[3] Howell, L.L., 2001, “Compliant Mechanisms”, John Wiley & Sons, Inc., New York, NY

[4] H. l. Ho, G. L. Yang, W. Lin, W. H. Chen, T. J. Teo, “Development of a 1-DOF Flexure Based Positioning Stage for Wafer-Bumps Inspection”, Technnical Report, STR/04/024/MECH, Singapore Institute of Manufacturing Technology, 2004

[5] V. Shilpiekandula, K. Youcef-Toumi, “Integrated Design and Control of Flexure Based Nanopositioning Systems-Part I: Methodology”, 18th IFAC World Congress, October 2010

[6] V. Shilpiekandula, K. Youcef-Toumi, “Dynamic Modelling and Performance Trade-offs in Flexure-based Positioning and Alingment System”, Motion Control, Federico Casolo (Ed.), ISBN 978-953-7619-55-8, INTECH, Croatia, pp , Jan 2010

[7] Y. C. Lee, B. McCarthy, J. Diao, Z. Zhang, K. F. Harsh, “Computer-Aided Design for Microelectomechanical System (MEMS)”, International Journal of Materials and Product Technology-Vol 18, No.4/5/6, pp. 356-380, 2003

0

20

40

60

0 50 100Dis

plac

emen

t (μm

)

Voltage (V)

APA60S 2APA60S 2-2

international journal of conceptions on mechanical and civil...

Documents