DESIGN AND ANALYSIS OF COMPLIANT MECHANISM FOR VIBRATION ISOLATOR USING TOPOLOGY OPTIMIZATION

International Journal of Innovative Research in Technology, Science & Engineering (IJIRTSE) ISSN: 2395-5619, Volume – 1, Issue – 4. June 2015

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DESIGN AND ANALYSIS OF COMPLIANT MECHANISM FOR VIBRATION ISOLATOR USING TOPOLOGY OPTIMIZATION 1

P.INDRAJITH,

2

M.UDAYAKUMAR

1

M.E ENGINEERING DESIGN, MECHANICAL DEPARTMENT 2 ASSISTANT PROFESSOR, MECHANICAL DEPARTMENT 12 K.RAMAKRISHNAN COLLEGE OF ENGINEERING TRICHY, INDIA 1 [email protected], [email protected] Abstract— Compliant Mechanism is the focus of active research because of the stability, robustness and ease of manufacturing endowed by their unitized construction. In this project , we explore an application of compliant mechanism for vibration isolation system with rigid foundation. Vibration isolators are specified for those rotating machines that could impart enough forces. By introducing compliance into the connection, the transmission of applied forces is reduced at some frequencies at the expense of increasing transmission at other frequencies. The force transmissibility is numerically identical to the motion transmissibility. Structural optimization approach is focused on the determination of the topology, shape and size of the mechanism. The building blocks are used to optimize a structure for force transmission. Flexible building blocks method for the optimal design of compliant mechanisms. The approach used to establish the actuator model of the block and its validation by commercial finite element software. These blocks are in limited number, the basis is composed of 36 elements. The design drawing model is analyzed for the displacement transmissibility or amplitude for varying disturbance frequency and the force transmitted for corresponding disturbance frequency. Isolation efficiency of design drawing model is proven to be high. Keywords— Compliant Mechanism, Force Transmission, Topological Optimization, Natural Frequency, Vibration Isolation, Building Blocks.

I. INTRODUCTION The concept of using flexible members to store energy and create motion has been used for millennia. Archaeological evidence suggests that bows have been in use since before 8000 B.C. and was the primary weapon and hunting tool in the most cultures. Consider the longbow illustrated in figure 1 Early bows were constructed of relatively flexible material such as wood and animal sinew. Strain energy in the bow is transformed to kinetic energy of the arrow.

Figure 1: Longbow in its unstrung, strung, and drawn positions. The number of products that rely of the flexible members to perform their functions has been increased significantly over that last few decades, thanks in part to the development of stronger and more reliable materials. The use of compliant mechanisms will probably continue to increase with time as materials and design methodologies are improved. The demand for increased product quality and decreased cost also pressures manufacturers to implement compliant mechanisms.

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A. COMPLIANT MECHANISM AND NATURE Humans and nature often have differing philosophies on mechanical design. Stiff structures are usually preferred by humans because for many, stiffness means strength. Devices that must be capable of motion are constructed of multiple stiff structures assembled in such a manner as to allow motion (e.g., door hinges, linkages and roller bearings). However, stiffness and strength cannot be equated- stiffness is a measure of how much something deflects under load, whereas strength is how much load can be endured before failure. Despite of human tendencies, it is possible to make things that are flexible and strong. Nature used stiff structures where needed- tree trunks, bones, teeth, and claws- but in living organisms, it more often relies on flexibility in living organisms. Bee wings, bird wings tree branches, leaf stems, fish, and single-celled organisms are only a few examples of creations that use compliance to their advantage. Nature also has advantage of growing living things, and no assembly is required . B. NOMENCLATURE Rigid body mechanisms are constructed of rigid links joined with kinematic pairs, such as pin joints and sliders. These components are easily identified and characterized. Since compliant mechanisms gain at least some of their motion from the deflection of flexible members, components such as links and joints are not as easily distinguished. Identification of such components is useful to allow the accurate communication of design and analysis information. C. LINK IDENTIFICATION A link is defined as the continuum connecting the mating surfaces of one or more kinematic pairs. Revolute (pin of turning) joints and prismatic (siding) joints are examples of kinematic pairs. Links can be identified by disassembling the mechanism at the joints and counting the resulting links. Note that the mechanism illustrated in figure 1.3 has no traditional joints, and therefore has zero links. Such mechanisms are termed fully compliant mechanisms since all their motion is obtained from the deflection of compliant members. Compliant mechanisms that contain one or more traditional pairs along with compliant members are called partially compliant mechanisms.

Figure 2: Fully compliant mechanism D. COMPLIANT MEMS Micro electromechanical systems (MEMS) integrate mechanical and electrical components with features sizes ranging from micrometres to millimetres they may be fabricated using method similar to those used to construct integrated circuits. MEMS have great potential of providing significant cost advantageous when batch fabricated. Their size also makes it possible to integrate them into a wide range of systems. Micro sensors (e.g., accelerometer for automobile crash detection and pressure sensor for biomedical applications) and micro actuators (e.g., for moving arrays of micro mirrors in a projection systems) are examples of commercial application of MEMS. This field is expected to grow dynamically overtime. . Compliant mechanisms present solution to the many of these problems. The advantages at the micro level that compliant mechanism:  Can be fabricated in plane  Require no assembly  Require less space and are less complex  Have less need for lubrication  Have reduced friction and wear  Have less clearance due to pin joints, resulting in higher precision  Integrate energy storage elements (springs) with other components

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E. VIBRATION ISOLATION Engineering system possessing mass and elasticity are capable of relative motion. If the motion of such a system repeats itself after a given interval of time, the motion is known as vibration. Vibration, in general, is a form of wasted energy and undesirable in many cases. This is particularly true in machinery; for it generates noise, breaks down parts, and transmits unwanted forces and movements to close-by objects. Vibrations are produced in machines having unbalanced masses. These vibrations will be transmitted to the foundation upon which the machines are installed. This is usually undesirable. To diminish the transmitted forces, machines are usually mounted on springs or dampers figure 3, or on some other vibration isolation material.

(a) (b) Figure 3 : (a) directly mounted (b) mounted through isolators Vibration Isolation reduces the level of vibration transmitted to or from a machine, building or structure from another source. The degree of isolation achieved depends on the ratio: ƒe - Frequency of disturbing vibration ƒn - Natural frequency of isolator Transmissibility (i.e. amount of vibration transmitted at a specific frequency ƒn as a fraction of the disturbing vibration at the same frequency ƒe). Transmissibility: > 1 = Increased transmitted vibration, = 1 = No vibration isolation , < 1 = Vibration isolation If no damping present in isolators i.e. C/Cc = 0 F. VIBRATION CONTROL/ISOLATION Vibration Control involves the correct use of a resilient mounting or material in order to provide a degree of isolation between a machine and its supporting structure to achieve efficient vibration isolation it is necessary to use a resilient support with sufficient elasticity so that the natural frequency fn of the isolated machine is substantially lower that the disturbing frequency fe of vibration. The ratio fe/fn should be greater than 1.4 and ideally greater than 2 to 3 in order to achieve a significant level of vibration isolation.

(a)

(b)

(c)

(d)

Figure 1: (a) Machine on isolators on the floor no foundation, (b) Active shock and vibration, (c) Machine on foundation, no isolators, (d) passive shock and vibration For an active shock and vibration isolation the foundation block for a dynamic machine should be isolated in order to reduce the effects of vibration and shock on nearby machines, people and the building structure. Controlling the source of a structural disturbance is known as active isolation.

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Applications include: isolation of foundations for: power presses, pumps, drop hammers, forging machines, metal forming and cutting machines, compressors, gensets, engines and test rigs, printing machines and rolling roads. For Passive Shock and Vibration Isolation when it is not possible to prevent or sufficiently lower the transmission of shock and vibration from the source a resiliently supported foundation block can be used for the passive isolation of sensitive equipment. Applications include: isolated foundations for: machining centers, grinding machines, measuring and inspection equipment, laser cutters, microscopes, Fans, pumps, and chillers G. TOPOLOGY OPTIMIZATION (DESIGN OF COMPLIANT MECHANISM USING TOPOLOGY OPTIMIZATION) By using the topology optimization the compliant mechanism is designed. The topology optimization predicts the optimal distribution of the material in the design domain. It is very promising for systematic design of compliant mechanism because topological design is automated by the given prescribed boundary conditions. The topological design of compliant mechanism is solved as a problem of material distribution using the optimality criteria method. H. DESIGN PROCEDURE The design of compliant mechanism involves the following steps.  The design domain size and shape must be identified.  Assume the design domain in some regular shape for simplify the problem during the meshing.  Located the input (force/displacement from PZT to compliant mechanism) and output (force/displacement from compliant mechanism to external environment)  Input all these design specification to the program to carry out the Finite Element Analysis and to calculate the displacement at each node.  Optimality Criteria is a mathematical tool is used to optimize the design domain based on the FEA result and the convergence criteria.  The design domain is plotted after some regular interval  The optimization loop will come out as the compliance value repeated.  The final topology plot from the program must be modeled in the Ansys and check for the output specification from the final topology. I. TOPOLOGICAL OPTIMIZATION Topological optimization has been successful used to determine both types and dimensions of compliant mechanism. It is very promising for systematic design of compliant mechanism because topological design is automated, given the prescribed boundary condition, input and output. Its success relies very much on the problem formulation. In topological optimization, the function approach employs mechanical advantage, geometrical advantage and work ratio as objective function, while displacement constraint and material constraint are imposed to narrow the domain of feasible search. The topological design of compliant mechanism is then solved as a problem of material distribution using the Optimality Criteria method. J. TOPOLOGY OPTIMIZATION FOR VIBRATION ISOLATOR USING FEA Topological optimization is a form of "shape" optimization sometimes referred to as "layout" optimization. The goal of topological optimization is to minimize/maximize the criteria selected (minimize the energy of structural compliance, maximize the fundamental natural frequency, etc.) while satisfying the constraints specified (volume reduction, etc.). The problem is defined for linear elastic analysis. Then define material properties (Young's modulus, Poisson's ratio, and possibly the material density). Then select the element 2D plane types for topological optimizations generate a finite element model. Load and boundary conditions for a single load case linear structural static analysis (see Figure 6 ). Figure 7 and figure 8 illustrates based on volume constraints for the specific load of 85kN and the force transfer path is identified for structural size of 500mm width and 165mm height. The optimized path for the transfer of maximum force is obtained using topology optimization. In this example the boundary condition specified as all the corners of the design domain is fixed and a point load is applied at the middle of the bottom face. The material property and the design variable and domain dimension are given below in table 1

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Table 1: specifications for topology optimization Design domain

500mm X 305mm X 165mm

Young’s modulus

200Gpa

Poisson’s ratio

0.29

Input force

85Kn

Upper limit of design variable

10mm2

Lower limit of design variable

0.1 mm2 25mm

Output displacement at output port

Figure 5: Design domain

Figure 6: Meshed Design domain with boundary condition for single load case

Figure 7: After 10% of volume reduction

Figure 8: After 50% of volume reduction

The scope of this study is limited to low frequency isolation because the use of compliant mechanisms in active vibration isolation systems has the greatest advantage in the low frequency range. Since many passive systems are effective and sufficient for high frequency isolation, the need of active systems for high frequency isolation is less than that for low frequency isolation.The preliminary results of FEA from ANSYS demonstrate that a compliant mechanism can be effectively used to reduce the amount of force transmitted to the surface. Figure 9 illustrates how a compliant mechanism can be integrated into a vibration isolation system.

Figure 9 : Models illustrating the concept of using a compliant Mechanism in vibration isolation

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K. OPTIMIZATION USING BUILDING BLOCKS Compliant mechanisms are single-body, elastic continua flexible structures, that deliver the desired motion by undergoing elastic deformation, as opposed to jointed rigid body motions of conventional mechanisms. When considering small scale systems (e.g. for micro robotics), there are many advantages of compliant mechanisms, among them: simplified manufacturing, reduced assembly costs, reduced kinematic noise, no wear, no backlash, and ability to accommodate unconventional actuation schemes. Compliant mechanisms have already been used in many applications including product design, Micro Electro Mechanical Systems (MEMS), adaptive structures for vibration damping, surgical tools .The optimal design of compliant mechanisms made of an assembly of basic building blocks chosen in a given library. A library of passive compliant elements is proposed in FlexIn. These blocks are in limited number: the basis is composed of 36 elements (see Figure 10).

Figure 10: Library of compliant building blocks for planar compliant mechanisms synthesis

Figure 11: Optimum compliant isolator design

II. ANALYSIS AND SUBMISSION A. HARMONIC ANALYSIS The harmonic response analysis solves the time-dependent equations of motion for linear structures undergoing steady-state vibration. The entire structure has constant or frequency-dependent stiffness, damping, and mass effects. All loads and displacements vary sinusoidally at the same known frequency. Element loads are assumed to be real (in-phase) only. The magnitude of the force transmitted to the foundation can be reduced by decreasing the natural frequency of the system otherwise the force transmitted to the foundation can also be reduced by decreasing the damping ratio. However, since vibration isolation requires, the machine should pass through resonance during start-up and stopping. Hence some damping is essential to avoid infinitely large amplitude in resonance. Although damping reduces the amplitude of the mass (X) for all frequencies, it reduces the maximum force transmitted to the foundation (Ft) only if . Above that value, the addition of damping increases the force transmitted. If the speed of the machine (forcing frequency) varies, we must compromise in choosing the amount of damping to minimize the force transmitted. The amount damping should be sufficient to limit the amplitude X and the force transmitted Ft while passing through the resonance, but not so much to increase unnecessarily the force transmitted at the operating speed. B. HARMONIC RESPONSE OF COMPLIANT ISOLATOR

The displacement amplitude (Figure 14) is calculated for various frequency ratios from 1.5 – 5 with damping ratio ζ =0.3 for compliant mechanism using ANSYS. The force transmitted (figure 18) for the corresponding amplitude and frequency ratios are also calculated. Displacement amplitude is calculated for compliant mechanism for varying frequency ratios from(1.5-5)

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Figure 12: Displacement transmissibility for various frequency ratios

Figure 13: Displacement amplitude for corresponding frequency ratio ranges from R, (0-7.5) for compliant mechanism

Figure 14: Displacement amplitude for corresponding frequency ratio ranges from R, (1.5-5) for compliant mechanism

Figure 15: Equivalent stress of a harmonic response

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Figure 16 : Minimum principal stress

Figure 17 : Maximum principal stress

Force transmitted (Figure 18 ) for the corresponding displacement amplitude is calculated using known material constant and damping coefficient, it is taken as ζ = 0.3 for maximum value and natural frequency of the coil spring isolator. Table 2: Force transmitted for varying frequency ratio Frequency ratio, R

Force transmitted, FT

1.5

42.85

2

25.68

2.5

16.17

3

13.6

3.5

9.5

4

7.4

4.5

6.3

5

5.1

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Figure 18: Force transmitted for varying frequency ratio C. TRANSMISSIBILITY RATIO

The force transmitted by using compliant mechanism is with constant damping ratio ζ = 0.3 (Figure 19).

Figure 19: Force transmission of the compliant mechanism Transmissibility Ratio Tr = (Force transmitted in KN / Disturbing force in KN) D. ISOLATION EFFICIENCY Isolation Efficiency η in percent transmission is related to Transmissibility as η = 100 (1-Tr) %

Figure 20: Isolation efficiency vs frequency ratio Table 3: Isolation efficiency of coil spring isolator and compliant mechanism

1.5

Compliant mechanism % 56.2

2 2.5 3 3.5 4 4.5

69.7 75 85 90 93 95

Frequency ratio

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5

98

III. CONCLUSION Compliant Mechanisms which are proposed to provide cost effective and high performance passive vibration isolation systems. Their function is to transmit the force for various displacement amplitude of corresponding frequency ratios. The preliminary results from FEA using ANSYS show that a compliant mechanism can provide effective vibration isolation from a sinusoidal disturbance with known frequency ratios. In this project, we demonstrated through harmonic analyses, that the disturbance of 0.01m amplitude, the isolation efficiency of 56% at 1.5 Hz and by 98% at 5Hz for the amplitude of 0.001m by using compliant mechanism.

References [1] Tanakron tantanawat, zhe li and Sridhar Kota, 2004. “Application of compliant mechanisms to active vibration isolation systems”, proceedings of detc 2004 -7439. [2] Frecker, M. and Canfield, S. 2000, “Topology Optimization of Compliant Mechanical Amplifiers for Piezoelectric Actuators”, Structural Optimization in press. [3] Mostafa M. Abdalla, Mary Frecker, Zafer Gürdal, Terrence Johnson and Douglas K. Lindner, 2003, “maximum energy-efficiency compliant mechanism design for piezoelectric stack actuators”, ASME International Mechanical Engineering Congress Washington, D.C., November 15–21, 2003-41509, [4] Colby C. Swan, and Salam F. Rahmatalla, 2004, “design and control of path-following compliant mechanisms”, proceedings of DETC 2004 -57453. [5] Kota S., J. Hetrick, S. Rodgers, Z. Li, Compliant Displacement Amplification Apparatus for Micro Electro Mechanical Systems. U.S. Patent No. 6,175,170. [6] Walsh, P. L., and Lamancusa, J. S., 1992, "Variable Stiffness Vibration Absorber for Minimization of Transient Vibrations," Journal of Sound and Vibration, 158(2), pp. 195-211. [7] Michael bruyneel and Pierre duysinx, 1999, “Note on topology optimization of continuum structures including self-weight”.

Authors Short Profile:

P.INDRAJITH M.E ENGG DESIGN, MECHANICAL DEPT. K.RAMAKRISHNAN COLLEGE OF ENGG. TRICHY.

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DESIGN AND ANALYSIS OF COMPLIANT MECHANISM FOR VIBRATION ISOLATOR USING TOPOLOGY OPTIMIZATION

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