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Optimal design of a QZS isolator using flexures for a wide range of payload

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Abstract

This paper presents an optimal design of QZS (Quasi-zero stiffness) isolator using flexures for wide range of payload. The QZS isolators have both appreciable static stiffness for gravity compensation and very small (theoretically zero) dynamic stiffness for vibration isolation. Since the stronger vertical spring brings out more gravity compensation within a given stroke of the gravity compensation, the QZS isolator need to have strong vertical stiffness to support wide range of payload. First, the dynamic model of QZS isolator using flexures is illustrated based on the previous non-dimensional analysis of flexure. Then, some design considerations for flexure are discussed and optimal design problem of the QZS isolator is formulated mathematically to maximize the stiffness of the vertical spring. As a result, optimal shape ratio of flexure to maximize stiffness of the vertical spring can be determined. Finally, the design procedure for flexure of the QZS isolator is summarized and illustrated with a design example.

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Abbreviations

A 1∼6 :

Coefficients for parasitic motion

B, b :

Dimensional and non-dimensional width of flexure

c :

Non-dimensional damping coefficient for isolator system

E :

Young’s modulus of flexure material

f :

Vertical direction force from flexure

g :

Number of flexures

H, h :

Dimensional and non-dimensional height of notched part of flexure

I :

Area inertia of notched part

k h :

Non-dimensional stiffness of horizontal coil spring

K v ,k v :

Dimensional and non-dimensional stiffness of vertical coil spring

L :

Total length of flexure

L a ,L b :

Length of notched and thick parts of flexure

m :

Non-dimensional mass of payload

MT, mt :

Dimensional and non-dimensional bending moment at notched part

MT M ,mt M :

Maximum dimensional and non-dimensional bending moment at notched part

n :

Shape ratio of flexure (n = L b /L a )

p :

Compression force

p cr.1,2 :

Non-dimensional compression force of 1st and 2nd buckling mode

s :

Number of flexures on one side of the payload

w(t) :

Disturbance or external force

x 0 :

Non-dimensional initial deformation of horizontal spring

x l :

Non-dimensional parasitic motion at the end of the flexure

y 0 :

Initial gravity compensation

Y m , y m :

Dimensional and non-dimensional vertical motion of the payload

β :

Safety factor for yield stress

γ :

Safety factor for compression force

σ E :

Yield stress of flexure material

σ M :

Allowable stress of flexure material

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Authors and Affiliations

  1. Graduate School, Department of Mechanical Engineering, Soongsil University, 369, Sangdo-ro, Dongjak-gu, Seoul, Korea, 156-743

    Kyoung-Rock Kim & Yo-han You

  2. Department of Mechanical Engineering, Soongsil University, 369, Sangdo-ro, Dongjak-gu, Seoul, Korea, 156-743

    Hyeong-Joon Ahn

Authors
  1. Kyoung-Rock Kim
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  2. Yo-han You
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  3. Hyeong-Joon Ahn
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Correspondence to Hyeong-Joon Ahn.

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Kim, KR., You, Yh. & Ahn, HJ. Optimal design of a QZS isolator using flexures for a wide range of payload. Int. J. Precis. Eng. Manuf. 14, 911–917 (2013). https://doi.org/10.1007/s12541-013-0120-0

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