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Design and dynamics of an innovative micro gyroscope against coupling effects

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Abstract

This paper presents an innovative micro gyroscope design. The proposed tri-axis gyroscope possesses the capability of detecting three-dimensional angular motions. The motion of each sensing element is, by elaborate mechanical design, restricted to move in orthogonal direction to each other such that the measurements by high-resolution capacitors with signal processing circuits are decoupled and precisely represent, to some extent, angular velocity components in three axes. The drive electrode comb is used to constantly vibrate the proof mass in tangential direction by sinusoidal voltage. The signal bandwidth is increased by distributed translational proof masses, placed ninety degree apart from each other. Each individual proof mass is designed to move solely in radial direction so that superior mode matching can be achieved. In order to ensure better repeatability and more reliability, the suspension flexures and damping effects are studied such that stress of the proposed micro gyroscope is reduced but the span of angular displacements is increased. Owing to the complicated geometry of the suspension flexures, finite element method (FEM) is employed to obtain more exact stiffness values and compared with theoretical analysis. The dynamic model of the proposed gyroscope is established to include non-linear terms and embedded mechanical constraints. The entire micro device can be produced merely by surface fabrication such that the mass production cost can be considered at the design stage, while the resolution, bandwidth and decoupling capability of tri-axis detection are enhanced.

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Abbreviations

〈X, Y, Z〉:

inertia frame

〈A, B, C〉:

chip frame (attached to the substrate)

〈U, V, W〉:

ring frame (attached to the outer-ring)

\({\underline{\omega}}\) :

angular velocity about Z-axis

θ x :

angular displacement about X-direction

\({\underline{\alpha}}\) :

angular acceleration about Z-axis

\({\underline{\Omega}}_{o}\) :

angular velocity of outer-ring

ϕ A :

tilt angle between outer-ring and substrate

β d :

the resulted angle of outer-ring w.r.t. the substrate, driven by comb-drive electrodes

φ V :

the tilt angle of inner-disk w.r.t. outer-ring

\({\underline{r}}_{p}\) :

displacement vector of translation proof mass

k ϕ :

torsional stiffness of outer-ring spring about A-axis

k β :

torsional stiffness of outer-ring angular displacement about W-axis

k φ :

torsional stiffness of inner-disk spring about V-axis

k rA , k rB :

translational stiffness for proof mass about A-axis and B-axis, respectively

C ϕ :

damping coefficient of outer-ring spring about A-axis

C β :

damping coefficient of outer-ring spring about W-axis

C φ :

damping coefficient of inner-disk spring about V-axis

C rA , C rB :

damping coefficients of proof mass about A-axis and B-axis respectively

M d :

moment induced by comb-drive electrode

F d :

electrostatic force generated by comb-drive electrode

Γ:

angle between normal direction of the adjoin radial rib and the spring connecting proof mass and ribs

J o :

polar moment of inertia of outer-ring

J i :

polar moment of inertia of inner-disk

M eq :

equivalent mass of translation proof mass

X :

state vector

A :

system matrix

B :

input matrix

u :

input vector

Δ:

bias vector representing the nonlinear terms in the state space representation

E :

disturbance input matrix

ξ:

disturbance vector

y :

output vector

C :

output matrix

ν:

sensor noise vector

ℓ:

the distance from geometric center of the inner ring to the position that departs outwards 3/4 length of the radial rib

\({\hat{G}}\) :

shear modulus of torsional spring S2

\({\hat{w}}\) :

width of torsional spring S2

\({\hat{t}}\) :

thickness of the entire suspended gyro structure

\({\hat{h}}\) :

length of torsional spring S2

\({\hat{h}}\) :

elevation of the proof mass from the substrate

R o :

outer radius of outer-ring

R i :

inner radius of outer-ring

r i :

radius of inner-disk

g comb :

gap between the comb fingers

μ p :

viscosity of air

p :

atmosphere pressure

A comb :

the overlapped area of the comb finger pairs that move towards to each other and separates apart alternatively

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Acknowledgments

The authors would like to thank the Center for Micro/Nano Technology Research, National Cheng Kung University, Tainan, Taiwan, and National Nano Devices Laboratory (NDL) for equipment access and technical support. This research was partially supported by National Science Council (Taiwan) with Grant NSC96-2221-E-005-255.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Nan-Chyuan Tsai, Chung-Yang Sue & Chih-Che Lin

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  1. Nan-Chyuan Tsai
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  2. Chung-Yang Sue
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  3. Chih-Che Lin
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Correspondence to Nan-Chyuan Tsai.

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Tsai, NC., Sue, CY. & Lin, CC. Design and dynamics of an innovative micro gyroscope against coupling effects. Microsyst Technol 14, 295–306 (2008). https://doi.org/10.1007/s00542-007-0517-8

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