Resonant sensors and vibrating Gyroscopes

Resonant sensors and vibrating Gyroscopes - Chap 9....

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1 Chap 9. Resonant sensors and vibratory gyroscopes Content: - Resonant pressure transducers - Poly-silicon beam resonant pressure sensor - H-beam resonant pressure sensor - Resonant accelerometers - Vibratory gyroscopes Hans.j.alker@hive.no
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2 Resonant pressure transducers Objectives for applying resonant beam-designs 2 design outlines are selected: 1. Single resonant beam 2. H-beam • In search of higher accuracy, we need: – => higher resolution – => higher stability • Resonant pressure sensors and accelerometers may improve on this, but have had limited commercial success – Rely on variable stress to change resonance frequency – high cost? – high complexity? (in the electrical circuitry) • Vibratory gyroscopes is a success
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3 Resonant pressure transducers Poly-silicon beam resonant pressure sensor Structural design: - Sensing element is a double-supported poly- silicon beam 2μm thick, over a sealed vacuum cavity - The beam is exited by an electrostatic force by a driving electrode and vibration is detected by a piezoresistor - The cavity is sealed by a top-side shell 2 22 The free-vifration frequency may be found by the differential eqation method Chapter §2.4. For a double-clamed beam (Eq.2.113/2.128) the vibration frequency is givebn by: 1.03 1 0.2949 where r tE l f lt ε ρ = + 2 0 00 2 0 2 and are beam thickness and length The strain consists of residual and displacement strain components , ( ) 1 0.2949( ) where 1.03 is the fundamental mode of vibration. As pr p tl l fp f t f l εεε εε = += ++ 2 2 3 2 p ssuming a circular diaphragm with radius and thickness : Diaphragm displacement (Eq. 2.168): 3 ( ) (1 )( ) 16 Pressure induced strain: () 1 ah p wr a r Eh z r r ν = −− = − −∂ 2 2 2 1 The beam is on top of the diaphragm ( ): 2 3 ( ) 1 3( ) 8 Usually two beam structures are used on the diaphragm; one at the edge and one at the center. The strain on the two beams have o p zh pa r r Eh a = −  =   2 2 2 2 0 1 pposite signs, causing vibration frequencies in opposite directions. The avarage stain for the center beam: 23 1 ( ) 82 The avarage stain for the edge beam: 1 l pc p a pe p a pa l r dr l Eh a r dr l = = = 2 2 2 3 13 () () 8 From here we can find the diffential frequency change caused by an applied pressure. pa l l Eh a a = −+
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4 Poly-silicon beam resonant pressure sensor Numerical example
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5 H-beam resonant pressure sensor (Yokogawa) Schematic design Pair of H-shaped beam resonators Beams located in corner and central region of the diaphragm Beams are made of bulk silicon material and sealed in vacuum cavities with poly-silicon shells Attained Q-factor in the order of 50.000 The diaphragm is square The H-shaped beams are excited into resonance by electro- magnetic scheme
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6 H-beam resonant pressure sensor Numerical example 22 3 2 24 3 Assuming square diaphragm of length 2 and thickness of , displacement is: ( , ) (1 ) (1 ) 47 where is the fixture regidity.
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Resonant sensors and vibrating Gyroscopes - Chap 9....

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