Research of Influence of Vibration Impact of the Basis in the Micromechanical Gyroscope

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Research o Inluence o Vibration Impact o the Basis in the Micromechanical Gyroscope GALINA VAVILOVA OLGA GALTSEVA INNA PLOTNIKOVA Institute o Non-Destructive Testing National Research Tomsk

1 Research o Inluence o Vibration Impact o the Basis in the Micromechanical Gyroscope GALINA VAVILOVA OLGA GALTSEVA INNA PLOTNIKOVA Institute o Non-Destructive Testing National Research Tomsk Polytechnic University 30 Lenin Av Tomsk RUSSIA rabota03tpu@mailru Abstract: - Analytical and experimental studies o the azimuthal module o two-component vibrational micromechanical gyroscope were conducted The algorithms o operation were proposed and the comparative analysis was carried out The inluence o mechanical disturbances on the movement o azimuthal module in the orm o translational and angular oscillations is shown; the errors o determining o the azimuth are deined Key-Words: - Micromechanical gyroscope Vibration Amplitude Freuency Errors Sensing element Introduction For developers there is a problem o decrease o dimensions o the modern systems o orientation (SO) and movement control o objects or various purposes and thereby o reduce o expenses at operation and prime cost One o the promising directions in the development o SO is application o micromechanical gyroscopes (MMG); they are made rom the modern engineering materials according to the new technologies in the micromechanics [-] These devices ully conorm to the reuired criteria although the MMG are inerior to other types o gyroscopes or precision [3-] With due regard or the high rate o improvement o accuracy parameters o MMG the authors consider the dynamic characteristics o twocomponent micromechanical gyroscope and automatic setting o system parameters o MMG which provide the best characteristics o SO based on these gyroscopes [5] SO are used or determining o position o moving objects and devices relatively o given basic directions (the directions o the midday line and local vertical at orientation in near-earth space) Experimental Researched system has two measurement channels: the azimuth channel (or measuring o azimuth o the object α) and the horizontal channel (or measuring o angles o deviation o the object rom the plane o the horizon γ δ) The sensing element (SE) o the azimuth channel is a two-component oscillatory vibratory micromechanical gyroscope [6]; its scheme is shown in Fig Fig: Scheme o two-component micromechanical gyroscope The micromechanical gyroscope o the azimuthal module contains an inertial body in the corps 7; it is ixed by means o two-axis elastic subweight and 3 Electrostatic vibrational drive 6 excites the harmonic oscillations o the gyroscope z( t) z0 sin ωt along the z-axis which is perpendicular to the plane o its sensing element Coriolis orces arise as a result o Earth's rotation and translational oscillations o the gyroscope at ISBN:

2 speed z ( t ) ; these orces are changed according to harmonic law with reuency o vibration exciter ω It leads to the appearance o translational oscillations x(t) y(t) o inertial mass along the axes OX and OY The amplitudes o these oscillations x a y a are measured by displacement sensors 5 and are ed to the computing device or calculating the azimuth α latitude φ and signal conditioning o resonant setting o system U RS The amplitude o the output signal decreases as a result o last increase o stiness The system o locked loop o reuency decides to return on a step backwards on basis o this inormation and to stop work The system o locked loop o reuency is implemented by a microcontroller 3 Results and Discussion Mechanical disturbances o the orm o translational and angular oscillations are on the object at the place o installation o SO; these disturbances will distort the inormation movement o the azimuthal module and cause to errors o deinition o azimuth The euations or calculation o the movement SE on the basis at the orward vibration have an appearance: m x µ x k x H y F cos t sin t () m y µ y k y Hx F cos t sin t ; where m m - inertial mass o the body and internal rame; x y moving o the inertial mass along the axes X Y; µ µ - coeicients o orces o viscous riction; Ω х Ω y - projections o the speed o Earth's rotation on the axis which are associated with the gyroscope; k c mg( z) ; mω H c ; k c mg( z) ; m Ω Н c ; mb ; ma ; ; H mωv ; F m z 0 ω H ; Ω H Ω E сosϕ ; Ω V Ω E sinϕ ; Ω E - speed o daily rotation o the Earth; c c - angular stiness o elastic connections; a b - amplitude and reuency o translational vibration o the basis At the condition o resonant setting and lack o vibration the algorithm o determining o the azimuth in the semi-analytical SO has orm [] ( xaµ ya H) α kπ arctg d ( x H y µ ) a a m where d H mω E sinϕ m р m Micromechanical gyroscope is a vibrating system with orces o viscous riction and two partial reuencies: ( m mp )K mk ω ( m mp )m m mp )K mk] ( m mp )m( KK F ) ( m m )m where K k ( m m p ) Ω y ; K k mω x ; F mω x Ω y These reuencies depend on the speed Ω х Ω y However this eect can be neglected at the excitation o oscillations o inertial mass at high reuencies; the natural reuencies are determined by the expression ( m m p ) κ mκ ω ( m m p )m () m m p ) κ mκ ] 6( m m p )mκ κ ( m m )m At excitation o oscillations o the inertial body on one o the partial reuencies o the system the amplitude o one coordinate reaches the maximum values and the amplitude o the other coordinate is by two times less (Fig) Given the acute nature o the resonance due to the high uality actor o silicon MMG it is necessary a precise resonant setting The system o auto-adjust o reuency is entered or this purpose; this system can be realized with regulating o stiness o subweight by means o the vibrodrive Stiness o the system changes at the voltage on the electrodes o the drive; and thereore the natural reuency o the gyroscope changes too The algorithm o the system o locked loop o reuency is designed in such a way that the initial value o the stiness k 0 is set on the irst step The value o this stiness should be such that the system worked obviously not in resonance [7] Ater then the current value o the stiness k begins to strive or resonant value k r and it increases on size k at each step The change o amplitude o the output signal o the gyroscope is also controlled in each step I the amplitude did not increase at some step as at resonance but it decreased it means that the resonance is passed and it is necessary take a step back p p ISBN:

3 Fig: Amplitude-reuency characteristics o MMG The work o system o locked loop o reuency is simulated using sotware Simulink MATLAB; the results are presented in Fig 3 The irst two graphs show the amplitudes o output signals o the gyroscope along the axes OX and OY The third graph represents the dependence o the output signal o Microcontroller block which implements the algorithm o work o system o the auto setting rom time On these graphs show system o the auto setting o the reuency gradually increases stiness bringing the system to resonance Fig3 The output signals o MMG at auto-adjust o its own reuencies The solution o the system o euations () we deined by the orm o the right parts (in the case o the translational vibration o the basis): x( t ) A B sinωt A cos t B sin t y( t ) M cosω t N sinωt () M cos t N sin t I the reuency o vibration o the basis does not coincide with working reuency o SE ω the amplitudes o the useul inormative oscillations o SE A B M N at the resonant setting are determined by the expressions ( mµ mh ) x a ω( H µ ) ( mµ mh ) y a ω( H µ ) where z 0 ωω E cosϕ Then the amplitudes o vibrations o inertial mass (taking into account the translational vibration o the basis) are o the orm B m k )( m k ) H ( m k )] µ Hµ H M A H ( [ µ ( m k )] m k ) ( H µ ) ] m k ) ( m k )] [ ( m k )( m k ) ( H µ )] [ ( m k ) ( m k )] [ H ( m k ) µ ( m k )] Hµ µ ( sin α µ m k ) ( m k )] [ m k ) ( H µ )] [ m k )( m k ) ( H µ )] sin α[ ( m k )( m k ) ] [ H ( m k ) µ ( m k )] m k) ( H µ )] Hµ ISBN:

4 H N m k ) ( m k )] [ ( m k )( m k) ( H µ )] m k ) ( m k )] H µ [ H ( m k ) µ ( m k )] H H µ µ H sin H m k ) ( m k )] α[ ( H µ ) ] m k ) ( m k )] m k ) ( H µ )] ( m µ k ) ( m )( m m k ) ( m k ) ] ( m ( H µ ) From these expressions and results o computer simulation (Fig ) it turns out that the oscillations with reuency o translational vibration are superimposed on the useul inormative oscillations x(t) y(t) with reuency at the presence o translational vibration o the basis These oscillations distort the inormative movement o SE and cause the calculation errors o the azimuth α Oscillations o the SE occur at the reuency o basis vibration ; these oscillations are due to the translational vibration Inormative oscillations occur at the operating reuency o vibrational excitation o SE ω I reuency o vibration o basis does not coincide with the operating reuency o the SE ω the band ilters are used or eduction o the useul signals Then all signals caused by vibration o the basis will be iltered out Thereore the azimuth o object is calculated by useul inormation signals These signals x * (t) and y * (t) remain at the exit o band ilters (Fig) It should be noted that the errors o calculation o the azimuth will remain the same as on ixed basis The presence o angular vibration o basis the movement o SE o azimuthal module is characterized by the euations k k ) k ) m x µ x k x ( H H sin χt) y F sin χt F F sin( χ ω) t sin( χ ω) t my µ y k y ( H H sin χt )x F sin χt F F sin( χ ω )t sin( χ ω )t where H mω H ( δ 0 γ 0 ) F mωv z0ωδ 0 F mωv z0ωγ 0 mgγ 0 mgδ 0 γ 0 δ 0 χ are the amplitudes and reuency o angular oscillations o object From the euations it is seen that at rotational vibration o basis on SE are useul orces F F with reuencyω ; the other orces are obstructions and distort the useul inormation o SE Fig : Characteristics o the SE at the translational vibration o the basis In addition SE is a system with periodically varying coeicients H sin χt y H sin χt x Parametric oscillations can occur in such systems at certain relations between natural reuency ω and the vibration reuency χ It can be avoided by appropriate choice o the coeicient o viscous ISBN:

5 riction orces µ ; it is carried out in the considered SE Thereore periodic members H sin χt y H sin χt x aren't considered by consideration o inluence o angular vibration o the basis on SE Moments-disturbances will cause oscillations o SE along the axes X and Y with vibration reuency χ and reuencies ( χ ω) ( χ ω) These oscillations distort the useul inormational oscillations o SE occurring at the operating reuency ω o SE The presence o band ilters in the channels o conversion o the output signals o SE also eliminates the inluence o the angular vibration o the basis on the accuracy o the calculation o azimuth [6] Lysova OM Zhaldybin LD Nesterenko TG Plotnikova IV RF Patent Byull Izobret No 009 [7] Lysova OM Nesterenko TG Plotnikov IA Plotnikova IV Control system o parameters o the azimuthal module Instruments and Systems: Monitoring Control and Diagnostics No6 00 pp Conclusion The inormation movement o SE is carried out with reuency o vibrational excitation o inertial weight All intererences at the mechanical indignations are iltered out at placing o band ilters at the exit o angular sensors or measuring o amplitudes o oscillations o SE Thus the accuracy o calculation o an azimuth remains same as well as at the absence o vibration Reerences: [] Apostolyuk V Theory and design o micromechariical vibratory gyroscopes - MEMS/NEMS Handbook Springer Vol 006 pp73-95 [] Doronin VP Kuznetsova MS Lebedeva VI Soloviev AV Tarasov AN Micromechanical vibratory gyroscope: Development production and test results ICINS pp Code 8 [3] Zhaldybin LD Lysova OM Nesterenko TG Plotnikova IV Plotnikov IA Micromechanical Gyroscope Finite-Element analysis IEEE Aerospace And Electronic Systems Magazine Vol3 No9 008 pp 8-3 [] Evstieev MI The main stages o development o domestic micromechanical gyroscopes Izvestiya vysshikh uchebnykh zavedeniy Priborostroenie Vol5 No6 0 pp [5] Park S Horowitz R Tan C-W Dynamics and control o a MEMS angle measuring gyroscope Sensors and Actuators: A Physical Vol No 008 pp ISBN:

Control of Vibrations in a Micromechanical Gyroscope Using Inertia Properties of Standing Elastic Waves

Preprints of the 9th World Congress The International Federation of Automatic Control Cape Town, South Africa August 4-9, 04 Control of Vibrations in a Micromechanical Gyroscope Using Inertia Properties