CN109490574A - A kind of Nonlinear Vibration method of resonant silicon micro-acceleration gauge - Google Patents
A kind of Nonlinear Vibration method of resonant silicon micro-acceleration gauge Download PDFInfo
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- CN109490574A CN109490574A CN201811440726.1A CN201811440726A CN109490574A CN 109490574 A CN109490574 A CN 109490574A CN 201811440726 A CN201811440726 A CN 201811440726A CN 109490574 A CN109490574 A CN 109490574A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
- G01P15/00—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration
- G01P15/02—Measuring acceleration; Measuring deceleration; Measuring shock, i.e. sudden change of acceleration by making use of inertia forces using solid seismic masses
Abstract
The invention discloses a kind of nonlinear analysis methods of resonant silicon micro-acceleration gauge, comprising: (1) establishes the model of nonlinear of resonant silicon micro-acceleration gauge；(2) the Non-Linear Vibration influence factor and rule of resonant silicon micro-acceleration gauge are analyzed；(3) the Non-Linear Vibration compensation method of resonant silicon micro-acceleration gauge is designed.The model of nonlinear of resonant silicon micro-acceleration gauge is the model of vibration using sensitive structure vibration characteristics as tie, containing axial tension, axial compressive force and residual internal force.The Non-Linear Vibration influence factor and law-analysing of resonant silicon micro-acceleration gauge are to study Non-Linear Vibration influence factor and rule according to bending coefficient, the bending degree of quantitative analysis resonance sensitive structure Non-Linear Vibration frequency response curve.The Non-Linear Vibration compensation method of resonant silicon micro-acceleration gauge is the accelerometer measures error according to caused by sensitive structure Non-Linear Vibration, establishes rate-adaptive pacemaker model caused by Non-Linear Vibration, designs differential error compensation scheme, proposes measurement Error Compensation method.
Description
Technical field
The invention belongs to field of inertia technology, are related to a kind of resonant silicon micro-acceleration gauge, in particular to a kind of directly frequency
The Nonlinear Vibration method of rate export resonance formula accelerometer, be suitable in the inexpensive navigation system of low precision and fixed
Position, orientation system etc..
Background technique
Based on resonant mode measuring principle, the resonant mode for working in the direct output frequency amount (quasi- digital quantity) of closed loop states adds
Velocity sensor (without A/D, is not necessarily to V/F), and output depends primarily on micromechanical resonance sensitive structure (two resonance beam groups
At) itself mechanical resonant state, hardly influenced by circuit parameter variations.Therefore, this type sensor performance stabilization can
It leans on, precision height, is easily matched with computer, be the mainstream of current silicon micro accerometer development and the emphasis of research.At this stage, with
The fast development of information technology, microelectric technique and new material technology, resonant silicon micro-acceleration gauge is by its miniaturization, low function
Consumption, the advantage of low cost are widely used in high-tech sectors such as Aeronautics and Astronautics, navigation, national defence, industry.With tradition
The macroscopic devices of mechanical processing technique are compared, and resonant silicon micro-acceleration gauge sensitive structure size is small, enhancing weak vibration letter
Number when sensitive structure amplitude increase.Large amplitude makes sensitive structure enter Non-Linear Vibration state, causes resonance beam intrinsic frequency inclined
It moves, so as to cause measurement error, or even can not work normally sensor.Therefore, the non-of resonant silicon micro-acceleration gauge is studied
Linear oscillator characteristic, which has become, guarantees resonant silicon micro-acceleration gauge high-precision, high reliability, the important prerequisite of long-life.
For the Study on Nonlinear Vibration of resonant silicon micro-acceleration gauge, firstly, accurate resonant silicon micro-acceleration gauge
The model of nonlinear of sensitive structure is most important to its individual features of Accurate Prediction.For the resonant mode of most of minute yardsticks
Accelerometer sensitive structure, classical Newtonian mechanics stand good, however are the micro- sensitivity of nanoscale silicon for some characteristic sizes
Mechanism then needs its dynamic response of quantum electronics description.Secondly, many silicon micro-sensitive structures need to work in closed loop states, to silicon
The modeling of micro-sensitive structure needs to consider influencing each other for sensitive structure and closed loop circuit.In addition, resonant silicon micro-acceleration gauge
Different nonlinear dynamic response characteristics is generated with working environment and working condition variation, measuring system is difficult to accurately lock resonance
The eigentone of beam, causes sensor measurement errors, and even resulting in sensor can not work, so the micro- acceleration of resonant silicon
The influence factor and regular problem of degree meter sensitive structure Non-Linear Vibration become very prominent.Finally, resonant silicon micro-acceleration
Meter sensitive structure usually has very high mechanical quality factor, and resonance frequency is approximately equal to intrinsic vibration under linear vibrational state
Frequency, locking resonance frequency approximation lock eigentone.But when being in Non-Linear Vibration state, the amplitude-frequency of sensitive structure is special
Property bends, and resonance frequency substantial deviation eigentone will cause biggish measurement error to sensor.So humorous
The compensation method research of vibration formula silicon micro accerometer sensitive structure Non-Linear Vibration error is very important.
For the present invention using frequency type silicon micro-sensor as research object, the Non-Linear Vibration for sensitive structure causes system to be surveyed
The problem of accuracy of measurement reduces is carried out the nonlinear vibration characteristics research of sensitive structure in a deep going way, is examined in the case of breakthrough Non-Linear Vibration
Consider sensor Technology Precision, solve the contradiction between transducer sensitive structure Non-Linear Vibration and measuring accuracy, is promoted
Measuring accuracy physics realization ability under sensitive structure large amplitude demand, for grinding for China's frequency type sensor Technology Precision
Study carefully and valuable Research foundation and Research Thinking are provided.
Summary of the invention
The technical problem to be solved in the present invention are as follows: resonant silicon micro-acceleration gauge sensitive structure is in a certain degree at this stage
Non-Linear Vibration state, cause sensor measurement errors, or even can not work normally sensor；Resonant silicon micro-acceleration
The vibration nonlinearity of meter sensitive structure makes its frequency response characteristic bend, and detection circuit is made to be difficult to accurately lock inherently
Vibration frequency causes sensor measurement errors.Establish the model of nonlinear of resonant silicon micro-acceleration gauge sensitive structure；It grinds
Study carefully the influence factor and rule of sensitive structure Non-Linear Vibration；Carry out estimation and the compensation side of sensitive structure Non-Linear Vibration error
Method research.Expected result will provide more efficient research approach and thinking for high precision silicon microsensor of new generation, and be generalized to
Other type sensors based on silicon microtechnology meet the needs of sensing technology high-precision detection of new generation.
The present invention solves the technical solution that above-mentioned technical problem uses are as follows: a kind of resonant silicon micro-acceleration gauge it is non-linear
Vibration analysis method, the specific steps are as follows:
The first step establishes the model of nonlinear of resonant silicon micro-acceleration gauge；Analyze resonant silicon micro-acceleration gauge
The kinetic model and Non-Linear Vibration condition of sensitive structure, establish the model of nonlinear of sensitive structure；
Second step analyzes the Non-Linear Vibration influence factor and rule of resonant silicon micro-acceleration gauge；Bending coefficient is introduced,
The bending degree of quantitative analysis resonance sensitive structure Non-Linear Vibration frequency response curve, study Non-Linear Vibration influence factor and
Rule；
Third step designs the Non-Linear Vibration compensation method of resonant silicon micro-acceleration gauge.It is non-linear to analyze sensitive structure
Sensor measurement errors caused by vibrating, establish rate-adaptive pacemaker model caused by Non-Linear Vibration, design differential error compensation knot
Structure proposes measurement Error Compensation method.
Further, the specific implementation process of the step 1:
Resonant silicon micro-acceleration gauge sensitive structure model of nonlinear including two resonance beams is described as one and contains
There is the second order differential equation of axial tension, axial compressive force and residual internal force:
Wherein, ρ, A respectively indicate the density and cross-sectional area of resonance beam, and w indicates that resonance beam transverse vibrational displacement, M indicate
Moment of flexure caused by resonance beam deformed, c indicate viscous damping coefficient, NnDue to by two fixing ends when expression resonance beam vibration
Constraint, NtIndicate resonance beam axial compressive force caused by exciting resistance static state thermal power, NpIndicate the resonance beam axis caused by measuring pressure
To pulling force, NrIndicate resonance beam axial direction residual internal force.
Further, the specific implementation process in the step 2:
(1) skeleton curve of resonance beam non-linear frequency response are as follows:
Wherein, ω indicates the driving frequency of resonance beam, ω1Indicate the single order eigentone of resonance beam,Indicate bending
Coefficient, a indicate resonance beam amplitude.
(2) skeleton curve expression formula is converted, is rewritten are as follows: f=f1+αI2；
Then bending coefficient are as follows:
Wherein,I indicates to flow through the current amplitude of pick-up resistance, size and resonance beam amplitude
It is directly proportional, SeIndicate that resonance beam amplitude is converted to the conversion coefficient of pick-up resistor current amplitude.Bending coefficient table after analysis is rewritten
The physical parameter of Da Shili is it is found that bending coefficient and the static stimulation power of the non-linear frequency response of resonance beam and be measured related.
(3) it is directed to the influence factor static stimulation power of bending coefficient, analyzes static stimulation changed power to bending coefficient
Affecting laws, and then analyze static stimulation changed power to the affecting laws of resonance beam Non-Linear Vibration.For bending coefficient
Influence factor be measured, analyze and be measured variation to the affecting laws of bending coefficient, and then analyze and be measured variation to resonance
The affecting laws of beam Non-Linear Vibration.
Further, the specific implementation process of the step 3:
(1) a kind of sensitive structure Non-Linear Vibration error differential compensation structure is designed.The collocation structure is mainly humorous by two
Vibration beam and periphery fixed structure composition, wherein a resonance beam is in the case where being measured effect, deformation occurs, resonance beam intrinsic frequency hair
Raw to change, this resonance beam is referred to as work beam.An other resonance beam is located at periphery fixed area, is measured because being isolated to resonance beam
It influences, therefore resonance beam is unrelated with being measured, the intrinsic frequency offset of the non-linear generation of resonance beam compensation work beam vibration claims this
Resonance beam is compensation beam；
(2) it since the material of two resonance beams, size and parameter are all identical, is in non-when resonance beam amplitude is excessive
When linear oscillator state, intrinsic frequency offset caused by work beam and compensation beam Non-Linear Vibration is also approximately uniform, by work
Rate-adaptive pacemaker of the difference of beam and compensation beam intrinsic frequency as sensor, establishes output error models；
(3) resonance beam intrinsic frequency knots modification caused by measured and dynamic excitation is analyzed, work beam and compensation beam can be obtained
Resonance frequency difference, can then obtain rate-adaptive pacemaker error caused by Non-Linear Vibration, for further analysis Non-Linear Vibration miss
The use scope of the influence factor of poor compensation effect and the differential compensation method is provided fundamental basis.
The principle of the invention lies in:
For the sensitive structure of resonant silicon micro-acceleration gauge, since support end is there are displacement constraint, when making its vibration not
Free Transform can be generated, causes to generate the internal stress directly proportional to vibration displacement, the presence of this internal stress inside sensitive structure
Eigentone is caused to change with the difference of sensitive structure vibration amplitude, to generate non-linear phenomena.For adopting
With the sensitive structure of silicon micromachining technique, since its structure size is small, Non-Linear Vibration phenomenon caused by large amplitude is more
It is significant.Sensitive structure is in Non-Linear Vibration state to a certain degree, causes sensor measurement errors, in addition make sensor without
Method works normally.The vibration nonlinearity of sensitive structure makes its frequency response characteristic bend simultaneously, keeps detection circuit difficult
Accurately to lock eigentone, sensor measurement errors are caused.The present invention is directed to capture sensitive structure nonlinear vibration dynamic model
The serial problems such as type solves, bending coefficient modeling, collocation structure design, the final precision for improving sensing detection technology and reliable
Property, theory and practice basis is provided for the research of the frequency type sensor detecting based on silicon microtechnology.
The advantages of the present invention over the prior art are that:
(1) incorporation engineering of the present invention is practical, using the vibration characteristics of sensitive structure as tie, completes to contain axial tension, axis
It is built to the sensitive structure model of nonlinear of pressure and residual internal force, does not need to establish complete sensitive structure vibration system
System has the characteristics that analysis is simple, effective.
(2) present invention proposes that the concept of bending coefficient, the power of quantitative description resonance beam Non-Linear Vibration are analyzed static sharp
It encourages power and is measured to Non-Linear Vibration affecting laws.
(3) measurement error caused by present invention analysis sensitive structure Non-Linear Vibration, directly design measurement Error Compensation knot
Structure studies sensitive structure Non-Linear Vibration error differential compensation principle and backoff algorithm.
Detailed description of the invention
Fig. 1 is that the Nonlinear Vibration method of resonant silicon micro-acceleration gauge of the invention realizes process schematic.
Specific embodiment
With reference to the accompanying drawing and specific embodiment further illustrates the present invention.
The Nonlinear Vibration method of resonant silicon micro-acceleration gauge of the present invention includes following three basic steps: (1)
Establish the model of nonlinear of resonant silicon micro-acceleration gauge；(2) Non-Linear Vibration of resonant silicon micro-acceleration gauge is analyzed
Influence factor and rule；(3) the Non-Linear Vibration compensation method of resonant silicon micro-acceleration gauge is designed.
As shown in Figure 1, the Nonlinear Vibration method of resonant silicon micro-acceleration gauge of the invention implements step
It is as follows:
(1) model of nonlinear of resonant silicon micro-acceleration gauge is established
The sensitive structure of resonant silicon micro-acceleration gauge can simplify as the clamped resonant beam structure of both-end, along resonance beam axial direction
Direction, which carries out force analysis, can obtain the model of sensitive structure Non-Linear Vibration.Sensitive structure Non-Linear Vibration need to consider four when modeling
A condition.
Condition one, due to the constraint by two fixing ends when resonance beam vibration, neutral surface Tensile and the axial tension that generates.
If ignoring resonance beam axial direction inertia, the axial tension on each cross section of resonance beam is identical, and when calculating carries out this axial force
Taylor expansion remains into second order term for convenience of calculation.
Condition two motivates resonance beam axial compressive force caused by resistance static state thermal power.
Condition three, resonance beam axial tension caused by being measured.
Condition four, resonance beam axial direction residual internal force.
(2) the Non-Linear Vibration influence factor and rule of resonant silicon micro-acceleration gauge are analyzed
(a) bending coefficient of resonance beam non-linear frequency response: in order to analyze the influence of sensitive structure Non-Linear Vibration because
Element analyzes the non-linear amplitude-frequency response of resonance beam, can obtain its skeleton curve as parabola, and the secondary term system of skeleton curve expression formula
Number is bending coefficient.This bending coefficient can be used for the bending direction and bending journey of quantitative description non-linear frequency response curve
Degree.
(b) influence factor of bending coefficient: for the affecting laws of more analyzing in detail bending coefficient, remap bending system
Several expression formulas.Analyze expression formula in physical parameter it is found that the non-linear frequency response of resonance beam bending coefficient and static stimulation function
Rate and be measured it is related.
(c) affecting laws of bending coefficient: for the influence factor static stimulation power of bending coefficient, static stimulation is analyzed
Changed power analyzes influence of the static stimulation changed power to resonance beam Non-Linear Vibration to the affecting laws of bending coefficient
Rule.It is measured for the influence factor of bending coefficient, analyzes and be measured variation to the affecting laws of bending coefficient, and then analyze
Variation is measured to the affecting laws of resonance beam Non-Linear Vibration.
(3) the Non-Linear Vibration compensation method of resonant silicon micro-acceleration gauge is designed
(a) a kind of sensitive structure Non-Linear Vibration error differential compensation structure is designed.The collocation structure is mainly humorous by two
Vibration beam and periphery fixed structure composition, wherein a resonance beam is in the case where being measured effect, deformation occurs, resonance beam intrinsic frequency hair
Raw to change, this resonance beam is referred to as work beam.An other resonance beam is located at periphery fixed area, is measured because being isolated to resonance beam
It influences, therefore resonance beam is unrelated with being measured, the intrinsic frequency offset of the non-linear generation of resonance beam compensation work beam vibration claims this
Resonance beam is compensation beam；
(b) it since the material of two resonance beams, size and parameter are all identical, is in non-when resonance beam amplitude is excessive
When linear oscillator state, intrinsic frequency offset caused by work beam and compensation beam Non-Linear Vibration is also approximately uniform, by work
Rate-adaptive pacemaker of the difference of beam and compensation beam intrinsic frequency as sensor, establishes output error models；
(c) resonance beam intrinsic frequency knots modification caused by measured and dynamic excitation is analyzed, work beam and compensation beam can be obtained
Resonance frequency difference, can then obtain rate-adaptive pacemaker error caused by Non-Linear Vibration, for further analysis Non-Linear Vibration miss
The use scope of the influence factor of poor compensation effect and the differential compensation method is provided fundamental basis.
Part of that present invention that are not described in detail belong to the well-known technology of those skilled in the art.
Above embodiments are provided just for the sake of the description purpose of the present invention, and are not intended to limit the scope of the invention.This
The range of invention is defined by the following claims.It does not depart from spirit and principles of the present invention and the various equivalent replacements made and repairs
Change, should all cover within the scope of the present invention.
Claims (4)
1. a kind of Nonlinear Vibration method of resonant silicon micro-acceleration gauge, it is characterised in that: the method comprising the steps of such as
Under:
The first step establishes the model of nonlinear of resonant silicon micro-acceleration gauge: analysis resonant silicon micro-acceleration gauge is sensitive
The kinetic model and Non-Linear Vibration condition of structure, establish the model of nonlinear of sensitive structure；
Second step analyzes the Non-Linear Vibration influence factor and rule of resonant silicon micro-acceleration gauge: bending coefficient is introduced, it is quantitative
The bending degree of resonance sensitive structure Non-Linear Vibration frequency response curve is analyzed, Non-Linear Vibration influence factor and rule are studied
Rule；
Third step designs the Non-Linear Vibration compensation method of resonant silicon micro-acceleration gauge: analysis sensitive structure Non-Linear Vibration
Caused sensor measurement errors establish rate-adaptive pacemaker model caused by Non-Linear Vibration, design differential error compensation scheme, mention
Measurement Error Compensation method out.
2. the Nonlinear Vibration method of resonant silicon micro-acceleration gauge according to claim 1, it is characterised in that: institute
State the specific implementation process of step 1:
The model of nonlinear of resonant silicon micro-acceleration gauge sensitive structure including two resonance beams is described as one and contains
The second order differential equation of axial tension, axial compressive force and residual internal force:
Wherein, ρ, A respectively indicate the density and cross-sectional area of resonance beam, and w indicates that resonance beam transverse vibrational displacement, M indicate resonance
Moment of flexure caused by beam deformed, c indicate viscous damping coefficient, NnDue to the pact by two fixing ends when expression resonance beam vibration
Beam, NtIndicate resonance beam axial compressive force caused by exciting resistance static state thermal power, NpIndicate that the resonance beam caused by measuring pressure is axial
Pulling force, NrIndicate resonance beam axial direction residual internal force.
3. the Nonlinear Vibration method of resonant silicon micro-acceleration gauge according to claim 1, it is characterised in that: described
Resonance type accelerometer Non-Linear Vibration influence factor and the specific implementation process of law analytical method in step 2:
(1) skeleton curve of resonance beam non-linear frequency response are as follows:
Wherein, ω indicates the driving frequency of resonance beam, ω1Indicate the single order eigentone of resonance beam,Indicate bending system
Number, a indicate resonance beam amplitude；
(2) skeleton curve expression formula is converted, is rewritten are as follows: f=f1+αI2；
Then bending coefficient are as follows:
Wherein,The current amplitude of pick-up resistance is flowed through in I expression, and size and resonance beam amplitude are at just
Than SeIndicate that resonance beam amplitude is converted to the conversion coefficient of pick-up resistor current amplitude；Bending coefficient expression formula after analysis is rewritten
In physical parameter it is found that bending coefficient and the static stimulation power of the non-linear frequency response of resonance beam and being measured related；
(3) the influence factor static stimulation power of bending coefficient, shadow of the analysis static stimulation changed power to bending coefficient are directed to
Rule is rung, and then analyzes static stimulation changed power to the affecting laws of resonance beam Non-Linear Vibration；For the shadow of bending coefficient
The factor of sound is measured, analyzes and is measured variation to the affecting laws of bending coefficient, and then it is non-to resonance beam to analyze measured variation
The affecting laws of linear oscillator.
4. the Nonlinear Vibration method of resonant silicon micro-acceleration gauge according to claim 1, it is characterised in that: institute
State the specific implementation process of step 3:
(1) a kind of sensitive structure Non-Linear Vibration error differential compensation structure is designed, the collocation structure is mainly by two resonance beams
With periphery fixed structure composition, wherein a resonance beam is in the case where being measured effect, deformation occurs, and resonance beam intrinsic frequency changes
Become, this resonance beam is referred to as work beam, and in addition a resonance beam is located at periphery fixed area, because the shadow being measured to resonance beam is isolated
It rings, therefore resonance beam is unrelated with being measured, the intrinsic frequency offset of the non-linear generation of resonance beam compensation work beam vibration claims this humorous
The beam that shakes is compensation beam；
(2) it since the material of two resonance beams, size and parameter are all identical, is in non-linear when resonance beam amplitude is excessive
When vibrational state, intrinsic frequency offset caused by work beam and compensation beam Non-Linear Vibration is also approximately uniform, by work beam and
Rate-adaptive pacemaker of the difference of beam intrinsic frequency as sensor is compensated, output error models are established；
(3) resonance beam intrinsic frequency knots modification caused by measured and dynamic excitation is analyzed, work beam can be obtained and compensates the humorous of beam
The difference of vibration frequency can then obtain rate-adaptive pacemaker error caused by Non-Linear Vibration, mend for further analysis Non-Linear Vibration error
The use scope of the influence factor and the differential compensation method of repaying effect is provided fundamental basis.
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Cited By (1)
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| CN112114164A (en) * | 2020-09-23 | 2020-12-22 | 中国矿业大学(北京) | Method for determining nonlinear vibration of silicon micro-resonance type accelerometer |
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