CN1673751A - Core kernel modeling method for micro inertial sensor device and core kernel base - Google Patents

Abstract

The micro inertial sensor kernel mold establishing method and kernel library belongs to the field of design technology of micro electromechanical system. Technologically, the present invention features that electromechanical micro structure behavior mold is first established by means of combined mechanical behavior mold establishing method and force coupling behavior mold establishing method and reusable kernel for micro inertial sensor is then formed according to kernel mold establishing method. The present invention also includes kernel library established based on the said method, the establishment of parameter kernel molds for typical functional structural parts of MEMS inertial devices in 3D space, and kernel library as the integration of kernel molds. The present invention has universal theoretical significance and may provide technological support for research and development of micro gyro, micro accelerometer, etc.

Description

The core modeling method and the core kernel of mini inertial sensor spare

Affiliated technical field:

The present invention relates to a kind of core modeling method and core kernel thereof of mini inertial sensor spare, belong to the design field of MEMS (micro electro mechanical system).It is computer-aided design (CAD) at inertia MEMS (micro electro mechanical system) and typical electrostatic microactrator and electrostatic detection microsensor.

Background technology:

Based on the inertia sensing device of MEMS technology, be the important kind of MEMS device research as micro-acceleration gauge, little gyro and Micro Inertial Measurement Unit etc.Based on the micro-inertia sensor spare of MEMS technology is to melt circuit and micro mechanical structure is the system of one, is the emphasis and the difficult point of its computer-aided design (CAD) to the modeling and simulation analysis of its global behavior (system-level behavior).Based on reusable core (Intellectual Property, IP) modeling method is to realize the effective ways of MEMS device system level modeling, this method is divided into a plurality of functional structure parts to MEMS, selects the core model corresponding with the functional structure parts for use and passes through to set core parameter and the system-level model of the network that connects core corresponding end interruption-forming as whole micro-system.This method needs the support of the reusable core model of the parametrization of functional structure parts.

Thus, the reusable core model of setting up micro-inertia sensor spare becomes international important research content at the modeling of MEMS inertia device.The NODAS of U.S. Carnegie Mellon university adopts mixed signal hardware descriptive language MAST to set up the reusable core of the typical MEMS functional structure parts (as beam, mass etc.) of doing plane motion, and these core models are confined to set up the system-level model of making the plane motion inertial MEMS.Similarly, U.S. UC Berkeley has set up the reusable core of supporting the system-level modeling of inertial MEMS on the MATLAB platform, but because it adopts the MATLAB Programming with Pascal Language, it is integrated to realize mixed signal simulation that model is not easy to circuit model.

At present, still there is not a pertinent literature report about being modeled in of the reusable core of micro-inertia sensor spare is domestic.

Summary of the invention:

For avoiding the defective of prior art, the present invention proposes a kind of core modeling method and core kernel thereof of mini inertial sensor spare, study the conventional method of the reusable core model of the functional structure parts of setting up MEMS inertia sensing device, based on this, in three dimensions, set up reusable core model bank, for the tool of the system-level modeling method of MEMS inertia sensing device lays the foundation at typical MEMS inertia sensing device.

The conduct of MEMS inertia sensing device is based on the important kind of the senser element of MEMS technology, proposition of the present invention has general theory directive significance to the core model of the functional structure parts of setting up the MEMS inertia device, for the tool of the system-level modeling method of MEMS inertia sensing device lays the foundation.Little gyro, micro-acceleration gauge that the reusable core kernel of MEMS inertia sensing device falls behind for innovation China, micromechanical gyro that research and development are advanced and accelerometer etc. provide support, also for shorten China and in the world the gap between the MEMS technology of system level design method and technical support are provided.

Technical characterictic of the present invention is:

MEMS inertia sensing device relates generally to two energy territories: machinery and electricity.According to machinery and two energy territories of electricity,, form the reusable core of micro-inertia sensor spare again according to core model definition method with the microstructure behavior model of mechanical behavior modeling method and power electric coupling behavior modeling method foundation machinery and electricity.

Described mechanical behavior modeling method is: according to the inertia micro-system is non-inertia motion by the relative motion principle measured chip of the functional structure parts in the chip, for the ease of obtaining the behavior model of functional structure parts in chip, the behavior of examination parts in different coordinate systems is to set up inertia MEMS functional structure parts behavior model.Set up the behavior model in the local coordinate system earlier, then with the behavior model be converted to behavior model in the global coordinate.

Behavior model in the described local coordinate system is:

The selection principle of local coordinate system is to be convenient to adopt analytical method to set up the behavior equation of functional structure parts.Functional structure parts discretize, the point of discretize is called end points, selects suitable end points to describe the behavior of microstructure according to the convenience of using.Be located at and selected n end points to describe the behavior of microstructure on the microstructure, then acting force on each end points and displacement can be expressed as respectively in three dimensions: F _i'=[F _Xi' F _Yi' F _Zi' M _Xi' M _Yi' M _Zi'] ^T(i=1 ... n)

r _i′＝[x _i′y _i′z _i′α _i′β _i′γ _i′] ^T(i＝1，…，n)

In the formula: F _i' r _i' represent the displacement and the acting force of i end points respectively.Then the functional structure parts can be expressed as at the behavior model of local coordinate system:

$\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">F</figure-callout>}}_1^{\&prime;}={\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">f</figure-callout>}}_1^{\&prime;}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">r</figure-callout>}}_1^{\&prime;},{\stackrel{\&CenterDot;}{r}}_1^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_i^{\&prime;},{\stackrel{\&CenterDot;}{r}}_i^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_n^{\&prime;},{\stackrel{\&CenterDot;}{r}}_n^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n^{\&prime;})\\ F_2^{\&prime;}=f_2^{\&prime;}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">r</figure-callout>}}_1^{\&prime;},{\stackrel{\&CenterDot;}{r}}_1^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_i^{\&prime;},{\stackrel{\&CenterDot;}{r}}_i^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_n^{\&prime;},{\stackrel{\&CenterDot;}{r}}_n^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n^{\&prime;})\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ F_n^{\&prime;}=f_n^{\&prime;}({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">r</figure-callout>}}_1^{\&prime;},{\stackrel{\&CenterDot;}{r}}_1^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_i^{\&prime;},{\stackrel{\&CenterDot;}{r}}_i^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_n^{\&prime;},{\stackrel{\&CenterDot;}{r}}_n^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n^{\&prime;})\end{array}.$

Behavior model in the described global coordinate is:

Because the functional structure parts have different initial orientation angles in chip, in order to reflect the initial orientation of parts in chip, need change its behavior model to global coordinate (global coordinate is fixed on the MEMS chip).If T is the direction cosine matrix between global coordinate and local coordinate system, then the behavior model of functional structure parts in global coordinate is:

$\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">F</figure-callout>}}_1=f_1({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">r</figure-callout>}}_1,{\stackrel{\&CenterDot;}{r}}_1,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,r_i,{\stackrel{\&CenterDot;}{r}}_i,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,r_n,{\stackrel{\&CenterDot;}{r}}_n,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n)\\ F_2=f_2({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">r</figure-callout>}}_1,{\stackrel{\&CenterDot;}{r}}_1,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,r_i,{\stackrel{\&CenterDot;}{r}}_i,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,r_n,{\stackrel{\&CenterDot;}{r}}_n,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n)\\ \&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;\\ F_n=f_n({\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="A20041002598500123.png"\; state="\{\{state\}\}">r</figure-callout>}}_1,{\stackrel{\&CenterDot;}{r}}_1,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,r_i,{\stackrel{\&CenterDot;}{r}}_i,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,r_n,{\stackrel{\&CenterDot;}{r}}_n,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n)\end{array}.$

In the formula: F _iAnd r _iBe respectively functional structure parts load vector sum motion vector in global coordinate, can be expressed as respectively:

F _i＝Ω ^TF _i′

r _i＝Ω ^Tr _i′

In the formula: Ω is a transition matrix, can be expressed as:

$\mathrm{\&Omega;}=\left[\begin{array}{cc}T& \\ & T\end{array}\right].$

In inertial coordinates system, when global coordinate is done translation and rotated, with the absolute linear acceleration and the absolute angle acceleration of movable member in the chip:

$\begin{array}{c}a={\stackrel{\&CenterDot;\&CenterDot;}{r}}_R+{\stackrel{\&CenterDot;\&CenterDot;}{r}}_r+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_R\&times;r+{\mathrm{\&omega;}}_R\&times;({\mathrm{\&omega;}}_R\&times;r)+{2\mathrm{\&omega;}}_R\&times;\stackrel{\&CenterDot;}{r}\\ a={\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_R+{\mathrm{\&omega;}}_R\&times;{\mathrm{\&omega;}}_r+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_r\end{array}$

Behavior model in the global coordinate is revised, obtained the behavior model of functional structure parts in non-inertia global coordinate.In following formula:

Be the absolute acceleration of global coordinate with respect to inertial coordinates system; Be the relative acceleration of object in global coordinate; ω _RAngular velocity for global coordinate; R is the position vector of object with respect to global coordinate; ω _rBe the relative angle speed of object in global coordinate.So when global coordinate was done non-inertia motion, the absolute acceleration of the end points of functional structure parts was:

${\stackrel{\&CenterDot;\&CenterDot;}{r}}_i={\left[\begin{array}{cc}{a}_i& {\mathrm{\&alpha;}}_i\end{array}\right]}^T(i=1,...,n)$

In the formula: a _iAnd α _iBe respectively the absolute linear acceleration and the absolute angle acceleration of i end points.

The mechanical behavior model of microstructure is by the absolute acceleration of movable member in the behavior model of functional structure parts in global coordinate, the chip and absolute angle acceleration with when global coordinate is done non-inertia motion, the definition of the absolute acceleration of the end points of functional structure parts.Because the translation physical quantity of describing global coordinate is arranged in the absolute linear acceleration of movable member and the absolute angle acceleration in the chip With Rotation Physics amount ω _RSo this model has reflected the non-inertia motion (line accelerated motion and rotation) of microstructure place chip in the space.

Described power electric coupling behavior modeling method is:

According to law of conservation of energy, the energy relationship of the system that is formed by two conductive structures (being the conservative system of an energy) can be expressed as:

dW _e′(q，x)＝q·dV+F _e·dx

In the formula: W _e' (q, x) for the complementary energy of the electrostatic energy stored between conductive structure (or claim with can, altogether can); V is the electric potential difference between two conductors; Q is the quantity of electric charge on the conductor, F _eBe the electrostatic force between conductor, x is the relative displacement between conductor.Wherein V and x are independent variables.

As the conservative system of energy, integration and the path independence of above-mentioned energy relationship in the x-V space then has:

$\begin{array}{c}{W}_e^{\&prime;}={\&Integral;}_0^k{F}_e(x^{\&prime;},V=0){\mathrm{dx}}^{\&prime;}+{\&Integral;}_0^{v}q(x,V^{\&prime;}){\mathrm{dV}}^{\&prime;}\\ ={\&Integral;}_0^{v}C\left(x\right)V^{\&prime;}{\mathrm{dV}}^{\&prime;}=\frac{1}{2}C\left(x\right)V^2\end{array}$

In the formula: C (x) is the electric capacity between two conductors.Thus, can get the electrostatic force between two conductors, i.e. the behavior model of power electric coupling microstructure is:

$F_e=\frac{{\&PartialD;W}_e^{\&prime;}}{\&PartialD;x}-q\frac{\&PartialD;V}{\&PartialD;x}=\frac{1}{2}\frac{\&PartialD;C\left(x\right)}{\&PartialD;x}{V}^2.$

In addition, because conductor structure has certain mass, set up its mechanical behavior model according to foregoing microstructure mechanical behavior modeling method.

Described core model definition is:

Corresponding with the end points on its core model the end points of microstructure, each end points on the core model all is provided with seven ports, is used to describe the mechanical motion in three dimensions (rotations of the translation of three directions and three directions) and the electric property of microstructure.Seven ports all are set on each end points, and each port has two port variables: one is flux, and another is the amount of striding.The flux in each energy territory and the amount of striding see Table 1:

The amount of striding and the flux in each energy territory of table 1

The energy territory	The amount of striding	Flux
			Electric field	Voltage	Electric current
The machinery translation	Displacement	Power
			Mechanical rotation	Corner	Torque

In addition, owing to all include the physical quantity (linear acceleration of describing the chip motion in the behavior model of each microstructure

And angular velocity omega _R), so the non-inertia motion of additional six ports (describing the six-freedom degree of chip motion respectively) reflection chip in the core model of microstructure, these ports-settings are overall input port.Specifically can adopt " external " statement of mixed signal hardware descriptive language MAST to realize that " of overall importance " of microstructure port defines.

With microstructure based on the domain geometric parameter of feature and part working process parameter (as thickness of structure and institute's materials used etc.) parameter as core, as the parameter of little beam its domain physical dimension parameter length and width and working process parameter thickness and employed material parameter (as Young modulus, Poisson ratio etc.) are arranged.

Chip motion core model definition: the core of describing the chip motion is called " environmental variance ", and it does not have concrete three-dimensional structure, is the aided modeling core of inertia MEMS, (uses linear acceleration in order to describe the chip motion And angular velocity omega _RDescribe).Chip motion core model definition is that the environmental variance definition is: 6 ports on the left side of this core are described the six-freedom degree of chip motion, and this port is the signal flow port, and each port has only a port variable; Six ports on the right are overall output port, and are corresponding with six ports on the left side and realize the conversion of the information between the movable member and energy in MEMS chip and the chip as the overall input port in overall output port and the microstructure core model is corresponding with this.Can realize environmental variance and microstructure core model like this under the situation of corresponding port virtual junctions (promptly directly line), realize with microstructure core model in describe the port that the chip six-freedom degree moves and connect mutually.

A kind of core kernel of setting up according to above-mentioned modeling method: set up the parametrization core model of the exemplary functions structure member of MEMS inertia device in three dimensions, the set of core model forms core kernel.It is characterized in that: this core kernel is made up of micromechanics core, power electric coupling core and aided modeling core model; The micromechanics core comprises anchor point, space beam, mass, bar connecting piece, and its behavior model obtains by the mechanical behavior modeling method of microstructure; Power electric coupling core comprises pectination variable condenser and flat variable condenser, and its mechanical behavior is obtained by the mechanical behavior modeling method of microstructure, and power electric coupling behavior model is obtained by the behavior modeling method of power electric coupling microstructure; Environmental variance is described the motion of MEMS chip, is the aided modeling core of inertial MEMS.

Description of drawings:

Fig. 1: the core modeling process of micro-inertia sensor spare

Fig. 2: the composition of the core kernel of inertia MEMS

Fig. 3: the core modular concept figure of space beam

Fig. 4: pectination variable condenser

(a) one-piece construction synoptic diagram

(b) broach partial enlarged drawing

Fig. 5: the core model of anchor point

Fig. 6: the core model of space beam

Fig. 7: the lump point mass core model of plate mass

Fig. 8: the multinode core model of plate mass

Fig. 9: the core model of thick stick connecting piece

Figure 10: the core model of flat variable condenser

Figure 11: the core model of pectination variable condenser

Embodiment:

Now in conjunction with the accompanying drawings the present invention is further described:

With space beam and comb structurally variable electric capacity is the core model of example definition inertia microstructure.

The core model of space beam:

Adopt the mechanical behavior modeling method of microstructure to set up its behavior model, define its core model according to microstructure core model definition method then.

■ is in local coordinate system

Reflect and study the stressed of beam and distortion situation with the two-end-point (representing two-end-point) of beam with subscript 1 and 2.Suppose tension and compression, the bending of beam and reverse separately that under little displacement of the lines and angular displacement situation, the behavior equation of beam under local coordinate system is:

$M^{\&prime;}\&CenterDot;{\stackrel{\&CenterDot;\&CenterDot;}{r}}^{\&prime;}+B^{\&prime;}\&CenterDot;{\stackrel{\&CenterDot;}{r}}^{\&prime;}+K^{\&prime;}\&CenterDot;r^{\&prime;}=F^{\&prime;}$

In the formula: M ', B ', K ' are respectively mass matrix, damping matrix and the stiffness matrix of beam, and r ' and F ' are respectively motion vector and the load vector on two end points of beam.

■ is in global coordinate

If T is the direction cosine matrix between global coordinate and local coordinate system, then the behavior equation of beam in global coordinate is:

$M\&CenterDot;\stackrel{\&CenterDot;\&CenterDot;}{r}+B\&CenterDot;\stackrel{\&CenterDot;}{r}+K\&CenterDot;r=F$

In the formula: M, B, K, F and r are respectively mass matrix, damping matrix, stiffness matrix, the load vector sum motion vector of beam in global coordinate, can be expressed as respectively:

M＝Ω ^TM′Ω

B＝Ω ^TB′Ω

K＝Ω ^TK′Ω

F＝Ω ^TF′

r＝Ω ^Tr′

In the formula: Ω is a transition matrix, can be expressed as:

$\mathrm{\&Omega;}=\left[\begin{array}{cccc}T& & & \\ & T& & \\ & & T& \\ & & & T\end{array}\right]$

■ is in non-inertia is overall

When global coordinate was done translation and rotated, the absolute acceleration of beam was:

$\stackrel{\&CenterDot;\&CenterDot;}{r}=(a_1.{\mathrm{\&alpha;}}_1,a_2,{\mathrm{\&alpha;}}_2)$

Can get the core of beam thus:

According to the behavior equation of beam in global coordinate $M\&CenterDot;\stackrel{\&CenterDot;\&CenterDot;}{r}+B\&CenterDot;\stackrel{\&CenterDot;}{r}+K\&CenterDot;r=F,$ With do translation when global coordinate and when rotating, the absolute acceleration of beam $\stackrel{\&CenterDot;\&CenterDot;}{r}=(a_1,a_1,a_2,{\mathrm{\&alpha;}}_2)$ Defined the mechanical behavior model of beam.According to the stress deformation (two-end-point is totally 12 degree of freedom) of beam and the needs of electricity behavior (two-end-point is totally 2 degree of freedom), beam is expressed as the core model with 14 ports, the core model synoptic diagram of beam is seen accompanying drawing 3.Displacement x=[x _iy _iz _iα _iβ _iγ _i] (i=1, two end points of 2 expression beams) conduct amount of striding, power F=[F _XiF _YiF _ZiM _XiM _YiM _Zi] (i=1,2) as the multiport core model of flux definable beam.In addition, also have the translation and the rotation of the port reflection chip of six " cannot see " in the model, with the non-inertia motion of reflection global coordinate in beam core model.

The core model of pectination variable condenser:

The pectination variable condenser is a power electric coupling micro-structural components, adopts the behavior modeling method of power electric coupling microstructure to set up its behavior model, defines its core model according to microstructure core model definition method then.

Figure 4 shows that a pectination variable condenser, it is made of fixed fingers and movable broach.Do following simplification during modeling: ignore fringing field effect, movable broach only along x and y to moving, so the capacitance of pectination is:

$C=\mathrm{tN}{\mathrm{\&epsiv;}}_0(x_0+x)(\frac{1}{g-y}+\frac{1}{g+y})$

In the formula: t is the thickness of broach, and N is movable broach number, ε ₀Be specific inductive capacity, x and y are respectively the displacement of movable broach with respect to fixed fingers, x ₀And g is respectively initial overlapping value and spacing between broach.The electrostatic force that is got between conductor by the behavior modeling method of power electric coupling microstructure is:

${\left[\begin{array}{cc}{F}_{\mathrm{ex}}& F_{\mathrm{ey}}\end{array}\right]}^T=\frac{{(V_r-V_s)}^2}{2}{\left[\begin{array}{cc}\frac{\&PartialD;C}{\&PartialD;x}& \frac{\&PartialD;C}{\&PartialD;y}\end{array}\right]}^T$

In the formula: F _Ex, F _EyBe respectively x and y to electrostatic force, V _r, V _sBe respectively the electromotive force on movable broach and the fixed fingers.

Broach has certain mass, and it is regarded as rigid body, sets up its mechanical motion behavior model according to the mechanical behavior modeling method of foregoing microstructure.

Thus, the pectination variable condenser can be modeled as have two end points core of (describing fixed fingers and movable broach respectively), each end points has seven ports (describing 6 mechanical degree of freedom and electrical characteristics respectively), port variable serves as the amount of striding with displacement and electromotive force, and power and electric current are as flux.Equally, also have the translation and the rotation of the port reflection chip of six " cannot see " in this core, with the non-inertia motion of reflection global coordinate in core.

In like manner, can obtain:

Anchor point core model is seen accompanying drawing 5.It has six ports, and to be used for retraining with its core that connects mutually be zero in the displacement of this end points.

Space beam core model is seen accompanying drawing 6.According to the stress deformation (two-end-point is totally 12 degree of freedom) of beam and the needs of electricity behavior (two-end-point is totally 2 degree of freedom), beam is expressed as core model with 14 ports.For the large deformation non-linear behavior of beam, adopt linear behavior and the non-linear method of statement respectively, thereby set up its behavior equation with the stiffness matrix of the linear behavior of the little sex change of stress reinforced stiffness matrix correction.

The lump point mass core model of plate mass is seen accompanying drawing 7.Mass is regarded as the behavior equation that rigid body is set up plate mass.How much topological relations between mass and other core can be established as the model with 8 each end points to dull and stereotyped quality for convenience of description, and each node has 7 ports (describe mechanical behavior for 6, describe the electricity behavior for 1), sees accompanying drawing 6.

The thick stick connecting piece is used for defining the geometry site between the core tie-point, is the rigid connection core that does not have quality.Its behavior equation can be derived by the coordinate transformation relation between coordinate system, Fig. 9 is the multiport core model of thick stick connecting piece, similar with the space beam, core has 14 ports (12 ports are described 12 degree of freedom of two-end-point and the electricity behavior that 2 some ports are described two-end-point).

Plate condenser and pectination capacitor, its electric capacity is derived by the electric capacity company between two conductors.Figure 10 shows that the core model synoptic diagram of plate condenser, have 2 end points (describe the motion of top crown, bottom crown is fixed), end points has 7 ports (describe mechanical behavior for 6, describe the electricity behavior for 1).Because bottom crown is general and matrix is connected, so the displacement of bottom crown directly is fixed as zero, bottom crown has an electric port (describing the electricity behavior of bottom crown).

For the pectination variable capacitance, can regard the parallel connection of many plane-parallel capacitors as, its behavior model can be derived by the formula of plane-parallel capacitor.Figure 11 shows that the core model synoptic diagram of pectination capacitor, it has two end points (being used for describing the motion of two pole plates of electric capacity respectively), and each end points has 7 ports (describe mechanical behavior for 6, describe the electricity behavior for 1).

Shown in Figure 2 is: with the parametrization core model of the exemplary functions structure member of setting up the MEMS inertia device in the above-mentioned three dimensions, as the core kernel of mechanical core, power electric coupling core and the formation of aided modeling core model set.

Claims (10)

1, a kind of core modeling method of mini inertial sensor spare, it is characterized in that: according to machinery and two energy territories of electricity, set up machinery and power electric coupling microstructure behavior model with mechanical behavior modeling method and power electric coupling behavior modeling method, form the reusable core of micro-inertia sensor spare again according to core model definition method.

2, the core modeling method of mini inertial sensor spare according to claim 1, it is characterized in that: described mechanical behavior modeling method is: the behavior of examination functional structure parts in different coordinate systems, set up inertia MEMS functional structure parts behavior model; Set up the behavior model in the local coordinate system earlier, then with the behavior model obtain behavior model in the global coordinate by coordinate conversion.

3, the core modeling method of mini inertial sensor spare according to claim 2, it is characterized in that: the behavior model in the described local coordinate system is:

$F_1^{\&prime;}=f_1^{\&prime;}(r_1^{\&prime;},{\stackrel{\&CenterDot;}{r}}_1^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;r_i^{\&prime;},{\stackrel{\&CenterDot;}{r}}_i^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_n^{\&prime;},{\stackrel{\&CenterDot;}{r}}_n^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n^{\&prime;})$

$F_2^{\&prime;}=f_2^{\&prime;}(r_1^{\&prime;},{\stackrel{\&CenterDot;}{r}}_1^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;r_i^{\&prime;},{\stackrel{\&CenterDot;}{r}}_i^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_n^{\&prime;},{\stackrel{\&CenterDot;}{r}}_n^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n^{\&prime;}).$

……

$F_n^{\&prime;}=f_n^{\&prime;}(r_1^{\&prime;},{\stackrel{\&CenterDot;}{r}}_1^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;r_i^{\&prime;},{\stackrel{\&CenterDot;}{r}}_i^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i^{\&prime;},\&CenterDot;\&CenterDot;\&CenterDot;,r_n^{\&prime;},{\stackrel{\&CenterDot;}{r}}_n^{\&prime;},{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n^{\&prime;})$

4, the core modeling method of mini inertial sensor spare according to claim 2, it is characterized in that: the behavior model in the described global coordinate is:

$F_1=f_1(r_1,{\stackrel{\&CenterDot;}{r}}_1,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1,\&CenterDot;\&CenterDot;\&CenterDot;r_i,{\stackrel{\&CenterDot;}{r}}_i,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,r_n,{\stackrel{\&CenterDot;}{r}}_n,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n)$

$F_2=f_2(r_1,{\stackrel{\&CenterDot;}{r}}_1,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1,\&CenterDot;\&CenterDot;\&CenterDot;r_i,{\stackrel{\&CenterDot;}{r}}_i,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,r_n,{\stackrel{\&CenterDot;}{r}}_n,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n).$

……

$F_n=f_n(r_1,{\stackrel{\&CenterDot;}{r}}_1,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_1,\&CenterDot;\&CenterDot;\&CenterDot;r_i,{\stackrel{\&CenterDot;}{r}}_i,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_i,\&CenterDot;\&CenterDot;\&CenterDot;,r_n,{\stackrel{\&CenterDot;}{r}}_n,{\stackrel{\&CenterDot;\&CenterDot;}{r}}_n)$

5, the core modeling method of mini inertial sensor spare according to claim 2 is characterized in that: described behavior model transition matrix is: $\mathrm{\&Omega;}=\left[\begin{array}{cc}T& \\ & T\end{array}\right].$

6, the core modeling method of mini inertial sensor spare according to claim 4 is characterized in that: in inertial coordinates system, when global coordinate is done translation and rotated, with the absolute linear acceleration and the absolute angle acceleration of movable member in the chip:

$a={\stackrel{\&CenterDot;\&CenterDot;}{r}}_R+{\stackrel{\&CenterDot;\&CenterDot;}{r}}_r+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_R\&times;r+{\mathrm{\&omega;}}_R\&times;({\mathrm{\&omega;}}_R\&times;r)+2{\mathrm{\&omega;}}_R\&times;\stackrel{\&CenterDot;}{r}$

$\mathrm{\&alpha;}={\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_R+{\mathrm{\&omega;}}_R\&times;{\mathrm{\&omega;}}_r+{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_r;$

Behavior model in the global coordinate is revised, obtained the behavior model of movable member in non-inertia global coordinate;

When global coordinate was done non-inertia motion, the absolute acceleration of the end points of functional structure parts was:

${\stackrel{\&CenterDot;\&CenterDot;}{r}}_i={\left[\begin{array}{cc}{a}_i& a_i\end{array}\right]}^T(i=1,...,n).$

7, the core modeling method of mini inertial sensor spare according to claim 1, it is characterized in that: described power electric coupling microstructure behavior modeling method is: according to law of conservation of energy, the energy relationship that is formed system by two conductive structures can be expressed as: dW _e' (q, x)=qdV+F _eDx as the conservative system of energy, then has:

$W_e^{\&prime;}={\&Integral;}_0^x{F}_e(x^{\&prime;},V=0){\mathrm{dx}}^{\&prime;}+{\&Integral;}_0^{V}q(x,V^{\&prime;}){\mathrm{dV}}^{\&prime;}$

$={\&Integral;}_0^{V}C\left(x\right)V^{\&prime;}{\mathrm{dV}}^{\&prime;}=\frac{1}{2}C\left(x\right)V^2$

Behavior model that can capable electric coupling microstructure is: $F_e=\frac{{\&PartialD;W}_e^{\&prime;}}{\&PartialD;x}-q\frac{\&PartialD;V}{\&PartialD;x}=\frac{1}{2}\frac{\&PartialD;C\left(x\right)}{\&PartialD;x}{V}^2.$

8, the core modeling method of mini inertial sensor spare according to claim 1 is characterized in that: described core model definition is: functional structure parts discretize, the point of discretize is called end points; Seven ports all are set on each end points, and each port has two port variables: one is flux, and another is the amount of striding; Additional six ports of describing the chip freedom of motion in the core model, these ports are overall input port.

9, according to the core modeling method of claim 1 or 8 described mini inertial sensor spares, it is characterized in that: chip motion core model is that the environmental variance definition is: the left side of this core has 6 ports to describe the six-freedom degree of chip motion, this port is the signal flow port, and each port has only a port variable; Six ports on the right are overall output port, and are corresponding with six ports on the left side.

10, a kind of core kernel of setting up according to above-mentioned modeling method, it is characterized in that: this core kernel is made up of micromechanics core, power electric coupling core and aided modeling core model; The micromechanics core comprises anchor point, space beam, mass, bar connecting piece, and its behavior model obtains by the mechanical behavior modeling method of microstructure; Power electric coupling core comprises pectination variable condenser and flat variable condenser, and its mechanical behavior is obtained by the mechanical behavior modeling method of microstructure, and power electric coupling behavior model is obtained by the behavior modeling method of power electric coupling microstructure; Environmental variance is described the motion of MEMS chip, is the aided modeling core of inertial MEMS.

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