CN110334418A - A kind of deformation analytical method of MEMS V-type beam - Google Patents

A kind of deformation analytical method of MEMS V-type beam Download PDF

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CN110334418A
CN110334418A CN201910527354.4A CN201910527354A CN110334418A CN 110334418 A CN110334418 A CN 110334418A CN 201910527354 A CN201910527354 A CN 201910527354A CN 110334418 A CN110334418 A CN 110334418A
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韩磊
秦瑞洁
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Southeast University
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Abstract

A kind of deformation analytical method of MEMS V-type beam, which comprises the following steps: establish based on MEMS V-type girder construction by the impact deformation model after acceleration impact loading；After the MEMS is by acceleration load impacting, it is based on impact deformation model, MEMS V-type beam internal stress is obtained, establishes internal stress model；MEMS V-type beam is obtained due to the strain that internal stress acts on and generates, establishes strain model；The deformation that MEMS V-type beam is generated due to strain is obtained, deformation model is established.Compared with prior art, present invention firstly provides based on the deformation model under acceleration impact loading, realize the impact analysis to MEMS V-type girder construction deformation after being impacted, the prediction for generating macroscopic deformation after being impacted to MEMS V-type beam is realized, has been filled up both at home and abroad to MEMS V-type girder construction by the blank that deformation occurs after acceleration impact loading.

Description

A kind of deformation analytical method of MEMS V-type beam
Technical field
The present invention relates to a kind of mechanical analyzing method, in particular under the conditions of a kind of impact loading based on acceleration MEMS V-type girder construction mechanical analysis deformation method.
Background technique
MEMS (Micro-Electro-Mechanical System, abbreviation MEMS) refers in micro-nano rank It is designed and manufactures, collection micro mechanical structure, energy converter, microactrator and a variety of components such as control circuit and detection circuit Inside a junior unit, and it is suitable for the system of low cost batch production.MEMS is not only tradition machinery on scale Microminaturization, it is and the important component as entire nanoscale science and technology based on modern science and technology, with a kind of brand-new Method of thinking guidance under product.In nearest 20 years, the development of MEMS and the in the market release of MEMS product are had been achieved with Rapid advances, realize cheap, complex devices the conceptions of good reliability.MEMS is integrated microsystem, it is tied Electronics, machinery or other (magnetic, liquid and heat etc.) elements have been closed, have generallyd use traditional semiconductor batch technology to make Make, size range from several millimeters to micron even nanometer.The sensitivity or execution pattern of these systems are designed to and external rings Border interaction, to generate status information or control to varying degrees external environment.In the past 10 years, MEMS technology In some industrial circles, it has been widely recognized as in the application including automobile, industry, medical treatment or even military affairs.MEMS technology master If growing up from microelectronic technique, main rapidoprint is also silica-base material, since silica-base material is more stable, tool There are preferable mechanical strength and anti-fatigue performance etc., but since silicon is fragile material, fracture is easy to happen under HI high impact, so Material employed in the present invention is Au, and brittle fracture will not occur under HI high impact, is made by acceleration shock loading Deformation situation needs after are analyzed, however, being both at home and abroad directed to MEMS V-type girder construction by acceleration load impacting Lower deformation analysis is still in blank stage.
Summary of the invention
To solve the above-mentioned problems, the invention proposes a kind of deformation analytical methods of MEMS V-type beam, which is characterized in that The following steps are included:
It establishes based on MEMS V-type girder construction by the impact deformation model after acceleration impact loading；
After the MEMS is by acceleration load impacting, it is based on impact deformation model, obtains MEMS V-type beam internal stress, Establish internal stress model；
MEMS V-type beam is obtained due to the strain that internal stress acts on and generates, establishes strain model；
The deformation that MEMS V-type beam is generated due to strain is obtained, deformation model is established.
Further, the impact deformation model are as follows:
qi=ρ wita
Wherein, qiFor the uniform load for acting on i-th of infinitesimal of V-type beam, ρ is density of material, wiFor MEMS V-type beam i-th The width of a infinitesimal, t are the thickness of MEMS V-type beam, and a is the size for the impact acceleration that structure is subject to.
Further, the MEMS V-type beam internal stress includes direct stress and shear stress, the internal stress model packet Include direct stress model and shear stress model.
Further, the direct stress model are as follows:
Wherein, M (x) is moment of flexure inside two-end fixed beam, and w is the width of MEMS V-type beam, and t is the thickness of MEMS V-type beam Degree, wherein qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam, i =1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from V-type beam anchoring area.
Further, the shear stress model are as follows:
Wherein, FsIt (x) is shearing inside two-end fixed beam, w is the width of MEMS V-type beam, and t is the thickness of MEMS V-type beam Degree, wherein qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam, i =1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from V-type beam anchoring area.
Further, shearing inside the MEMS V-type beam are as follows:
Wherein, qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam It spends, i=1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from anchoring area.
Further, moment of flexure inside the MEMS V-type beam are as follows:
Wherein, qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam It spends, i=1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from anchoring area.
Further, the strain model are as follows:
Wherein, E is Young's modulus, and G is modulus of shearing, and ν is Poisson's ratio；εx、εy、εzRespectively in coordinate system x, y, z direction On infinitesimal normal strain, γxy、γyz、γzxThe shearing strain of infinitesimal respectively in x/y plane, yz plane and zx plane, σx、σy、σzThe respectively maximum value σ of direct stressmaxDecomposition direct stress in the x, y, z-directions, τxy、τyz、τzxRespectively shearing is answered The maximum value τ of powermaxShear stress in x/y plane, yz plane and zx plane.
Further, the deformation model are as follows:
Wherein, θiI-th of infinitesimal is represented by the curved angle of stress, dx represents each infinitesimal on V-type beam.
Further, the curved angle are as follows:
Wherein, t is the thickness of MEMS V-type beam, and i represents i-th of infinitesimal,For the plastic strain of i-th of infinitesimal.
The present invention is in order to fill up both at home and abroad to MEMS V-type girder construction by deformation occurs after acceleration impact loading Research blank, propose it is a kind of based on MEMS V-type beam by the stress and deformation analytical method under acceleration shock loading. The present invention mainly takes four steps to handle MEMS V-type beam by the modeling after shock loading, to obtain shock loading pair The analytic modell analytical model that V-type girder construction affects.The first step, which impacts acceleration, is converted into power suffered in V-type girder construction, and second Step is calculated the stress of inside configuration by power suffered in V-type girder construction, and third step calculates V-type girder construction by internal stress Strain, the 4th step are converted into the height of V-type girder construction warpage by strain data.Based on the above parameter, MEMS V is rebuild Type girder construction mechanical model analyzes influence of the acceleration shock loading to MEMS V-type girder construction.
A kind of deformation analytical method of MEMS V-type beam proposed by the present invention solves MEMS V-type beam by acceleration Deformation analysis problem when shock loading, compared with prior art, present invention firstly provides made based on acceleration shock loading Deformation model under gives the double deformation analysis models of MEMS V-type girder construction elasticity and moulding, realizes to being impacted The impact analysis of MEMS V-type girder construction deformation afterwards realizes and generates the pre- of macroscopic deformation after being impacted to MEMS V-type beam It surveys, has filled up both at home and abroad to MEMS V-type girder construction by the research blank that deformation occurs after acceleration impact loading.
Detailed description of the invention
Fig. 1 is a kind of flow diagram of the deformation analytical method of MEMS V-type beam of the invention；
Fig. 2 is the structural schematic diagram of MEMS V-type beam of the present invention；
Fig. 3 is MEMS V-type beam of the present invention by the stress diagram after acceleration shock loading.
Specific embodiment
Below by specific embodiment combination Fig. 1 to Fig. 3, invention is further described in detail, so as to more preferably Ground understands the advantages of contents of the present invention and its various aspects.Below in an example, following specific embodiments are provided Purpose is easy for becoming apparent from thorough explanation to the contents of the present invention, rather than limiting the invention.
Embodiment 1
The invention proposes a kind of deformation analytical method of MEMS V-type beam, in the present embodiment, in MEMS component by outer When power is impacted, by constructing the impact deformation model of external force, and then establish after MEMS is impacted on impact deformation model basis Under internal stress model, and then establish the internal strain model due to caused by internal stress, finally obtain since inside is answered The macroscopic deformation model of the MEMS component of change and formation.MEMS component in the present embodiment generally refers to MEMS V-type beam structure Part, MEMS V-type girder construction is connected by clamped anchoring area with substrate, and when by external impacts, the position of stress can be beam Structure is also possible to underlying structure.As shown in Fig. 2, 1 is anchoring area, 2 be V-type beam.
As shown in Figure 1, the present invention by taking MEMS V-type beam as an example, analyzes V-type beam by the shape after acceleration shock loading Become situation.In the present embodiment to each parameter value, the material of MEMS V-type beam electrostatic drive switch beam is Au, density ρ, beam Length li, the width w of beami, the thickness t of beam, acceleration magnitude of load is a.
A kind of deformation analytical method for MEMS V-type beam that the present embodiment proposes, specifically includes the following steps:
Step 1: establishing based on MEMS V-type girder construction by the impact deformation model after acceleration impact loading.
Establish the stress model based on acceleration impact loading on MEMS V-type beam, the acceleration that V-type beam is subject to Degree shock loading is equivalent to act on the uniform load of V-type beam are as follows:
Q=ρ wta
Wherein, q is the uniform load for acting on V-type beam, and ρ is density of material, and w is the width of MEMS V-type beam, t MEMS The thickness of V-type beam, a are the size for the impact acceleration that MEMS V-type beam is subject to.
V-type beam is decomposed into i infinitesimal, then the acceleration shock loading that each infinitesimal of V-type beam is subject to is equivalent to act on V The uniform load of the type beam infinitesimal is
qi=ρ wita
Wherein, qiFor the uniform load for acting on i-th of infinitesimal of V-type beam, ρ is density of material, wiFor MEMS V-type beam i-th The width of a infinitesimal, t are the thickness of MEMS V-type beam, and a is the size for the impact acceleration that structure is subject to.
Above-mentioned uniform load qiStatement relationship be MEMS V-type girder construction by acceleration impact loading after Impact deformation model.
Step 2: after the MEMS is by acceleration load impacting, being based on impact deformation model, obtain in MEMS V-type beam Portion's stress establishes internal stress model.
Based on the MEMS V-type girder construction mechanical analysis deformation method under the conditions of acceleration impact loading, as MEMS V When different location when type beam is by acceleration effect in V-type beam generates different load effects, it can generate and answer inside V-type beam Power, shearing and moment of flexure when MEMS V-type beam is in different location are respectively as follows:
Wherein, qiFor the uniform load for obtaining different location on i-th of infinitesimal of V-type beam in step 1, liIt is i-th of V-type beam The equivalent length of infinitesimal, i=1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from anchoring area.
Due to the design feature of V-type beam, the stress condition of V-type beam different location is different, so as to cause on different infinitesimals Uniform load and equivalent length are different, in the present embodiment, have carried out area mainly for the both ends part of V-type beam and middle section Point, it is both ends part close to the part of anchoring area as shown in Figures 2 and 3, the uniform load of the both ends part is q1, equivalent length Degree is l1, the part far from anchoring area is middle section, and the uniform load of the middle section is q2, equivalent length l2.This implementation In example, V-type beam is only divided into two parts to construct stress model respectively, it is not limited to this, it can be according to actual use Situation is divided to multiple portions, such as five parts, seven parts, nine parts.
Further, it is available MEMS V-type beam by acceleration be a shock loading when different location when just Stress maximum value are as follows:
Wherein, w is the width of MEMS V-type beam, and t is the thickness of MEMS V-type beam, wherein qiTo obtain V-type in step 1 The uniform load of different location, l on i-th of infinitesimal of beamiFor the equivalent length of i-th of infinitesimal of V-type beam, i=1,2,3...n, this In embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from V-type beam anchoring area.
MEMS V-type beam by acceleration be a shock loading when different location when shear stress maximum value are as follows:
Wherein, w is the width of MEMS V-type beam, and t is the thickness of MEMS V-type beam, wherein qiTo obtain V-type in step 1 The uniform load of different location, l on i-th of infinitesimal of beamiFor the equivalent length of i-th of infinitesimal of V-type beam, i=1,2,3...n, this In embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from V-type beam anchoring area.
The maximum value of MEMS V-type beam internal stress, i.e. direct stress maximum value σ are obtainedmaxWith shear stress maximum value τmax, using the maximum value of direct stress and the maximum value of shear stress as the internal stress model of MEMS V-type beam, i.e., it is positive respectively Stress model and shear stress model.
Step 3: obtaining MEMS V-type beam due to the strain that internal stress acts on and generates, establish strain model.
Based on MEMS V-type beam by acceleration shock loading stress model, in conjunction with the obtained MEMS V-type in step 2 Beam internal stress model can further obtain being caused by V-type beam internal stress the strain per a bit of infinitesimal to be, strain mould Type are as follows:
Wherein, E is Young's modulus, and G is modulus of shearing, and ν is Poisson's ratio；εx、εy、εzRespectively in coordinate system x, y, z direction On infinitesimal normal strain, γxy、γyz、γzxThe shearing strain of infinitesimal respectively in x/y plane, yz plane and zx plane, σx、σy、σzThe respectively maximum value σ of direct stressmaxDecomposition direct stress in the x, y, z-directions, τxy、τyz、τzxRespectively shearing is answered The maximum value τ of powermaxShear stress in x/y plane, yz plane and zx plane.
Step 4: obtaining the deformation that MEMS V-type beam is generated due to strain, establish deformation model.
Under acceleration impact loading, the deformation for straining and ultimately causing macroscopically, MEMS V are generated by internal stress Type beam is as follows by the deformation of the different location after acceleration shock loading:
When V-type beam is impacted by certain acceleration, V-type beam can simplify in girder construction different location by difference The beaer of load, in the girder construction of transverse curvature, span shears the shadow to bending deformation much larger than the beam of cross-sectional height Sound can be ignored, so only considering influence plastic deformation and deviatoric tensor of stress that the deformation that direct stress generates generates bending deformation Relationship be following formula:
Δεp=σij′dλ
Wherein, σij' be i-th section of infinitesimal deviatoric tensor of stress, d λ is a non-negative ratio system, with stress, plastic strain The position of increment and point and change.
Since other than axial direct stress, the stress of y-axis and z-axis is zero, i.e. σy=0, σz=0, above formula will be reduced to The curved angle model of infinitesimal stress of clamped beam, is divided into several infinitesimals for V-type beam, wherein i-th of infinitesimal is curved by stress Bent angle are as follows:
Wherein, t is the thickness of MEMS V-type beam, and i represents i-th section of infinitesimal,For the average principal strain of i-th of infinitesimal.
Then in first segment infinitesimal dl1In from deformation generate height by geometrical relationship
Δh1=dl1tanθ1
Wherein, θ1The 1st infinitesimal is represented by the curved angle of stress, dl1Represent the length of first segment infinitesimal.
Second segment infinitesimal dl2In from deformation generate height by geometrical relationship
Δh2=dl2tan(θ1+θ2)
Wherein, θ1The 1st infinitesimal is represented by the curved angle of stress, θ2The 2nd infinitesimal is represented by the curved angle of stress Degree, dl2Represent the length of second segment infinitesimal, and so on i-th of infinitesimal by the curved angle of stress be θi。
Due to V-type beam aboutSymmetrically, thusThe deformation beam at place is maximum, we only consider that 0 arrives Between deformation quantity can obtain:
Wherein, θiI-th of infinitesimal is represented by the curved angle of stress, dx represents each section of infinitesimal of two-end fixed beam.
So the beam curvilinear equation after V-type beam is impacted at x is
?The solution on right side aboutSection is full symmetric.
In conclusion the deformation that available MEMS V-type beam is generated due to strain, i.e. deformation model:
Wherein, θiI-th of infinitesimal is represented by the curved angle of stress, dx represents each section of infinitesimal on V-type beam.
So far, obtained MEMS V-type beam by the final deformation shape after acceleration load impacting by deformation model State obtains the relationship of acceleration shock loading Yu the beam deformation of MEMS V-type, and the shape of MEMS V-type beam can be obtained by deformation model Variable, and the maximum value by acceleration load impacting of MEMS V-type beam can be set accordingly, in order to prevent MEMS device from existing By brittle fracture occurs under HI high impact, the parameter index by presetting the power that is hit realizes that reducing MEMS device is damaged Risk.
Fig. 3 is MEMS V-type beam of the present invention by the stress diagram after acceleration shock loading, it can be seen from the figure that A is the size for the impact acceleration that MEMS V-type beam is subject to, qiTo obtain different location on i-th of infinitesimal of V-type beam in step 1 Uniform load, liFor the equivalent length of i-th of infinitesimal of V-type beam, i=1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, X, y, z is three directions of three-dimensional cartesian coordinate system.
The model established according to the present invention can calculate the V-type deflection of beam under by different impact acceleration load Deformation situation, it is accurate to predict MEMS V-type beam deformation quantity because of caused by stress, by establishing the relationship between stress and deformation, It can judge that the critical stress value of non-reversible deformation occurs in it according to the material property of MEMS V-type beam, to prejudge MEMS device Whether part can occur brittle fracture under HI high impact, improve the service life of MEMS device, reduce and make because of MEMS device damage At the application risk that complete machine is damaged, fills up and shape is occurred by after acceleration impact loading to MEMS V-type girder construction both at home and abroad The research blank of change.
The foregoing is merely better embodiment of the invention, protection scope of the present invention is not with above embodiment Limit, as long as those of ordinary skill in the art's equivalent modification or variation made by disclosure according to the present invention, should all be included in power In the protection scope recorded in sharp claim.

Claims (10)

1. a kind of deformation analytical method of MEMS V-type beam, which comprises the following steps:
It establishes based on MEMS V-type girder construction by the impact deformation model after acceleration impact loading；
After the MEMS is by acceleration load impacting, it is based on impact deformation model, obtains MEMS V-type beam internal stress, is established Internal stress model；
MEMS V-type beam is obtained due to the strain that internal stress acts on and generates, establishes strain model；
The deformation that MEMS V-type beam is generated due to strain is obtained, deformation model is established.
2. a kind of deformation analytical method of MEMS V-type beam according to claim 1, which is characterized in that the impact deformation Model are as follows:
qi=ρ wita
Wherein, qiFor the uniform load for acting on i-th of infinitesimal of V-type beam, ρ is density of material, wiIt is micro- for i-th of beam of MEMS V-type The width of member, t are the thickness of MEMS V-type beam, and a is the size for the impact acceleration that structure is subject to.
3. a kind of deformation analytical method of MEMS V-type beam according to claim 1, which is characterized in that the MEMS V-type Beam internal stress includes direct stress and shear stress, and the internal stress model includes direct stress model and shear stress model.
4. a kind of deformation analytical method of MEMS V-type beam according to claim 3, which is characterized in that the direct stress mould Type are as follows:
Wherein, M (x) is moment of flexure inside two-end fixed beam, and w is the width of MEMS V-type beam, and t is the thickness of MEMS V-type beam, In, qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam, i=1,2, 3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from V-type beam anchoring area.
5. a kind of deformation analytical method of MEMS V-type beam according to claim 3, which is characterized in that the shear stress mould Type are as follows:
Wherein, FsIt (x) is shearing inside two-end fixed beam, w is the width of MEMS V-type beam, and t is the thickness of MEMS V-type beam, In, qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam, i=1,2, 3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from V-type beam anchoring area.
6. a kind of deformation analytical method of MEMS V-type beam according to claim 5, which is characterized in that the MEMS V-type Shearing inside beam are as follows:
Wherein, qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam, i =1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from anchoring area.
7. a kind of deformation analytical method of MEMS V-type beam according to claim 4, which is characterized in that the MEMS V-type Moment of flexure inside beam are as follows:
Wherein, qiFor the uniform load of different location on i-th of infinitesimal of V-type beam, liFor the equivalent length of i-th of infinitesimal of V-type beam, i =1,2,3...n, in the present embodiment, i distinguishes value 1 and 2, and x is distance of the V-type beam apart from anchoring area.
8. a kind of deformation analytical method of MEMS V-type beam according to claim 1, which is characterized in that the strain model Are as follows:
Wherein, E is Young's modulus, and G is modulus of shearing, and ν is Poisson's ratio；εx、εy、εzRespectively on coordinate system x, y, z direction The normal strain of infinitesimal, γxy、γyz、γzxThe shearing strain of infinitesimal respectively in x/y plane, yz plane and zx plane, σx、σy、 σzThe respectively maximum value σ of direct stressmaxDecomposition direct stress in the x, y, z-directions, τxy、τyz、τzxRespectively x/y plane, yz are flat Shear stress in face and zx plane.
9. a kind of deformation analytical method of MEMS V-type beam according to claim 1, which is characterized in that the deformation model are as follows:
Wherein, y (x) is total deformation quantity, θiI-th of infinitesimal is represented by the curved angle of stress, dx represents every on V-type beam Duan Weiyuan.
10. a kind of deformation analytical method of MEMS V-type beam according to claim 9, which is characterized in that described curved Angle are as follows:
Wherein, t is the thickness of MEMS V-type beam, and i represents i-th of infinitesimal,For the plastic strain of i-th of infinitesimal.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20180316287A1 (en) * 2015-10-19 2018-11-01 Massachusetts Institute Of Technology Micro ElectroMechanical System (MEMS) Energy Harvester With Residual Stress Induced Instability
CN109446544A (en) * 2018-09-04 2019-03-08 东南大学 A kind of MEMS V-type girder construction mechanical analyzing method under the bending condition based on flexible base board

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20180316287A1 (en) * 2015-10-19 2018-11-01 Massachusetts Institute Of Technology Micro ElectroMechanical System (MEMS) Energy Harvester With Residual Stress Induced Instability
CN109446544A (en) * 2018-09-04 2019-03-08 东南大学 A kind of MEMS V-type girder construction mechanical analyzing method under the bending condition based on flexible base board

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