CN101135563A

CN101135563A - A dual-mass tuned output silicon MEMS gyroscope

Info

Publication number: CN101135563A
Application number: CNA2007101758863A
Authority: CN
Inventors: 房建成; 李建利; 盛蔚; 楚中毅; 秦杰; 乙冉冉; 宋星
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2007-10-15
Filing date: 2007-10-15
Publication date: 2008-03-05
Anticipated expiration: 2027-10-15
Also published as: CN100487376C

Abstract

A dual-mass tuned output silicon MEMS gyroscope is mainly composed of a fixed tooth, a movable tooth, two mass blocks, two outer frames, two pairs of rods and two tuning fork resonators. The first mass block and the second mass block are respectively connected to the first outer frame and the second outer frame through four inner folded beams, and the two outer frames are fixed to the anchor points through outer support beams respectively, and the two outer frames are connected by A pair of folded beams are connected. The left and right sides of the first outer frame are connected with the free ends of the two tuning fork resonators through the opposite direction force amplification levers, and the left and right sides of the second outer frame are connected with the two tuning fork resonator free ends through the same direction force amplification levers. The external input rotational speed is calculated by measuring the resonance frequency difference of the tuning fork resonators at both ends. The gyroscope reduces the vibration noise of the device, eliminates the error caused by the external acceleration, improves the performance of the device, and can be applied to the inertial navigation system of micro-miniature systems and intelligent weapons.

Description

A dual-mass tuned output silicon MEMS gyroscope

技术领域 technical field

本发明涉及一种双质量块调谐输出式硅MEMS陀螺仪，可应用于微小型系统的导航及控制，并可以应用于工作时间短、成本低、动态范围大的战术武器的惯性导航系统。The invention relates to a dual-mass tuning output silicon MEMS gyroscope, which can be applied to the navigation and control of micro-miniature systems, and can be applied to the inertial navigation system of tactical weapons with short working time, low cost and large dynamic range.

背景技术 Background technique

陀螺仪是一种惯性转速传感器，可用来测量载体的运动角速度，利用三个陀螺仪和三个加速度计组成的IMU(Inertial Measurement Unit，惯性测量单元)可以为载体提供位置、姿态信息，被广泛应用于惯性导航领域。从20世纪80年代末开始，随着MEMS(Micro-Electromechanical System，微机电系统)技术的发展，各种传感器实现了微小型化，以MEMS技术为基础的陀螺仪相对于传统的机械及光学陀螺仪而言，具有成本低、体积小、功耗低、可与电路集成等优点，具有广泛的应用前景，受到了各国的高度重视，先后投入巨资加以研究。The gyroscope is an inertial speed sensor that can be used to measure the angular velocity of the carrier. The IMU (Inertial Measurement Unit) composed of three gyroscopes and three accelerometers can provide position and attitude information for the carrier. It is widely used Applied in the field of inertial navigation. Since the late 1980s, with the development of MEMS (Micro-Electromechanical System, micro-electromechanical system) technology, various sensors have been miniaturized. Compared with traditional mechanical and optical gyroscopes, gyroscopes based on MEMS technology As far as the instrument is concerned, it has the advantages of low cost, small size, low power consumption, and can be integrated with circuits. It has a wide range of application prospects and has been highly valued by various countries.

从检测原理上讲，目前MEMS陀螺仪普遍采用电容检测方式，通过检测哥氏力产生位移的大小来间接估计转速。当器件的结构尺寸缩小到一定程度时，电容检测的灵敏度大大降低，严重影响陀螺仪的性能，同时电容式检测必须附加复杂的闭环电路，增加了器件的设计、加工难度，并且受一定的电-机耦合的影响，仪器的信噪比相对比较小。为此，人们一直在探索新的结构及检测方式，1998年美国加利福尼亚大学伯克利分校的T.A.W.Roessig提出了调谐输出式硅MEMS加速度计，为MEMS陀螺仪的谐振式检测奠定了基础。2002年，美国加利福尼亚大学伯克利分校的A.A.Seshia等人首次提出了调谐输出式硅MEMS陀螺仪，采用一个高频振动的质量块作为敏感单元，音叉谐振器作为检测单元，并成功研制了原理样机。该陀螺仪将敏感角速率产生的哥氏力转换成音叉谐振器谐振频率的变化，通过测量两端音叉谐振器谐振频率差来计算转速的大小，陀螺仪输出是准数字信号，易于数字电路集成，具有动态范围大、灵敏度较高、输出线性度好优点。然而由于单质量块的高频振动，引起了器件干扰噪声，增加了机械损耗；理想陀螺仪仅敏感输入轴向的角速度，然而单质量块调谐输出式硅MEMS陀螺仪不仅敏感输入轴向的角速度，同时敏感外部加速度，引入了加速度干扰误差，从而导致器件的测量误差。From the point of view of the detection principle, the current MEMS gyroscope generally adopts the capacitive detection method, and indirectly estimates the rotational speed by detecting the displacement generated by the Coriolis force. When the structural size of the device is reduced to a certain extent, the sensitivity of capacitance detection is greatly reduced, which seriously affects the performance of the gyroscope. - Influenced by machine coupling, the signal-to-noise ratio of the instrument is relatively small. For this reason, people have been exploring new structures and detection methods. In 1998, T.A.W.Roessig of the University of California, Berkeley proposed a tuned output silicon MEMS accelerometer, which laid the foundation for the resonant detection of MEMS gyroscopes. In 2002, A.A. Seshia of the University of California, Berkeley and others first proposed a tuned output silicon MEMS gyroscope, using a high-frequency vibrating mass as the sensitive unit, and a tuning fork resonator as the detection unit, and successfully developed a prototype. The gyroscope converts the Coriolis force generated by the sensitive angular rate into the change of the resonant frequency of the tuning fork resonator, and calculates the speed by measuring the difference between the resonant frequencies of the tuning fork resonator at both ends. The output of the gyroscope is a quasi-digital signal, which is easy for digital circuit integration , has the advantages of large dynamic range, high sensitivity and good output linearity. However, due to the high-frequency vibration of the single-mass block, it causes device interference noise and increases the mechanical loss; the ideal gyroscope is only sensitive to the angular velocity of the input axis, but the single-mass tuned output silicon MEMS gyroscope is not only sensitive to the angular velocity of the input axis , while being sensitive to external acceleration, the acceleration interference error is introduced, which leads to the measurement error of the device.

发明内容 Contents of the invention

本发明的技术解决问题是：克服现有调谐输出式硅MEMS陀螺仪振动噪声大、无法消除外部加速度引起的误差等不足，提出一种双质量块调谐输出式硅MEMS陀螺仪。The technical problem of the present invention is: to overcome the shortcomings of the existing tuned output silicon MEMS gyroscope, such as large vibration noise and inability to eliminate errors caused by external acceleration, and propose a dual-mass tuned output silicon MEMS gyroscope.

本发明的技术解决方案为：一种双质量块调谐输出式硅MEMS陀螺仪，其特征在于：主要由静齿、动齿、第一质量块、第二质量块、第一外框架、第二外框架、杠杆41、42、51、52和两个音叉谐振器81、82组成。静齿和动齿构成了电容式极板，第一质量块通过四个内折叠梁11、12、13、14连接在第一外框架上，第二质量块通过四个内折叠梁71、72、73、74连接在第二外框架上，第一外框架通过外支撑梁31、32固连在锚点21、22上，第二外框架通过外支撑梁61、62固连在锚点23、24上，第一外框架和第二外框架之间通过折叠梁361、362相连；第一外框架左右两侧分别通过杠杆41、42与音叉谐振器81、82自由端相连，第二外框架左右两侧分别通过杠杆51、52与音叉谐振器81、82自由端相连；锚点411、421分别是杠杆41、42的支撑点，锚点511、521分别是杠杆51、52的支撑点，音叉谐振器81、82固定端分别与锚点91、92相连，通过测得两端音叉谐振器的谐振频率差计算外部输入转速。The technical solution of the present invention is: a dual-mass tuned output silicon MEMS gyroscope, characterized in that it mainly consists of static teeth, movable teeth, a first mass block, a second mass block, a first outer frame, a second The outer frame, levers 41, 42, 51, 52 and two tuning fork resonators 81, 82 are composed. The static teeth and movable teeth constitute a capacitive plate, the first mass is connected to the first outer frame through four inner folding beams 11, 12, 13, 14, and the second mass is through four inner folding beams 71, 72 , 73, 74 are connected to the second outer frame, the first outer frame is fixedly connected to the anchor points 21, 22 through the outer support beams 31, 32, and the second outer frame is fixed to the anchor points 23 through the outer support beams 61, 62 , 24, the first outer frame and the second outer frame are connected by folded beams 361, 362; the left and right sides of the first outer frame are respectively connected with the free ends of tuning fork resonators 81, 82 through levers 41, 42, and the second outer frame The left and right sides of the frame are respectively connected to the free ends of the tuning fork resonators 81 and 82 through the levers 51 and 52; the anchor points 411 and 421 are the support points of the levers 41 and 42 respectively, and the anchor points 511 and 521 are the support points of the levers 51 and 52 respectively , the fixed ends of the tuning fork resonators 81 and 82 are connected to the anchor points 91 and 92 respectively, and the external input rotational speed is calculated by measuring the resonance frequency difference of the tuning fork resonators at both ends.

所述的第一质量块和第二质量块结构完全相同，内部嵌入梳状动齿，第一质量块和第二质量块沿Y轴做同频、等幅、反相振动；The structure of the first mass block and the second mass block is exactly the same, and comb-shaped movable teeth are embedded inside, and the first mass block and the second mass block vibrate at the same frequency, equal amplitude, and anti-phase along the Y axis;

所述的第一外框架左右两侧的杠杆41、42和第二外框架左右两侧的杠杆51、52的放大比例是通过调节杠杆支撑点位置设置的，实现哥氏力的放大功能，杠杆41、42、51、52的放大比例相同；The magnification ratio of the levers 41, 42 on the left and right sides of the first outer frame and the levers 51, 52 on the left and right sides of the second outer frame is set by adjusting the position of the lever support point to realize the amplification function of the Coriolis force. 41, 42, 51, and 52 have the same magnification ratio;

所述的杠杆41与杠杆42实现的力放大方向相同，杠杆51与杠杆52实现的力放大方向相同；The force amplification direction that described lever 41 realizes with lever 42 is identical, and the force amplification direction that lever 51 realizes with lever 52 is identical;

所述的杠杆41、42与杠杆51、52实现的力放大方向相反。The directions of force amplification realized by the levers 41, 42 and the levers 51, 52 are opposite.

本发明的原理如图1所示，静齿与动齿间构成了电容极板，在静齿上施加直流偏置电压和U₀和频率为ω_p的等频、反相交流电压，动齿上施加0伏电压，动齿与静齿间产生静电驱动力，该静电驱动力驱动第一质量块和第二质量块沿Y轴做频率为ω_p的等幅、反相振动。当垂直于芯片平面(Z)轴有外部转速Ω输入时，两质量块产生沿X轴方向的反相哥氏力，且分别通过内折叠梁传递到第一外框架和第二外框架上，第一外框架承载的哥氏力通过杠杆反方向放大后沿轴向作用到音叉谐振器自由端，第二外框架承载的反相哥氏力通过杠杆同方向放大后沿轴向作用到音叉谐振器自由端，实现了差分效应。当哥氏力作用在音叉谐振器一端时，谐振梁承受正弦变化的压缩和拉伸力，从而周期地调制音叉谐振器的谐振频率f，通过测得两端音叉谐振器的谐振频率差Δf，计算出作用在器件上的外部输入转速Ω。The principle of the present invention is shown in Figure 1, the capacitive plate is formed between the fixed teeth and the movable teeth, a DC bias voltage and U ₀ and an equal-frequency, anti-phase AC voltage with a frequency of ω _p are applied on the fixed teeth, and the movable teeth When a voltage of 0 volts is applied to the top, an electrostatic driving force is generated between the movable tooth and the fixed tooth, and the electrostatic driving force drives the first mass block and the second mass block to vibrate with equal amplitude and anti-phase at frequency ω _p along the Y axis. When there is an external rotational speed Ω input perpendicular to the chip plane (Z) axis, the two mass blocks generate anti-phase Coriolis forces along the X-axis direction, and transmit them to the first outer frame and the second outer frame through the inner folded beam respectively, The Coriolis force carried by the first outer frame is amplified in the opposite direction by the lever and acts on the free end of the tuning fork resonator in the axial direction, and the anti-phase Coriolis force carried by the second outer frame is amplified in the same direction by the lever and acts on the tuning fork resonator in the axial direction The free end of the device realizes the differential effect. When the Coriolis force acts on one end of the tuning fork resonator, the resonant beam bears sinusoidal compression and tension, thereby periodically modulating the resonant frequency f of the tuning fork resonator. By measuring the resonant frequency difference Δf of the tuning fork resonator at both ends, Calculate the external input speed Ω acting on the device.

双质量块调谐输出式硅MEMS陀螺仪每一个质量块内的静齿与动齿间的电容为：The capacitance between the fixed teeth and the movable teeth in each mass block of the dual-mass tuned output silicon MEMS gyroscope is:

$C C = = 22 nϵ nϵ \frac{{((L L - - y the y))}^{t t}}{{d d}_{00}} + + ((22 n no - - 11)) ϵ ϵ \frac{bt bt}{y the y},, - - - - - - ((11))$

式中，n为静齿数，ε为介电常数，L为静、动齿的长度，d₀为齿间距，t为齿厚，b为尺宽，y为动(静)齿端与静(动)齿根间的间距。由静电场理论可知，静电驱动力与成正比，对式(1)求偏导：In the formula, n is the number of static teeth, ε is the dielectric constant, L is the length of the static and movable teeth, d ₀ is the tooth spacing, t is the tooth thickness, b is the ruler width, y is the distance between the dynamic (static) tooth end and the static ( moving) spacing between tooth roots. According to the electrostatic field theory, the electrostatic driving force and is directly proportional to the partial derivative of formula (1):

$\frac{&PartialD; &PartialD; C C}{&PartialD; &PartialD; y the y} = = - - \frac{22 nϵt nϵt}{{d d}_{00}} - - \frac{((22 n no - - 11)) ϵbt ϵ bt}{{y the y}^{22}},, - - - - - - ((22))$

在工作过程中，y的变化量对静电力影响相对很小，动静齿间的静电力可近似写成：During the working process, the change of y has relatively little influence on the electrostatic force, and the electrostatic force between the moving and static teeth can be approximately written as:

${F f}_{d d} = = \frac{11}{22} \frac{&PartialD; &PartialD; C C}{&PartialD; &PartialD; y the y} {U u}_{D D.}^{22} \approx \approx - - \frac{11}{22} ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{D D.}^{22},, - - - - - - ((33))$

式中，y₀为静止时动(静)齿端与静(动)齿根间的间距。该静电力可近似为一常值，式中U_D表示在静齿上施加的直流偏置电压U_o、交流驱动电压U_i之和，第一质量块所受的静电力可表示为：In the formula, _y0 is the distance between the moving (static) tooth end and the static (moving) tooth root at rest. The electrostatic force can be approximated as a constant value, where U _D represents the sum of the DC bias voltage U _o and the AC drive voltage U _i applied to the fixed teeth, and the electrostatic force on the first mass can be expressed as:

${F f}_{d d 11} \approx \approx 22 ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} sin sin (({ω ω}_{p p} t t)),, - - - - - - ((44))$

式中，ω_D卢为交流驱动电压的频率。同理，第二质量块所受的静电力为：In the formula, ω _D Lu is the frequency of the AC driving voltage. Similarly, the electrostatic force on the second mass block is:

${F f}_{d d 22} \approx \approx - - 22 ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} sin sin (({ω ω}_{p p} t t)),, - - - - - - ((55))$

由式(4)和式(5)可知，质量块所受静电驱动力大小、频率相等，方向相反，耦合到支撑结构的能量相互转换抵消，减小了结构的振动噪声及器件的能量损耗，提高了陀螺仪的性能。It can be seen from formulas (4) and (5) that the magnitude and frequency of the electrostatic driving force on the mass block are equal and opposite, and the energy coupled to the supporting structure is mutually converted and offset, reducing the vibration noise of the structure and the energy loss of the device. Improved gyroscope performance.

为降低陀螺仪驱动模态的刚度，同时不加大结构平面尺寸，采用折叠梁结构，该梁可近似为四个悬臂梁串联，悬臂梁刚度可表示为：In order to reduce the stiffness of the gyroscope driving mode without increasing the plane size of the structure, a folded beam structure is adopted. The beam can be approximated as four cantilever beams connected in series. The stiffness of the cantilever beam can be expressed as:

${K K}_{c c} = = \frac{33 EI EI}{{L L}_{}},, - - - - - - ((66))$

式中，E为硅材料的弹性模量；I为梁转动惯量：L_b为梁的长度。折叠梁相当四个悬臂梁串联，其刚度可表示为：In the formula, E is the modulus of elasticity of the silicon material; I is the moment of inertia of the beam; L _b is the length of the beam. A folded beam is equivalent to four cantilever beams connected in series, and its stiffness can be expressed as:

${K K}_{t t} = = \frac{33 EI EI}{44 {L L}_{}^{b b}},, - - - - - - ((77))$

陀螺仪每个质量块通过四个相同的内折叠梁与外框架相连，每个质量块沿驱动模态的总刚度可表示为：Each mass of the gyroscope is connected to the outer frame through four identical inner folded beams, and the total stiffness of each mass along the driving mode can be expressed as:

$\begin{matrix} K K = = 44 K K,, = = \frac{33 EI EI}{{L L}_{b b}^{33}},, & I I = = \frac{{hw hw}^{33}}{1212},, - - - - - - ((88)) \end{matrix}$

式中，h为结构的厚度；w为内折叠梁的宽度。驱动模态自然频率可近似为：In the formula, h is the thickness of the structure; w is the width of the inner folded beam. The driving modal natural frequency can be approximated as:

$f f \approx \approx \frac{\sqrt{K K / / ((m m + + 0.375 0.375 {m m}_{l l}))}}{22 π π} = = \frac{11}{44 π π} \sqrt{\frac{E E. {w w}^{33}}{ρ ρ ((S S + + 0.375 0.375 {S S}_{l l})) {L L}_{}^{b b}}},, - - - - - - ((99))$

式中，m为每个质量块的有效质量；m_l为四个内折叠梁的总质量；ρ为硅材料的密度；S为每个质量块的表面积；S_l为四个内折叠梁的总表面积，驱动模态固有角速率可近似为：In the formula, m is the effective mass of each mass block; m _l is the total mass of the four inner folded beams; ρ is the density of the silicon material; S is the surface area of each mass block; S _l is the mass of the four inner folded beams The total surface area, driven mode intrinsic angular rate can be approximated as:

${ω ω}_{d d} = = 22 πf πf = = \frac{11}{22} \sqrt{\frac{E E. {w w}^{33}}{ρ ρ ((S S + + 0.375 0.375 {S S}_{l l})) {L L}_{}^{b b}}},, - - - - - - ((1010))$

第一质量块在静电力F_d1作用下沿驱动方向做恒幅振动，调制驱动交流电压角速率ω_p与驱动模态固有角速率ω_d一致时，第一质量块振幅最大，振动运动方程可表示为：The first mass vibrates with a constant amplitude along the driving direction under the action of the electrostatic force F _d1 , and when the angular rate ω _p of the modulated driving AC voltage is consistent with the intrinsic angular rate ω _d of the driving mode, the amplitude of the first mass is the largest, and the vibration equation can be expressed as Expressed as:

${y the y}_{11} = = Q Q \frac{{F f}_{d d 11}}{K K} = = \frac{Q Q}{K K} 22 ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} sin sin (({ω ω}_{p p} t t)),, - - - - - - ((1111))$

式中，Q为系统品质因子，表示驱动频率等于系统谐振频率的运动被放大了Q倍。同理，第二质量块的振动运动方程可表示为：In the formula, Q is the quality factor of the system, which means that the motion with the drive frequency equal to the resonance frequency of the system is amplified by Q times. Similarly, the vibration motion equation of the second mass block can be expressed as:

${y the y}_{22} = = Q Q \frac{{F f}_{d d 22}}{K K} = = - - \frac{Q Q}{K K} 22 ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} sin sin (({ω ω}_{p p} t t)),, - - - - - - ((1212))$

由方程(11)可知，第一质量块的运动速度为：It can be seen from equation (11) that the motion speed of the first mass block is:

${\overset{\cdot &Center Dot;}{y the y}}_{11} = = \frac{{Qω Qω}_{P P}}{K K} 22 ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} sin sin (({ω ω}_{p p} t t)),, - - - - - - ((1313))$

由方程(12)可知，第二质量块的运动速度为：It can be known from equation (12) that the motion speed of the second mass block is:

${\overset{\cdot \cdot}{y the y}}_{22} = = - - \frac{Q Q {ω ω}_{P P}}{K K} 22 ϵt ϵt ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} cos cos (({ω ω}_{p p} t t)),, - - - - - - ((1414))$

当垂直陀螺仪平面的Z轴有角速度Ω输入时，两质量块敏感Ω，产生沿X轴的哥氏力，第一质量块产生的哥氏力为：When the Z-axis perpendicular to the gyroscope plane has an angular velocity Ω input, the two mass blocks are sensitive to Ω and generate a Coriolis force along the X-axis. The Coriolis force generated by the first mass block is:

${F f}_{c c 11} = = 22 mΩ mΩ {\overset{\cdot &Center Dot;}{y the y}}_{11} = = \frac{44 mΩQ mΩQ {ω ω}_{P P} ϵt ϵt}{K K} ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} cos cos (({ω ω}_{p p} t t)),, - - - - - - ((1515))$

第二质量块产生的哥氏力为：The Coriolis force generated by the second mass block is:

${F f}_{c c 22} = = 22 mΩ mΩ {\overset{\cdot &Center Dot;}{y the y}}_{22} = = - - \frac{44 mΩQ mΩQ {ω ω}_{P P} ϵt ϵt}{K K} ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} cos cos (({ω ω}_{p p} t t)),, - - - - - - ((1616))$

两质量块产生的哥氏力F_c1和F_c2分别通过两对杠杆放大后传递到外框架两侧的两个音叉谐振器轴向上。The Coriolis forces F _c1 and F _c2 generated by the two mass blocks are respectively amplified by two pairs of levers and transmitted to the axial direction of the two tuning fork resonators on both sides of the outer frame.

$F_{1} = \frac{1}{2} C_{1} F_{c 1},$ $F_{2} = \frac{1}{2} C_{2} F_{c 2},$ C₁＝-C₂， (17) $f_{1} = \frac{1}{2} C_{1} f_{c 1},$ $f_{2} = \frac{1}{2} C_{2} f_{c 2},$ C ₁ =-C ₂ , (17)

式中，C₁为第一外框架左右两侧杠杆的放大系数，C₂分别为第二外框架左右两侧杠杆的放大系数，两质量块作用到每个音叉谐振器轴向自由端的哥氏力矢量和为：In the formula, C ₁ is the amplification factor of the levers on the left and right sides of the first outer frame, C ₂ is the amplification factor of the levers on the left and right sides of the second outer frame respectively, and the Coriolis force of the two mass blocks acting on the axial free end of each tuning fork resonator The force vector sum is:

$F f = = {F f}_{11} + + {F f}_{22} = = \frac{11}{22} {C C}_{11} (({F f}_{c c 11} - - {F f}_{c c 22})) = = \frac{44 {C C}_{11} mΩQ mΩQ {ω ω}_{P P} ϵt ϵt}{K K} ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} cos cos (({ω ω}_{p p} t t)),, - - - - - - ((1818))$

由于两个质量块产生的哥氏力通过杠杆差分后输入音叉谐振器，消除了外界加速度引起的误差，提高了器件性能。Since the Coriolis force generated by the two mass blocks is input to the tuning fork resonator through the difference of the lever, the error caused by the external acceleration is eliminated, and the performance of the device is improved.

音叉谐振器受到轴向时变哥氏力作用，弹性系数随之被调制，音叉运动方程可表示为：The tuning fork resonator is subjected to the axial time-varying Coriolis force, and the elastic coefficient is modulated accordingly. The tuning fork motion equation can be expressed as:

m_rq+c_rq+(k_r+k_lcos(ω_pt))q＝F_r， (19)m _r q+c _r q+(k _r +k _l cos(ω _p t))q=F _r , (19)

式中，m_r为音叉谐振器的质量，c_r为音叉谐振器的阻尼系数，k_r为音叉谐振器在未受哥氏力作用时系统的弹性系数，k_l为余弦轴向力对结构产生的调制弹性系数，F_r为外加在音叉谐振器上的驱动力。当考虑k_l调制作用，且k_l<<k_r时，音叉谐振器谐振频率为：In the formula, m _r is the mass of the tuning fork resonator, c _r is the damping coefficient of the tuning fork resonator, k _r is the elastic coefficient of the system when the tuning fork resonator is not subjected to the Coriolis force, k _l is the cosine axial force on the structure The resulting modulating elastic coefficient, F _r is the driving force applied to the tuning fork resonator. When k _l modulation is considered, and k _l <<k _r , the resonant frequency of the tuning fork resonator is:

${ω ω}_{r r} = = \sqrt{\frac{{k k}_{r r} + + {k k}_{l l} cos cos (({ω ω}_{P P} t t))}{{m m}_{r r}}} = = {ω ω}_{r r 00} + + \frac{{ω ω}_{r r 00}}{22} \frac{{k k}_{l l}}{{k k}_{r r}} cos cos (({ω ω}_{P P} t t)) - - \frac{{ω ω}_{r r 00}}{88} {((\frac{{k k}_{11}}{{k k}_{r r}} cos cos (({ω ω}_{p p} t t))))}^{22} + + \cdot &Center Dot; \cdot &Center Dot; \cdot &Center Dot;,, - - - - - - ((2020))$

式中，ω_r0为音叉谐振器初始谐振角速度，忽略二阶小量得：In the formula, ω _r0 is the initial resonance angular velocity of the tuning fork resonator, ignoring the second-order small quantity:

${ω ω}_{r r} \approx \approx {ω ω}_{r r 00} + + \frac{{ω ω}_{r r 00}}{22} \frac{{k k}_{l l}}{{k k}_{r r}} cos cos (({ω ω}_{p p} t t)),, - - - - - - ((21 twenty one))$

其中：in:

$\frac{{k k}_{l l}}{{k k}_{r r}} = = F f {S S}_{r r} = = 0.293 0.293 \frac{F f {L L}_{r r}^{22}}{E E. {t t}_{b b} {w w}_{} {b b}_{33}},, - - - - - - ((22 twenty two))$

式中，L_r为音叉谐振器中梁的长度，t_b为音叉谐振器中梁的厚度，w_b为音叉谐振器中梁的宽度，S_r为轴向力对音叉谐振器的调制系数。F为作用到音叉谐振器每个梁轴上的哥氏力。由调频技术的理论可知，在调制信号为单频正弦信号时，调频波的最大频偏与调制信号的振幅有关，与调制信号的频率无关，每个音叉谐振器的输出频率是在其谐振频率f_r0左右摆动，因哥氏力以等幅反相的形式作用在两个音叉谐振器上，构成差分输出，所以任一瞬时，左侧音叉谐振器频偏Δf₁大小等于右侧音叉谐振器频偏Δf₂，方向相反，即有：Δf₁＝-Δf₂，两个音叉谐振器的谐振频率差：In the formula, L _r is the length of the beam in the tuning fork resonator, t _b is the thickness of the beam in the tuning fork resonator, w _b is the width of the beam in the tuning fork resonator, and S _r is the modulation coefficient of the axial force on the tuning fork resonator. F is the Coriolis force acting on each beam axis of the tuning fork resonator. According to the theory of frequency modulation technology, when the modulation signal is a single-frequency sinusoidal signal, the maximum frequency deviation of the frequency modulation wave is related to the amplitude of the modulation signal and has nothing to do with the frequency of the modulation signal. The output frequency of each tuning fork resonator is at its resonant frequency f _r0 swings left and right, because the Coriolis force acts on the two tuning fork resonators in the form of equal amplitude and antiphase to form a differential output, so at any instant, the frequency deviation Δf ₁ of the left tuning fork resonator is equal to the right tuning fork resonator The frequency offset Δf ₂ is in the opposite direction, that is: Δf ₁ =-Δf ₂ , the resonance frequency difference between the two tuning fork resonators:

$δf δ f = = {Δf Δ f}_{11} + + {Δf Δf}_{22} = = \frac{0.586 0.586}{π π} {S S}_{r r} {ω ω}_{r r 00} \frac{{C C}_{11} mΩQ mΩQ {ω ω}_{P P} ϵt ϵt}{K K} \cdot \cdot ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} cos cos (({ω ω}_{p p} t t)) \cdot \cdot Ω Ω - - - - - - ((23 twenty three))$

外部转速与两音叉谐振器谐振频率差之间关系可表示为：The relationship between the external speed and the resonance frequency difference between the two tuning fork resonators can be expressed as:

Ω＝S·δfΩ＝S·δf

$S S = = 11 / / ((\frac{0.586 0.586}{π π} {S S}_{r r} {ω ω}_{r r 00} \frac{{C C}_{11} mΩQ mΩQ {ω ω}_{P P} ϵt ϵt}{K K} \cdot \cdot ((\frac{22 n no}{{d d}_{00}} + + ((22 n no - - 11)) \frac{b b}{{y the y}_{00}^{22}})) {U u}_{00} {U u}_{i i} cos cos (({ω ω}_{p p} t t)))) - - - - - - ((24 twenty four))$

式中，S为双质量块调谐输出式硅MEMS陀螺仪的标度因数。当垂直陀螺仪平面Z轴有角速度Ω输入时，两质量块产生的哥氏力通过杠杆放大后输入到音叉谐振器的自由端，周期变化的压缩、拉伸力对音叉谐振器的谐振频率进行调解，两个音叉谐振器的谐振频率可以通过音叉谐振器的测量静齿端测出，通过测得两端音叉谐振器的谐振频率差的大小来计算外部转速。In the formula, S is the scale factor of the dual-mass tuned output silicon MEMS gyroscope. When the Z axis of the vertical gyro plane has an angular velocity Ω input, the Coriolis force generated by the two mass blocks is amplified by the lever and then input to the free end of the tuning fork resonator, and the periodically changing compression and stretching force adjusts the resonance frequency of the tuning fork resonator For mediation, the resonant frequency of the two tuning fork resonators can be measured by measuring the static tooth end of the tuning fork resonator, and the external rotational speed can be calculated by measuring the difference between the resonant frequencies of the tuning fork resonators at both ends.

本发明与现有技术相比的优点在于：双质量块调谐输出式硅MEMS陀螺仪采用两块同频、等幅、反相振动的质量块作为敏感单元，两个高频振动质量块耦合到支撑结构的能量相互抵消，可以减小器件的振动噪声和能量损耗；杠杆差分效应消除了外界加速度引起的误差，提高了器件性能。Compared with the prior art, the present invention has the advantages that: the dual-mass tuning output silicon MEMS gyroscope adopts two mass blocks vibrating at the same frequency, equal amplitude and anti-phase as sensitive units, and the two high-frequency vibrating mass blocks are coupled to The energy of the supporting structure cancels each other, which can reduce the vibration noise and energy loss of the device; the leverage differential effect eliminates the error caused by the external acceleration and improves the performance of the device.

附图说明 Description of drawings

图1为双质量块调谐输出式硅MEMS陀螺仪工作原理框图；Figure 1 is a block diagram of the working principle of a dual-mass tuned output silicon MEMS gyroscope;

图2为双质量块调谐输出式硅MEMS陀螺仪结构图；Figure 2 is a structural diagram of a dual-mass tuned output silicon MEMS gyroscope;

图3为双质量块调谐输出式硅MEMS陀螺仪静齿和动齿结构图。Fig. 3 is a structural diagram of the static and movable teeth of the dual-mass tuned output silicon MEMS gyroscope.

具体实施方式 Detailed ways

本发明技术解决方案的具体实施结构如图2和图3所示，一种双质量块调谐输出式硅MEMS陀螺仪主要由静齿101、动齿102、第一质量块1、第二质量块7、第一外框架3、第二外框架6、杠杆41、42、51、52和两个音叉谐振器81、82组成。静齿101和动齿102构成了电容式极板，第一质量块1和第二质量块7内部嵌入梳状动齿，结构完全相同，两质量块沿Y轴做同频、等幅、反相振动，第一质量块1通过四个内折叠梁11、12、13、14连接在第一外框架3上，第二质量块7通过四个内折叠梁71、72、73、74连接在第二外框架6上，考虑陀螺仪功耗及灵敏度，设计两质量块沿Y轴的固有频率为1000～10000Hz，本实施方案设计两质量块沿Y轴的固有频率为2000Hz，第一外框架3通过外支撑梁31、32固连在锚点21、22上，第二外框架6通过外支撑梁61、62固连在锚点23、24上，第一外框架3和第二外框架6之间通过折叠梁361、362相连。第一外框架3左右两侧分别通过反方向力放大杠杆41、42与音叉谐振器81、82自由端相连，第二外框架6左右两侧分别通过同方向力放大杠杆51、52与音叉谐振器81、82自由端相连，锚点411、421分别为杠杆41、42支撑点，锚点511、521分别为杠杆51、52支撑点，通过调节支撑点位置设置杠杆的放大比例，实现哥氏力的放大功能，杠杆41、42、51、52放大比例相同，杠杆41、42与杠杆51、52实现的哥氏力放大方向相反，在结构尺寸约束下，设计两杠杆的放大倍数为10～100，本实施方案设计两杠杆的放大倍数为50，音叉谐振器81、82固定端分别与锚点91、92相连。双质量块调谐输出式硅MEMS陀螺仪采用LIGA技术制备而成，是通过溅射、刻蚀等工艺制备的整体硅结构。为了保证产生适合的静电驱动力，本实施方案在静齿101上施加12伏直流偏置电压和角频率为2000Hz的等频、反相交流12伏电压，动齿102上施加0伏电压，动齿与静齿间产生的静电驱动力驱动第一质量块1和第二质量块7沿Y轴做角频率为ω_p的反相、等幅振动，为了保证静齿端不与动齿根相碰，提高器件工作可靠性，设计质量块振幅小于静齿端到动齿根距离的五分之一至三分之一，本实施方案设计质量块振幅小于静齿端到动齿根距离的五分之一。当垂直于芯片平面(Z)轴有外部转速Ω输入时，两质量块产生沿X轴方向的反方向哥氏力，第一质量块1通过四个内折叠梁11、12、13、14将哥氏力传递到第一外框架3上，第二质量块7通过四个内折叠梁71、72、73、74将哥氏力传递到第二外框架6上，第一外框架3承载的哥氏力通过反方向力放大杠杆41、42放大后轴向作用到音叉谐振器81、82自由端，第二外框架6承载的哥氏力通过同方向力放大杠杆51、52放大后轴向作用到音叉谐振器81、82自由端，实现了差分效应。由谐波检测原理可知，音叉谐振器81、82的固有频率应大于第一质量块1和第二质量块7振动频率一个数量级以上，本实施方案设计的音叉谐振器81、82的固有频率为30000Hz，当哥氏力作用在音叉谐振器81、82一端时，谐振梁承受正弦变化的压缩和拉伸力，从而周期地调制音叉谐振器81、82的谐振频率f，通过测得两端音叉谐振器的谐振频率差Δf，计算出作用在器件上的外部输入转速Ω。The specific implementation structure of the technical solution of the present invention is shown in Figure 2 and Figure 3, a dual-mass tuned output silicon MEMS gyroscope is mainly composed of a fixed tooth 101, a movable tooth 102, a first mass 1, a second mass 7. Composed of the first outer frame 3, the second outer frame 6, levers 41, 42, 51, 52 and two tuning fork resonators 81, 82. The fixed teeth 101 and the movable teeth 102 constitute capacitive plates. The first mass 1 and the second mass 7 are embedded with comb-shaped movable teeth, which have the same structure. phase vibration, the first mass block 1 is connected to the first outer frame 3 through four inner folded beams 11, 12, 13, 14, and the second mass block 7 is connected to the On the second outer frame 6, considering the power consumption and sensitivity of the gyroscope, the natural frequency of the two mass blocks along the Y axis is designed to be 1000-10000 Hz. In this embodiment, the natural frequency of the two mass blocks along the Y axis is designed to be 2000 Hz. The first outer frame 3 is fixed on the anchor points 21 and 22 through the outer support beams 31 and 32, and the second outer frame 6 is fixed on the anchor points 23 and 24 through the outer support beams 61 and 62. The first outer frame 3 and the second outer frame 6 are connected by folding beams 361 and 362. The left and right sides of the first outer frame 3 are respectively connected to the free ends of the tuning fork resonators 81 and 82 through opposite direction force amplification levers 41 and 42, and the left and right sides of the second outer frame 6 are respectively through the same direction force amplification levers 51 and 52 to resonate with the tuning fork The free ends of 81 and 82 are connected, the anchor points 411 and 421 are the support points of the levers 41 and 42 respectively, and the anchor points 511 and 521 are the support points of the levers 51 and 52 respectively. Force amplification function, the amplification ratio of levers 41, 42, 51, and 52 is the same, and the amplification direction of the Coriolis force realized by levers 41, 42 and levers 51, 52 is opposite. Under the constraint of structural size, the amplification factor of the two levers is designed to be 10~ 100. In this embodiment, the magnification of the two levers is designed to be 50, and the fixed ends of the tuning fork resonators 81 and 82 are connected to the anchor points 91 and 92 respectively. The double-mass tuned output silicon MEMS gyroscope is prepared by LIGA technology, and is an integral silicon structure prepared by sputtering, etching and other processes. In order to ensure that a suitable electrostatic driving force is generated, in this embodiment, a 12-volt DC bias voltage and an equal-frequency, anti-phase AC 12-volt voltage with an angular frequency of 2000 Hz are applied to the fixed teeth 101, and a 0-volt voltage is applied to the movable teeth 102. The electrostatic driving force generated between the teeth and the fixed teeth drives the first mass block 1 and the second mass block 7 to vibrate along the Y-axis with anti-phase and constant amplitude at the angular frequency _ωp , in order to ensure that the end of the fixed tooth does not align with the root of the movable tooth To improve the reliability of the device, the amplitude of the design mass is less than one-fifth to one-third of the distance from the fixed tooth end to the movable tooth root. In this embodiment, the designed mass amplitude is less than five one-third. When there is an external rotational speed Ω input perpendicular to the chip plane (Z) axis, the two mass blocks generate a Coriolis force in the opposite direction along the X-axis direction, and the first mass block 1 is moved by four inner folded beams 11, 12, 13, 14 The Coriolis force is transmitted to the first outer frame 3, and the second mass block 7 transmits the Coriolis force to the second outer frame 6 through four inner folded beams 71, 72, 73, 74. The first outer frame 3 carries The Coriolis force acts on the free ends of the tuning fork resonators 81 and 82 in the axial direction after being amplified by the force amplification levers 41 and 42 in the opposite direction. Acting on the free ends of the tuning fork resonators 81 and 82, a differential effect is realized. It can be seen from the principle of harmonic detection that the natural frequencies of the tuning fork resonators 81 and 82 should be greater than the vibration frequencies of the first mass block 1 and the second mass block 7 by an order of magnitude or more. The natural frequencies of the tuning fork resonators 81 and 82 designed in this embodiment are 30000Hz, when the Coriolis force acts on one end of the tuning fork resonator 81, 82, the resonant beam bears sinusoidally changing compression and tension, thereby periodically modulating the resonant frequency f of the tuning fork resonator 81, 82, by measuring the tuning fork resonator at both ends The resonant frequency difference Δf of the resonator is used to calculate the external input speed Ω acting on the device.

该双质量块调谐输出式硅MEMS陀螺仪克服了现有调谐输出式硅MEMS陀螺仪振动噪声大、外部加速度引起的测量误差大等的不足，具有振动噪声和能量损耗小、无外界加速度引起的误差，精度高等优点可应用于微小型系统的导航及控制，并可以应用于工作时间短、成本低、动态范围大的战术武器的惯性导航系统。The dual-mass tuned output silicon MEMS gyroscope overcomes the shortcomings of the existing tuned output silicon MEMS gyroscope, such as large vibration noise and large measurement error caused by external acceleration, and has small vibration noise and energy loss, and no external acceleration. The advantages of error and high precision can be applied to the navigation and control of micro-miniature systems, and can be applied to the inertial navigation system of tactical weapons with short working time, low cost and large dynamic range.

本发明说明书中未作详细描述的内容属于本领域专业技术人员公知的现有技术。The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Claims

1. A dual-mass tuning output silicon MEMS gyroscope is characterized in that: it mainly consists of stationary teeth (101), movable teeth (102), first mass (1), second mass (7), the first mass An outer frame (3), a second outer frame (6), levers (41), (42), (51), (52) and two tuning fork resonators (81), (82) form. The static tooth (101) and the movable tooth (102) constitute a capacitive pole plate, and the first mass block (1) is connected on the first On the outer frame (3), the second quality block (7) is connected on the second outer frame (6) by four inner folding beams (71), (72), (73), (74), and the first outer frame (3) be fixedly connected on the anchor points (21), (22) by the outer support beams (31), (32), and the second outer frame (6) is fixedly connected on the anchor points by the outer support beams (61), (62) On points (23), (24), the first outer frame (3) and the second outer frame (6) are connected by folded beams (361), (362); the left and right sides of the first outer frame (3) are respectively The free ends of the tuning fork resonators (81), (82) are connected through the levers (41), (42), and the left and right sides of the second outer frame (6) are respectively connected with the tuning fork resonators (81) through the levers (51), (52). ), (82) free ends; anchor points (411), (421) are respectively the supporting points of levers (41), (42), and anchor points (511), (521) are respectively levers (51), (52 ), the fixed ends of the tuning fork resonators (81), (82) are connected to the anchor points (91), (92) respectively, and the external input speed is calculated by measuring the resonance frequency difference of the tuning fork resonators at both ends;

2. The dual-mass tuned output silicon MEMS gyroscope according to claim 1, characterized in that: the first mass (1) and the second mass (7) are identical in structure, and are embedded in a comb-shaped Moving teeth, the first mass (1) and the second mass (7) vibrate at the same frequency, equal amplitude, and anti-phase along the Y axis;

3. The dual-mass tuning output silicon MEMS gyroscope according to claim 1, characterized in that: the levers (41), (42) and the second outer frame on the left and right sides of the first outer frame (3) (6) The enlargement ratio of the levers (51), (52) on the left and right sides is set by adjusting the position of the support point of the lever, so as to realize the enlargement function of the Coriolis force, the levers (41), (42), (51), ( 52) have the same magnification ratio;

4. according to claim 1 or 3 described dual-mass tuning output silicon MEMS gyroscopes, it is characterized in that: the force amplification direction that described lever (41) and lever (42) realize is identical, and lever (51) and lever (52) The force amplification directions realized are the same;

5. The dual-mass tuning output silicon MEMS gyroscope according to claim 1 or 3, characterized in that: the force amplification direction realized by the lever (41), (42) and the lever (51), (52) on the contrary.