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受到体积、质量条件约束,具有多轴测量的微小型传感器,相互交错的内部结构、无法直接采用机械加工或者3D打印技术实现。文中采用分立元件交错组合的方法设计传感器。传感器主要由基座外壳、封装外壳、弹片、质量块和光纤光栅组成。为满足传感器的微型化,使结构更加紧凑,将一个弹片和三个质量块组成设计为一个弹性元件,再将三个两两垂直且互不干扰的弹性元件在空间上交错组合于外壳上,最后在三个弹性元件和外壳之间使用两点封装方式固定三个光栅,实现三轴振动测量。传感器结构示意如图1所示。
当外界产生作用于传感器的振动时,固定在弹片上的质量块会沿着垂直于弹片的方向做往复运动,从而拉伸光纤光栅使其产生轴向应变,中心波长发生漂移,通过监测中心波长的变化即可监测振动[12]。
当受到沿着X轴方向的加速度时,固定在弹片上的质量块会绕着X轴方向做往复运动,传感器的力学分析图如图2所示。
传感器处于稳态时,力矩平衡方程为:
$$ mad-{k}_{f}h\Delta l-K\theta =0 $$ (1) 式中:m为质量块的总重量;a为沿着X轴方向的加速度;d为非接触弹片中心到质量块质心的距离;kf为光纤的弹光系数;h为非接触弹片中心到FBG所处位置的高度;Δl为FBG的形变量;K为非接触弹片的转动刚度;θ为弹片的转动角度。
光纤的弹光系数为:
$$ {k}_{f}=\frac{{A}_{f}{E}_{f}}{l} $$ (2) 式中:kf为光纤的弹光系数;Af为光纤的横截面积;Ef为FBG的弹性模量;l为FBG两个固定点之间的长度。根据几何关系可以得到:
$$ \Delta l=h\theta $$ (3) 根据弹性元件的刚度公式,镍钛合金弹片的刚度为[12]:
$$ K=\frac{a{c}^{3}E}{4{b}^{3}} $$ (4) 式中:K为钛合金弹片的刚度;a为弹片宽度;b为弹片无接触的长度;c为弹片厚度;E为镍钛合金弹片的杨氏模量。
传感器的灵敏度与FBG中心波长偏移量和加速度的关系可以表示为:
$$ S=\frac{\Delta \lambda }{a} $$ (5) 式中:S为传感器的灵敏度;Δλ为FBG中心波长偏移量;a为加速度。
为了方便求解计算,将转动惯量转化为[13]:
$$ J=2{d}^{3}m $$ (6) 式中:J为转动惯量。
根据系统的动力学方程得到系统的固有频率f为[14]:
$$ f=\frac{1}{2\pi }\sqrt{\frac{{K}_{f}{h}^{2}+K}{J}}=\frac{1}{2\pi }\sqrt{\frac{{K}_{f}{h}^{2}+K}{2{d}^{2}m}} $$ (7) 式中:f为转动惯量。
由上述公式可知,FBG振动传感器的谐振频率和灵敏度两个重要性能指标存在相互制约的关系,对传感器结构进行设计时,需综合考虑传感器性能和尺寸,并对结构参数进行分析。
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由理论分析可知,传感器的固有频率和灵敏度主要与弹片厚度c、质量块质量m有关。由公式(4)、(5)和(7)分析可得,弹片厚度c越大,传感器固有频率f越大,灵敏度越小,因此弹片厚度c应尽量小;由公式(2)、(5)和(7)可知,传感器的灵敏度与FBG的长度l有直接关系,但与固有频率无关,当长度l越小,FBG中心波长的漂移量∆λ越大,灵敏度S则越大[13],故确定FBG的有效长度l为1 mm。光纤与传感器的结构参数如表1所示。
表 1 光纤与传感器结构参数
Table 1. Optical fiber and sensor structure parameters
Parameter Parameter name Value $l$ Optical fiber span/mm 1 Ef Young's modulus of optical fibers/GPa 72 Af Cross sectional area of the optical fiber/mm2 0.005024 df Fiber diameter/mm 0.08 a Width of the sheet/mm 6 b Shrapnel non-contact length/mm 2 c Thickness of sheet/mm 0.3 d The distance from the top of the mass to
the center of the shrapnel/mm10 h The distance from the center of gravity
of the mass to the center of the shrapnel/mm5.5 经迭代发现传感器的质量块质量是影响传感器性能最重要的因素,但受限于传感器的微型化特点,因此需要采用高密度、可机械加工的材料制作质量块。金属钽具有密度大、温度稳定性好、热膨胀系数较低等性能,满足制作质量块的要求,最终确定的质量块质量为3.48 g。基座外壳采用黄铜材料,弹片采用高屈服强度的镍钛合金。
确定结构参数和材料后,使用Solidworks软件对传感器进行建模,为验证传感器的性能,将传感器模型导入COMSOL软件中进行有限元仿真分析。先对导入的传感器元件进行参数设置,使用密度高的钽材料制作质量块,钽的杨氏模量别为186 GPa,泊松比为0.34。弹片的材料为镍钛合金,镍钛合金的杨氏模量为118.6 GPa,泊松比为0.33。基座外壳采用黄铜制作,黄铜的杨氏模量为90 GPa,泊松比为0.324。再添加物理场,对传感器的外壳和弹片施加固定约束,并沿着垂直镍钛合金弹片的方向施加1 g的标准地球重力,添加特征频率研究进行仿真,得到传感器振型图,如图3所示。由仿真的振型图可知,传感器的特征频率为1792.8 Hz。
接着添加频域研究,设置频率范围为0~2700 Hz,步长为50 Hz,通过仿真先得到应力分布图,如图4所示,再得到传感器幅频响应仿真结果,如图5所示。
由应力分布图4可知传感器产生的形变主要集中于外壳和质量块之间无接触的弹片上,满足应力集中原理。由图5可得,传感器的特征频率为1792.8 Hz,并且传感器的平坦区间为0~1500 Hz。
Research on miniature three-axis vibration sensor based on FBG
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摘要: 为了研制一种微小型、三轴测量的高灵敏度振动传感器,提出一种分立元件交错组合的超紧凑光纤光栅三轴振动传感器设计方法。采用分立元件组合设计方法降低了设计加工难度,与一体化设计对比,分立元件组合结构的零件结构简单、易于加工、结构设计也更为灵活,缩短了传感器结构的优化迭代周期。通过理论模型分析和有限元仿真,优化传感器结构参数,最终封装完成的尺寸为15 mm×15 mm×15 mm,质量约为24.26 g。最后进行实验测试和传感器性能分析。实验结果表明:该传感器的工作频段为0~1 200 Hz,在X、Y、Z轴方向的固有频率分别为1 850 Hz、1 770 Hz和1 860 Hz,三个轴向的灵敏度分别达到77.37 pm/g、80.73 pm/g和75.04 pm/g,横向抗干扰小于5%。该传感器满足航天振动测量轻量化、工作范围和灵敏度的应用需求,在遥感卫星微振动测量等领域具有重要应用前景。Abstract:
Objective Vibration measurement plays an essential role in machinery fault diagnosis and structural health monitoring, and vibration sensors are the most important tool in measuring equipment. Electrical vibration sensor technology is relatively mature, with the benefits of low cost, but there are drawbacks such as poor circuit stability, poor signal noise, and easy electromagnetic interference. In contrast, fiber Bragg grating vibration sensor has numerous advantages such as anti-electromagnetic interference, high and low temperature resistance, corrosion resistance, and so on, and is widely used in aerospace, large-scale structure monitoring, industrial propulsion, etc. Methods The high-density tantalum block serves as the mass block, the nickel-titanium alloy serves as the elastic beam, and the ultra-short fiber grating serves as the sensitive element in the vibration sensor. The mass block fixed to the shrapnel will reciprocate as the sensor vibrates due to external forces. This reciprocating motion will stretch the fiber grating and cause axial strain, which causes the center wavelength to wander. The shift in the center wavelength can be used to track the vibration. The vibration sensor's packaging is finished, and the amplitude-frequency and sensitivity characteristics of the sensor are carefully investigated by developing the necessary packaging platform and test equipment. Results and Discussions The sensor has a broad frequency spectrum, high sensitivity and excellent lateral anti-interference performance. The frequency range for operation is 0 to 1 200 Hz. The characteristic frequencies are 1 850 Hz, 1 770 Hz and 1 860 Hz in the X, Y and Z directions, respectively. The sensitivities in the three directions are 77.37 pm/g, 80.73 pm/g, and 75.04 pm/g respectively, and lateral anti-interference is less than 5%. Conclusions This article successfully designs an ultra-compact three-axis vibration sensor. The packaged sensor has considerable application possibilities in the satellite micro-vibration measurement due to its advantages of light weight, a wide operating frequency band, and high sensitivity. -
Key words:
- fiber Bragg grating /
- triaxial vibration sensor /
- microminiaturization /
- high sensitivity
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表 1 光纤与传感器结构参数
Table 1. Optical fiber and sensor structure parameters
Parameter Parameter name Value $l$ Optical fiber span/mm 1 Ef Young's modulus of optical fibers/GPa 72 Af Cross sectional area of the optical fiber/mm2 0.005024 df Fiber diameter/mm 0.08 a Width of the sheet/mm 6 b Shrapnel non-contact length/mm 2 c Thickness of sheet/mm 0.3 d The distance from the top of the mass to
the center of the shrapnel/mm10 h The distance from the center of gravity
of the mass to the center of the shrapnel/mm5.5 -
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