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摘要:
双连孔力传感器在航空航天和工业计量等领域中应用广泛，但因其结构中存在变截面设计，导致其载荷位移特性和应变载荷关系较难解析描述，进而影响含双连孔结构的多维力传感器设计与性能优化。基于此，基于弹性梁理论，推导得到变截面力敏单元的柔度矩阵和应变载荷关系，进而通过柔度矩阵建模方法构建出双连孔力传感器的整体柔度模型，并以此为桥梁，获得双连孔结构上力敏单元应变片感知应变与传感器测力端作用载荷间的解析映射关系。通过有限元和实验分别对所构建的模型和应变解析关系进行验证。结果表明：期望维解析柔度相对有限元结果误差控制在3%以内，桥路输出电压理论相对于实验结果误差控制在5%以内，说明推导得到的解析公式可用于正确评价双连孔力传感器载荷位移特性和桥路输出应变与测力载荷间的映射，进而为含双连孔结构的多维力传感器优化设计提供可靠的理论技术支持。
Abstract:Double-hole force sensors are widely used in aerospace, industrial metrology and other fields, but their load-displacement characteristics and strain-load relationship are difficult to be formulated analytically due to the variable cross-section design, which will affect the design and performance optimization of multi-axis force sensors with double-hole structure. This study uses the compliance matrix modeling method to build the overall compliance model of the double-hole force sensor after determining the compliance matrix and strain-load relationship of the force-sensitive element with variable cross-section based on the elastic-beam theory. The analytical relationship between the sensed strain of the strain gauges on the force-sensitive element of the double-hole structure and the applied load acting on the force-measuring end of the sensor is finally obtained with the compliance model. The presented model and strain analytical relationship are validated by the finite element analysis and experiment, respectively. The results show that the relative errors for the expected-dimensional analytical compliances relative to finite element results are within 3%, and the bridge output voltages are within 5% compared with experimental results. These findings demonstrate that the analytical equations that were derived are capable of accurately assessing the load-displacement characteristics of double-hole force sensors as well as the mapping between applied loads and bridge output strains. They can also offer dependable technical assistance for the best possible design of multi-axis force sensors that have double-hole structures.
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Key words:
- force sensor /
- double-hole structure /
- compliance modeling /
- strain analysis /
- calibration experiment
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图 10 桥路输出电压与作用载荷间的关系
Figure 10. Relationships between bridge output voltage and applied loads
表 1 力传感器结构参数
Table 1. Structural parameters of force sensors
mm 算例 w r t lfs r0 lb h l 1 12 6 1 12 6 20 20 7 2 12 7 1.1 14 7 16 20 7 3 14 7 1.2 14 7 16 20 7 4 12 8 1.2 16 8 12 20 7 
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表 2 期望维解析柔度与有限元结果对比
Table 2. Comparison of analytical results relative to finite element results
算例 An/10−6(m·N−1) FE/10−6(m·N−1) Err/% 1 13.997 14.198 1.42 2 10.574 10.759 1.72 3 7.291 7.450 2.13 4 8.019 8.200 2.21
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表 3 输出应变和最大等效应力结果对比
Table 3. Comparison for the output strain and the maximum equivalent stress
算例 εout σmax/MPa Fx=1 N Fy=1 N Fz=1 N Mx=1 N·mm My==1 N·mm Mz=1 N·mm Fx=1 N Fy=1 N Fz=1 N Mx=1 N·mm My==1 N·mm Mz=1 N·mm 1 2.3×10−6 −46.2 3.9×10−5 −2.5×10−6 −3.1×10−6 −4.2×10−5 8.4×10−2 4.1 1.6 6.0×10−2 3.5×10−2 7.9×10−3 2 2.5×10−7 −36.1 −3.9×10−5 1.8×10−6 9.6×10−7 −2.8×10−5 7.5×10−2 3.2 1.3 5.1×10−2 3.1×10−2 7.1×10−3 3 6.8×10−6 −26.1 1.2×10−4 2.2×10−6 −4.5×10−6 −4.8×10−5 5.8×10−2 2.3 0.9 3.5×10−2 2.1×10−2 5.5×10−3 4 −3.9×10−5 −28.4 2.9×10−5 7.7×10−8 −9.5×10−7 −1.3×10−5 6.8×10−2 2.57 1.2 4.3×10−2 2.7×10−2 6.4×10−3
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