Development of internal strain gauge balance with variable cross-section axial force flex beam based on Finite Element Analysis
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摘要: 内式应变天平的轴向力元件结构在受到大载荷尤其是大力矩载荷后，其支撑片上的最大应力是限制天平最大承载能力的主要因素。研制了一台大力矩内式应变天平，并采用有限元分析方法对轴向力元件的支撑片和测量梁进行了优化和改进。将支撑片的外形由传统的等截面改进为变截面，减小支撑片中间部位的厚度，并增加两端的厚度，在保持天平轴向刚度一致的基础上，降低了支撑片上的最大应力；采用变截面结构的轴向力测量梁，减小了测量梁上的应变梯度。有限元分析结果表明：与传统的等截面支撑片相比，变截面支撑片上的应力分布比较均匀，其根部最大应力减小了20%以上；与等截面测量梁相比，变截面测量梁上的应变梯度降低了79%。天平校准结果与有限元分析结果一致，风洞测力试验也表明该天平具有良好的稳定性。Abstract: When the axial section of internal strain gauge balance is applied large load, especially large moment load, the maximum stress of its flex beam often becomes the main factor limiting the maximum load capacity of the balance. This paper introduces the development of a large moment internal strain gauge balance. The flex beam and measuring beam of the axial section are optimized and improved by using finite element simulation analysis. The shape of the flex beam is improved from traditional constant cross section to variable cross section. The thickness of the middle part of the flex beam is reduced, and the thickness of both ends is increased. The maximum stress on the flex beam is reduced on the basis of maintaining the same axial stiffness of the balance. The axial force measuring beam adopts variable section structure, which reduces the strain gradient on the measuring beam. The finite element analysis shows that the stress distribution on the variable-section flex beam is more uniform than that of the traditional flex beam, and the maximum stress at the root of the variable-section flex beam is reduced by more than 20%. The strain gradient on the measuring beam with variable cross section is reduced by 79% compared with that on the beam with constant cross section. The calibration results of the balance are in good agreement with the finite element analysis results, and the wind tunnel force test also shows that the balance has good stability.
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Key words:
- strain gauge balance /
- finite element /
- axial section /
- flex beam /
- stress
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图 5 轴向力测量元件在滚转力矩作用下的应变
Figure 5. The strain of axial measuring beam caused by rolling moment
图 10 轴向力测量元件在滚转力矩作用下的应变
Figure 10. The strain of axial force measuring beam by rolling moment
表 1 天平设计载荷
Table 1. The design loads of balance
Y / N Mz /（N·m） X / N Mx /（N·m） Z / N My /（N·m） 15000 1200 1500 1400 4000 600 
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表 2 天平有限元应变分析结果
Table 2. Finite element strain analysis results of balance
天平分量 Y Mz X Mx Z My 设计应变/10–6 496 654 422 917 238 591 灵敏度/（mV·V–1） 1.09 1.44 0.93 1.84 0.52 1.30 对X干扰应变/10–6 11.0 0 —— 1.0 0.5 0 对X干扰占比/% 2.2 0 —— 0.1 0.2 0
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表 3 天平静态校准结果
Table 3. Balance calibration results
天平分量 Y Mz X Mx Z My 灵敏度/（mV·V–1） 1.03 1.36 0.91 1.79 0.50 1.25 对X一次干扰/% 3.0 0.8 —— 0.1 1.2 0.9 综合加载误差/% FS 0.03 0.06 0.11 0.09 0.05 0.06
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表 4 Ma = 0.75时重复性试验纵向气动导（系）数
Table 4. Longitudinal aerodynamic coefficient of repeatability test at Ma = 0.75
车次号 CLα ${C_{m{C_L}}}$ Cm0 CD0 Kmax 20202361 0.07858 0.01331 0.00619 0.01192 18.44076 20202420 0.07819 0.01193 0.00616 0.01193 18.51446
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