STUDY ON THE EFFECT OF VARIABLE STIFFNESS CHARACTERISTICS ON PROPULSION PERFORMANCE OF ANGUILLIFORM FISH
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摘要: 生物学研究表明, 波动推进鱼类的鱼体刚度对其推进性能有着重要影响, 通过改变鱼体刚度可获得优异的游动特性, 但鱼类肌肉驱动模式与鱼体刚度和游动性能的关系尚不清晰. 鉴于此, 本文以鳗鲡科鱼类作为研究对象, 基于粘弹性梁理论和Taylor流体理论, 建立由生物学钙离子肌肉驱动的鳗鲡科鱼类游动模型, 研究肌肉驱动和鱼体刚度变化对推进性能的影响. 结果表明, 肌肉驱动力随刚度增加呈先快速增加后缓慢下降的变化趋势, 而随着肌肉驱动力增加, 鱼体游动速度随刚度增加而增加并逐渐趋于稳定. 当肌肉驱动频率由1Hz增加到2Hz时, 游动速度和启动加速度可分别提升55%和129%, 可见增大鱼体刚度可显著提升推进性能. 为了验证上述结论, 设计了基于串并联结构的变刚度实验平台, 实验表明鱼体的变刚度特性能显著提升推进性能. 当舵机驱动频率由1 Hz增加到2 Hz时, 通过统一变化弹簧刚度大小推力可提升2.5倍. 上述研究结果可为改变鱼体刚度提升游动性能提供参数设计指导, 为研制变刚度仿生机器鱼提供了理论依据.Abstract: Biological studies show that the stiffness of fish body has a significant impact on their propulsive performance, and the excellent swimming abilities can be achieved by varying body stiffness. However, the complex relations among the muscle actuations, the body stiffness and the swimming performance are still unclear. Therefore, the body of anguilliform fish, taken as the research object, is modelled by a viscoelastic beam in present study, and the Taylor resistance fluid theory is adopted to establish swimming fish model, in which the kinetic model of calcium ions is used to model the muscle actuations. The effects of muscle actuation and the variable body stiffness on the propulsive performance are analyzed. The results showed that with the increase of body stiffness, the force of muscle actuation was increased rapidly and then decreased slowly. When the force of muscle actuation increased, the forward speed increased with the body stiffness, and then phoned to stable gradually. When the frequency of muscle actuation was increased from 1Hz to 2Hz, the swimming speed and the start acceleration can be increased by 55% and 129%, respectively. These results indicated that the propulsion performance of swimming fish can be significantly improved by increasing the body stiffness. To verify these conclusions, an experiment platform, based on the series-parallel mechanism with variable stiffness, was proposed in present study, and the results also found that the variable stiffness of fish body had a significantly influence on the propulsive performance. In the experiments, the thrust can be increased by 2.5 times when the driving frequency of the servo was increased from 1Hz to 2Hz, and the spring stiffness was uniformly changed. Overall, these results throw a light to design robotic fish with better swimming performance by changing the body stiffness, and provide a theoretical basis for developing a robotic fish with variable stiffness.
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Key words:
- anguilliform fish /
- muscle actuation /
- variable stiffness /
- swimming performance
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图 1 基于粘弹性变截面梁的鱼游模型
Figure 1. The dynamic model of fish body based on the viscoelastic rod with variable cross-sections
图 4 基于钙离子肌肉力模型产生的驱动力
Figure 4. The driving force generated based on the kinetic model of calcium ions
图 8 不同频率下肌肉驱动幅值系数对游动速度的影响
Figure 8. The effects of muscle force coefficient on swimming speed at different frequencies
图 9 不同驱动幅值下鱼体刚度对游动速度的影响
Figure 9. The effects of Young’s modulus of fish body on swimming speed under different driving amplitudes
图 10 不同驱动幅值下鱼体刚度对启动加速度的影响
Figure 10. The effects of Young’s modulus of fish body on the start acceleration under different driving amplitudes
图 11 不同肌肉驱动频率下鱼体刚度对游动速度的影响
Figure 11. The effects of fish body stiffness on swimming speed under different muscle driving frequencies
图 12 鱼体变刚度特性对游动速度的影响
Figure 12. The effects of the variable stiffness of fish body on the swimming speed
图 13 不同肌肉驱动频率下鱼体刚度对加速度的影响.
Figure 13. The effects of fish body stiffness on the start acceleration under different muscle driving frequencies
图 14 鱼体变刚度特性对启动加速度的影响
Figure 14. The effects of the variable stiffness of fish body on the start acceleration
图 17 变刚度条件下推力随驱动频率变化的实验结果
Figure 17. Experiment results of the thrust varied with driving frequency under the condition of variable body stiffness
表 1 鳗鲡科鱼体模型参数
Table 1. The parameters of anguilliform fish model
Parameter Definition Value f Frequency of muscle activation 1 Hz D Muscle force coefficient 0.03 N/m3 E Young's modulus 10−3 MPa μ Damping factor 50 N·s/m2 μf Dynamic viscosity 10−3 Pa·s Len Length of fish body 21 cm ρf Fluid density 1 g/cm3 ρ Density of fish body 1 g/cm3 N Number of discrete sections 21 Vcur Wave velocity of muscles activation 1 BL/s t Duration of muscle activation 0.36 s 
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表 2 不同驱动幅值对应最优速度表
Table 2. Table of the optimal speeds varied with different driving amplitudes
f /Hz D/(N/m3) Vmas/(BL/s) 1 0.13 0.483 1.25 0.25 0.603 1.5 0.49 0.735 1.75 0.96 0.853 2 1.89 0.965
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表 3 不同肌肉驱动频率和杨氏模量条件下的鱼体最优速度
Table 3. The optimal velocity of fish body under different muscle drive frequencies and Young's modulus
f /Hz D/(N/m3) Vmas/(BL/s) 1 0.0631 0.709 1.25 0.0801 0.889 1.5 0.0881 1.026 1.75 0.0871 1.105 2 0.0881 1.126
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表 4 不同肌肉驱动频率和杨氏模量条件下的鱼体最优启动加速度
Table 4. The optimal start acceleration of fish body under different muscle drive frequencies and Young's modulus
f /Hz E/MPa Vmas /(BL/s2) 1 0.0561 0.445 1.25 0.0761 0.654 1.5 0.0921 0.818 1.75 0.0991 0.911 2 0.0992 0.943
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表 5 鱼体关节尺寸参数
Table 5. The joint parameters of fish body
Parameter/cm Joint 1 Joint 2 Joint 3 Joint 4 Lh 5 5 5 5 ra 2.77 2.34 2 1.6 rb 3.29 2.77 2.34 2 Lc 5 5 5 5
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表 6 实验中弹簧力k·ΔL计算结果
Table 6. Results of the spring force k·ΔL in the experiments
k·ΔL/N Joint 1 Joint 2 Joint 3 Joint 4 k1·ΔL 0.36 0.33 0.31 0.31 k2·ΔL 1.25 1.13 1.05 1.06 k3·ΔL 3.32 3.01 2.8 2.81 k4·ΔL 7.5 6.81 6.33 6.37
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表 7 模型中弹簧力λ·Δl计算结果
Table 7. Results of spring force λ·Δl in the simulations
λ·Δl/N E/MPa N = 3 N = 6 N = 9 N = 12 aNbNEπΔl/2 0.05 0.70 0.61 0.52 0.43 aNbNEπΔl/2 0.1 1.39 1.21 1.03 0.85
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表 8 实验中转动刚度Q计算结果
Table 8. Results of the rotational stiffness Q in the experiments
k
(N/cm)Q1
(N·cm/rad)Q2
(N·cm/rad)Q3
(N·cm/rad)Q4
(N·cm/rad)k1 11.22 7.4 4.59 2.58 k2 38.49 25.4 15.74 8.87 k3 102.26 67.48 41.83 23.56 k4 231.32 152.64 94.62 53.3
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表 9 模型中弯曲刚度G计算结果
Table 9. Results of the bending stiffness G in the simulations
E
(MPa)G3
(Kg·mm2)G6
(Kg·mm2)G9
(Kg·mm2)G12
(Kg·mm2)0.1 54.57 36.06 22.29 12.56 0.05 27.29 18.03 11.14 6.28
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