Simulation test of underwater vehicle shafting based on particle damping in longitudinal vibration suppression
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摘要: 在简谐激励条件下，应用轴系颗粒阻尼纵振抑制模拟试验装置研究了旋转工况下的颗粒阻尼减振比；探讨了单腔体多颗粒和多腔体多颗粒时的轴系模拟系统加速度变化，讨论了颗粒的材料、粒径、质量填充比、腔体数量、转速、激励频率与位移等参数对系统减振比的影响规律。研究结果表明：在单腔体多颗粒条件下，填充有铜、钢、橡胶包钢颗粒的系统减振比处于7.83%~8.91%，橡胶颗粒的系统减振比接近于0；铜、钢、橡胶包钢颗粒有明显的抑振效果，颗粒的材料密度和阻尼比越大，抑振效果越好；当颗粒质量填充比为15%时，系统减振比最高为13.77%，但当质量填充比超过15%时，减振比有所降低，故质量填充比一般应根据实际情况控制在15%左右；粒径、转速、激励频率与位移幅值的变化对系统减振比的影响分别为1.76%~8.68%、6.77%~12.50%、4.41%~10.12%与2.19%~7.05%；在多腔体多颗粒工况下，当颗粒总质量填充比和转速一定时，腔体数量对系统减振比有明显影响；当腔体数量为3时，转速为100 r·min-1和质量填充比为25%的最佳系统减振比为22.5%；在多腔体多粒径颗粒工况下，当总质量填充比为10%，转速为50~150 r·min-1的系统减振比波动不大，平均为14.18%，这表明多腔体多粒径组合对转速不十分敏感，具有较好的减振效果，可拓宽转速使用范围。Abstract: Under the condition of simple harmonic excitation, a simulation test device of shafting longitudinal vibration suppression based on the particle damping was used to investigate the vibration reduction ratio of particle damping in a rotating condition. The acceleration variations of shafting simulation system for single- and multiple-cavity particle dampers were explored, and the parameters influencing the vibration reduction ratio of the system, such as material, size and filling ratio of particle, cavity number, rotating speed, frequency, and amplitude of excitation, were examined. Research results show that when there are multiple particles in a single cavity, the vibration reduction ratio of a system filled with copper, steel, and rubber-coated steel particles is between 7.83% and 8.91%, and that of a system filled with rubber particles is close to zero. This indicates that copper, steel, and rubber-coated steel particles have an obvious suppression effect, and the higher the material density and damping ratio of the particles, the better the damping effect. When the particle mass filling ratio is 15%, the maximum vibration reduction ratio of the system is 13.77%. However, when the mass filling ratio exceeds 15%, the vibration damping ratio of the system decreases. Therefore, the mass filling ratio should be controlled at approximately 15% according to the actual situation. The influences of particle size, rotating speed, excitation frequency, and displacement amplitude on the vibration reduction ratio of the system are 1.76%-8.68%, 6.77%-12.50%, 4.41%-10.12%, and 2.19%-7.05%, respectively. Under a multicavity and multiparticle condition, when the total mass filling ratio of the particles and the rotating speed are constant, the cavity number has a significant impact on the vibration reduction ratio of the system. When the cavity number is 3, the best vibration reduction ratio of the system is 22.5% under a rotating speed of 100 r·min-1 and a mass filling ratio of 25%. Under multicavity and multiple particle sizes, when the total mass filling ratio is 10% and the rotating speed is 50-150 r·min-1, the vibration reduction ratio of the system fluctuates little, with an average of 14.18%. This shows that the combined multicavity and multiple-particle-size system is not very sensitive to the rotating speed, and it has a better vibration reduction effect. As a result, the range of the rotating speed can be widened. 14 tabs, 18 figs, 30 refs.
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图 2 颗粒阻尼轴系纵振模拟试验装置
Figure 2. Simulation test device of shafting longitudinal vibration based on particle damping
图 5 不同粒径的减振比变化趋势
Figure 5. Variation trends of vibration reduction ratios under different particle sizes
图 6 颗粒质量填充比对系统加速度的影响
Figure 6. Influence of particle mass filling ratio on system acceleration
图 8 激励位移幅值对系统加速度的影响
Figure 8. Influence of excitation displacement amplitude on system acceleration
图 10 两个腔体系统减振比变化趋势
Figure 10. Variation trends of vibration reduction ratio of 2 cavity system
图 11 三个腔体系统减振比变化趋势
Figure 11. Variation trends of vibration reduction ratio of 3 cavity system
图 12 四个腔体系统减振比变化趋势
Figure 12. Variation trends of vibration reduction ratio of 4 cavity system
图 13 两个腔体与2种粒径颗粒组合的系统减振比变化趋势
Figure 13. Variation trends of vibration reduction ratio for combined system of 2 cavities and 2 kinds of particle size
图 14 三个腔体与3种粒径颗粒组合的系统减振比变化趋势
Figure 14. Variation trends of vibration reduction ratio for combined system of 3 cavities and 3 kinds of particle size
图 15 四个腔体与4种粒径颗粒组合系统减振比变化趋势
Figure 15. Variation trends of vibration reduction ratio for combined system of 4 cavities and 4 kinds of particle size
图 16 转速对多腔体混合颗粒抑振的影响
Figure 16. Influence of rotating speed on vibration suppression of multi-cavity mixed particles
表 1 不同材料颗粒的恢复系数和阻尼比
Table 1. Particle recovery coefficients and damping ratios of different materials
参数 钢 铜 橡胶 橡胶包钢 e 0.669 0.615 0.711 0.691 ξ 0.13 0.15 0.11 0.12 
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表 2 无颗粒阻尼器系统的固有频率
Table 2. Natural frequencies of particle-free damper system
Hz 频率 1 2 3 4 5 6 fn 211.3 493.0 556.4 706.5 856.8 1 411.6
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表 3 不同材料的减振比
Table 3. Vibration reduction ratios of different materials
% 减振比 钢 铜 橡胶 橡胶包钢 λ 8.64 8.91 0 7.83
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表 4 不同粒径的减振比
Table 4. Vibration reduction ratios of different particle sizes
A/mm R/mm 2 3 4 5 1.0 5.50 8.39 2.60 3.57 2.0 1.76 4.71 3.53 4.71 2.5 4.51 7.79 5.74 7.79 3.0 6.94 8.68 4.51 7.29 Σ 18.71 29.57 16.38 23.36
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表 5 不同颗粒质量填充比下的减振比
Table 5. Vibration reduction ratios of different particle mass filling ratios
% δ 5 10 15 20 λ 5.55 8.62 13.77 11.13
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表 6 不同激励频率下的减振比
Table 6. Vibration reduction ratios of different excitation frequencies
f/Hz 3 5 10 λ/% 4.41 10.12 8.13
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表 7 不同激励位移幅值下的减振比
Table 7. Vibration reduction ratios of different excitation displacement amplitudes
A/mm 1 2 3 λ/% 3.38 2.19 7.05
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表 8 不同转速下的减振比
Table 8. Vibration reduction ratios at different rotating speeds
n/(r·min-1) 50 80 100 120 150 λ/% 9.41 12.50 6.77 6.54 7.94
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表 9 两个腔体系统的减振比
Table 9. Vibration reduction ratios of 2 cavity system
n/(r·min-1) δ/% 10 15 20 25 50 2.86 3.89 4.93 6.30 80 6.54 4.90 7.52 9.80 100 4.25 3.56 2.52 3.91 120 6.86 7.81 9.09 12.92 150 8.89 6.06 10.15 14.54 Σ 29.40 26.22 34.21 47.47
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表 10 三个腔体系统的减振比
Table 10. Vibration reduction ratio of three 3 cavity system
n/(r·min-1) δ/% 10 15 20 25 50 9.20 11.98 17.04 19.97 80 4.56 11.11 14.61 17.94 100 8.54 14.79 18.37 22.50 120 2.25 10.75 14.88 21.06 150 3.33 9.63 13.97 17.97 Σ 27.88 58.26 78.87 99.44
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表 11 四个腔体系统的减振比
Table 11. Vibration reduction ratios of 4 cavity system
n/(r·min-1) δ/% 10 15 20 25 50 6.32 11.78 13.79 18.67 80 4.27 12.53 13.10 17.09 100 9.64 14.87 15.97 20.66 120 3.65 9.55 15.44 20.22 150 3.33 9.16 13.33 20.27 Σ 27.21 57.89 71.63 96.91
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表 12 两个腔体与2种粒径颗粒组合的系统减振比
Table 12. Vibration reduction ratios of combined system of 2 cavities and 2 kinds of particle size
n/(r·min-1) R/mm (2, 3) (2, 4) (2, 5) (3, 4) (3, 5) (4, 5) 50 6.17 7.51 8.46 12.40 8.71 7.15 80 14.07 13.22 14.90 19.70 16.52 8.40 100 17.46 17.57 16.87 19.68 17.67 8.96 120 16.09 17.33 17.89 20.85 6.73 13.26 150 15.60 15.65 12.07 16.60 13.89 9.82 Σ 66.39 71.28 70.19 89.23 63.52 47.59
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表 13 三个腔体与3种粒径颗粒组合的系统减振比
Table 13. Vibration reduction ratios of combined system of 3 cavities and 3 kinds of particle size
n/(r·min-1) R/mm (2, 3, 4) (2, 3, 5) (2, 4, 5) (3, 4, 5) 50 6.17 7.10 8.63 6.76 80 11.70 12.93 12.93 12.74 100 10.78 13.01 13.03 12.79 120 11.97 13.80 12.43 12.94 150 11.39 13.32 13.37 13.21 Σ 52.01 60.16 60.39 58.44
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表 14 四个腔体与4种粒径颗粒组合的系统减振比
Table 14. Vibration reduction ratios of combined system of 4 cavities and 4 kinds of particle size
n/(r·min-1) R/mm (2, 3, 4, 5) 50 11.45 80 15.01 100 13.89 120 15.23 150 13.34
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