EXPERIMENTAL AND NUMBERICAL SIMULATION OF SMA-FRICTION DAMPER BASED ON GEAR MECHANISM
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摘要: 基于齿轮机构对形状记忆合金(SMA)丝非比例拉伸的特点，提出了一种新型SMA-摩擦阻尼器，并阐述了该阻尼器的基本构造和工作原理。对SMA丝进行循环拉伸试验，考察了加载幅值、加载速率对其力学性能的影响规律；分别对齿轮摩擦单元和SMA-摩擦阻尼器试件进行了低周往复荷载下的力学性能试验，得到了摩擦材料、预紧力以及位移幅值对单次循环耗能、割线刚度、等效阻尼比和自复位率等力学性能指标的影响规律；建立了SMA-摩擦阻尼器的简化力学模型并进行了数值模拟。研究结果表明：所用复合树脂材料较黄铜材料出力更大，性能更稳定；新型阻尼器具有良好的耗能能力、承载能力及自复位能力，可实现大行程设计；利用OpenSees有限元模型计算得到的滞回曲线与试验曲线吻合较好，验证了力学模型和材料本构二次开发的正确性。Abstract: Based on the non-proportional stretching of shape memory alloy (SMA) wire by the gear mechanism, a novel SMA-friction damper is proposed and the basic configuration and working principle of the damper are expounded. The effects of loading amplitude and loading rate on the mechanical properties of SMA wires are investigated by cyclic tensile tests. The mechanical properties of the gear friction unit and SMA-friction damper specimens under cyclic loading are tested respectively to investigate the effects of friction materials, of preloading forces and of displacement amplitudes on the mechanical performance indexes, such as energy consumption per cycle, secant stiffness, equivalent damping ratio and self-centering rate. The simplified mechanical model of a SMA-friction damper is established and numerically simulated. The results show that the composite resin material has a greater friction and higher stability compared with brass material. The novel damper has excellent energy dissipation capacity, bearing capacity and self-centering capacity, and can be applied in a large displacement situation. The hysteresis curves computed using the OpenSees finite element model are in a good agreement with the experimental ones, which proves that the mechanical model and the secondary development of the material constitutive are valid.
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Key words:
- passive control /
- friction damper /
- mechanical experiment /
- shape memory alloy /
- gear mechanism /
- numerical simulation
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图 3 不同设计参数比下θ与伸长率λ和位移变化系数β的关系
Figure 3. Relationship between θ and elongation λ and displacement variation coefficient β under different design parameter ratios
图 7 SMA丝变幅加载应力-应变曲线
Figure 7. The stress-strain curve of SMA wire under variable loading amplitude
图 8 SMA丝变速率加载应力-应变曲线
Figure 8. The stress-strain curve of SMA wire under variable loading rate
图 13 滑动摩擦力变异系数影响因素分析
Figure 13. Influence factors analysis of coefficient of variation of sliding friction
图 15 不同位移幅值下试件SFDG-1力学性能参数变化曲线
Figure 15. Test curve of mechanical property parameters with various loading amplitudes for SFDG-1
图 16 不同预紧力下试件SFDG-1力学性能参数变化曲线
Figure 16. Test curves of mechanical property parameters with various preloading forces for SFDG-1
图 19 阻尼器试验曲线与模拟曲线对比
Figure 19. Comparison between the experimental and numerical curves of the damper
表 1 SMA丝试验工况
Table 1. SMA test conditions
序号 丝材直径/
mm丝材长度/
mm加载速率/
(mm/min)应变幅值/
(%)总循环次数/
次1 1.8 200 20 7 20 2 1.8 200 20 2~8 7 3 1.8 200 10~60 7 6 注：工况2应变幅值增量为1%，各级加载循环一次；工况3加载速率增量为10 mm/min，各级加载循环一次。 
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表 2 SMA丝训练前后力学参数对比
Table 2. Comparison of mechanical parameters of SMA wire before and after training
N/
次σMs/
MPaσMf/
MPaσAs/
MPaσAf/
MPaΔW/
JKs/
(N/mm)ξeq/
(%)1 674.69 781.63 364.87 193.44 12.93 147.83 7.11 20 520.56 619.64 305.10 169.85 6.66 133.02 4.07 注：N为循环次数；σMs为马氏体相变起点应力；σMf为马氏体相变终点应力；σAs为奥氏体相变起点应力；σAf为奥氏体相变终点应力；ΔW为单次循环耗能；Ks为割线刚度；ξeq为等效阻尼比。
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表 3 SMA丝变幅加载力学参数
Table 3. Mechanical parameters of SMA wire under variable loading amplitude
Am/
(%)σMs/
MPaσMf/
MPaσAs/
MPaσAf/
MPaΔW/
JKs/
(N/mm)ξeq/
(%)2 531.57 553.59 303.53 152.55 0.99 352.01 0.23 3 520.56 600.77 289.38 150.98 2.65 255.59 0.81 4 512.70 613.35 305.10 152.55 3.98 184.65 1.75 5 514.27 586.62 309.82 154.12 5.42 150.92 2.92 6 506.41 605.49 308.25 161.99 6.50 139.72 3.78 7 503.26 687.27 292.52 147.83 8.15 132.39 5.00 8 503.26 690.41 281.51 139.97 9.90 125.76 6.40 注：Am为应变幅值；σMs为马氏体相变起点应力；σMf为马氏体相变终点应力；σAs为奥氏体相变起点应力；σAf为奥氏体相变终点应力；ΔW为单次循环耗能；Ks为割线刚度；ξeq为等效阻 尼比。
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表 4 SMA丝变速率加载力学参数
Table 4. Mechanical parameters of SMA wire under variable loading rate
V/
(mm/min)σMs/
MPaσMf/
MPaσAs/
MPaσAf/
MPaΔW/
JKs/
(N/mm)ξeq/
(%)10 504.05 661.32 307.46 148.62 8.36 130.12 5.22 20 508.77 666.04 304.32 147.05 7.31 132.45 4.48 30 507.20 645.60 299.60 150.20 6.88 131.99 4.23 40 508.77 650.31 302.74 154.91 6.78 138.53 3.98 50 500.9 634.58 313.75 151.77 6.51 130.60 4.05 60 493.04 647.17 320.04 158.06 6.34 132.28 3.89 注：V为加载速率；σMs为马氏体相变起点应力；σMf为马氏体相变终点应力；σAs为奥氏体相变起点应力；σAf为奥氏体相变终点应力；ΔW为单次循环耗能；Ks为割线刚度；ξeq为等效阻尼比。
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表 5 阻尼器试验工况
Table 5. Cases of the specimens
序号 试件编号 SMA数量 SMA面积/mm2 摩擦材料 预紧力/kN 1 FDG-1 0 0.00 刹车片 0.5 2 5 2 FDG-2 0 0.00 黄铜 0.5 2 5 3 SFDG-1 2 5.09 刹车片 0.5 2 5 4 SFDG-2 2 5.09 黄铜 0.5 2 5
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表 6 FDG试件力学性能参数
Table 6. Mechanical property parameters of FDG
试件 位移幅值/mm 预紧力0.5 kN 预紧力2.0 kN 预紧力5.0 kN ΔW/J Ks/(kN/mm) ξeq/(%) ΔW/J Ks/(kN/mm) ξeq/(%) ΔW/J Ks/(kN/mm) ξeq/(%) FDG-1 10 19.25 0.051 58.87 87.15 0.226 59.85 187.16 0.499 58.09 15 27.95 0.033 58.83 133.47 0.154 60.26 287.58 0.339 59.33 20 37.55 0.026 55.83 178.84 0.119 59.19 383.67 0.250 60.20 25 46.67 0.022 54.73 221.39 0.097 57.54 477.64 0.200 60.42 FDG-2 10 9.97 0.028 54.29 56.48 0.146 59.40 128.53 0.338 59.63 15 15.53 0.020 53.27 84.76 0.100 58.36 199.22 0.227 60.72 20 20.22 0.015 52.51 111.08 0.076 57.32 268.64 0.171 61.30 25 26.00 0.013 49.63 136.03 0.058 59.18 341.29 0.141 61.50 注：ΔW为单次循环耗能；Ks为割线刚度；ξeq为等效阻尼比。
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表 7 SFDG试件力学性能参数
Table 7. Mechanical property parameters of SFDG
试件 位移幅值/mm 预紧力0.5 kN 预紧力2.0 kN 预紧力5.0 kN ΔW/J Ks/(kN/mm) ξeq/(%) δ/(%) ΔW/J Ks/(kN/mm) ξeq/(%) δ/(%) ΔW/J Ks/(kN/mm) ξeq/(%) δ/(%) SFDG-1 10 33.07 0.207 24.71 3.89 88.31 0.317 43.29 2.81 214.51 0.660 50.37 4.93 15 61.06 0.197 21.64 13.14 140.82 0.259 37.82 3.07 338.03 0.481 48.74 3.96 20 93.34 0.177 20.79 18.27 196.81 0.226 34.21 3.28 461.04 0.392 46.26 3.05 25 132.53 0.187 17.89 23.19 256.98 0.221 29.25 4.71 588.11 0.363 40.97 2.78 SFDG-2 10 23.11 0.154 23.88 5.18 64.81 0.245 40.87 3.20 165.82 0.513 50.02 4.63 15 41.37 0.166 17.40 20.17 104.23 0.210 34.61 3.34 263.48 0.390 46.85 3.99 20 65.70 0.154 16.81 28.87 148.75 0.185 31.68 3.53 363.44 0.316 45.21 2.93 25 95.32 0.163 14.78 30.80 195.20 0.184 26.77 7.32 462.48 0.290 40.22 2.84 注：ΔW为单次循环耗能；Ks为割线刚度；ξeq为等效阻尼比；自复位率δ=(D−D0)/D，D为最大加载位移，D0为残余位移。
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表 8 数值模拟参数
Table 8. Parameters selected for numerical simulation
SMA丝参数 摩擦单元参数 L0=182 mm E=33 000 MPa k=650,2200,5600 N/mm Y=550 MPa n=3 λ=0.01 As=5.087 mm2 α=0.01 Dy=1 ft=1.3 a=200 A=8 c=0.001 fm=10 000 B=2 m=3 εmf =0.09 γ=2，η=7 注：预紧力为0.5 kN、2.0 kN和5.0 kN工况所对应的k值用逗号
隔开。
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表 9 试验结果和数值模拟结果对比
Table 9. Comparison between experimental and numerical results
预紧力
/kN位移幅值/mm ΔW/J 误差/(%) Ks/(kN/mm) 误差/(%) ξeq/(%) 误差/(%) δ/(%) 误差/(%) 试验 模拟 试验 模拟 试验 模拟 试验 模拟 0.5 10 33.07 31.27 5.76 0.207 0.214 3.27 24.71 23.40 5.60 3.89 12.64 69.22 15 61.06 59.31 2.95 0.197 0.194 1.55 21.64 21.38 1.22 13.14 18.53 29.09 20 93.34 94.62 1.35 0.177 0.188 5.85 20.79 19.65 5.80 18.27 20.86 12.41 25 132.53 136.53 2.93 0.187 0.196 4.59 17.89 17.48 2.35 23.19 21.03 10.27 2.0 10 88.31 86.50 2.09 0.317 0.320 0.94 43.29 41.44 4.46 2.81 7.71 63.55 15 140.82 138.91 1.38 0.259 0.253 2.37 37.82 37.86 0.11 3.07 5.89 47.88 20 196.81 195.06 0.90 0.226 0.220 2.72 34.21 34.63 1.21 3.28 4.96 33.87 25 256.98 254.42 1.01 0.221 0.222 0.45 29.25 28.73 1.81 4.71 6.02 21.76 5.0 10 214.51 213.19 0.62 0.660 0.649 1.69 50.37 50.41 0.08 4.93 6.63 25.64 15 338.03 332.13 1.78 0.481 0.475 1.26 48.74 48.27 0.97 3.96 4.74 16.46 20 461.04 453.60 1.64 0.392 0.390 0.51 46.26 45.46 1.76 3.05 3.89 21.59 25 588.11 577.46
1.84 0.363 0.378 3.96 40.97 38.40 6.69 2.78 3.48 20.12 注：ΔW为单次循环耗能；Ks为割线刚度；ξeq为等效阻尼比；自复位率δ=(D−D0)/D，D为最大加载位移，D0为残余位移。
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