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摘要:
针对目前国产超声变幅杆耐用性较差的问题，设计一种新型复合变幅杆，满足振幅的条件下，使变幅杆具有较小的工作应力。通过波动方程建立新型复合变幅杆参数方程，着重计算了放大倍数、形状因数及应力极大点等参数。首先，采用有限元分析软件对变幅杆进行动力学分析，得到的结果与理论结果进行比较，验证了理论公式的正确性。然后，在此基础上与圆锥形变幅杆、指数形变幅杆及小端接圆柱杆的复合圆锥形变幅杆进行比较，结果表明新型复合变幅杆具有更好的综合性能和更小的最大应力。最后，基于ANSYS Workbench优化设计功能对变幅杆进行优化修整，对优化后的变幅杆进行阻抗分析和振动性能测试，测试结果表明新型复合变幅杆理论性能参数与实验测试结果基本一致，变幅杆的谐振频率为20 013 Hz，当换能器输出振幅峰峰值为13 μm时，变幅杆的输出端振幅峰峰值可达40 μm，变幅杆振幅实际放大倍数为3.08，满足切削实验振幅的要求。
Abstract:Aimed at the problem of poor durability of the domestic ultrasonic horn, a new type of compound horn is designed to meet the amplitude and make the horn have a small working stress.The new composite horn parameter equation is established by the wave equation, and the parameters such as magnification, shape factor and stress maximum point are calculated.Frist, the finite element analysis software was used to analyze the kinetics of the horn. The obtained results were compared with the theoretical results to verify the correctness of the theoretical formula. Second, on the basis of this, compared with the conical horn, the exponential deformation horn and compound conical horn with cylinder at big end, the results show that the new composite horn has better comprehensive performance and smaller maximum stress. Finally, based on ANSYS Workbench optimization design function, the horn is optimized and trimmed, and the optimized horn is subjected to impedance analysis and vibration performance test. The test results show that the theoretical performance parameters of the new composite horn are basically consistent with the experimental test results. The resonant frequency of the rod is 20 013 Hz. When the transducer peak-to-peak value of the output amplitude is 13 μm, the peak-to-peak value of the output amplitude of the horn can reach 40 μm, and the amplitude amplification factor of the horn is 3.08, which satisfies the requirements of the cutting experiment amplitude.
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Key words:
- comprehensive performance /
- life /
- maximum stress /
- optimization design /
- finite element analysis
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表 1 N对变幅杆性能参数的影响
Table 1. Effect of N on performance parameters of horn
样本编号 N l2/mm Mp φ xm/mm 1 1.077 94.31 1.09 1.05 33.13 2 1.167 95.50 1.20 1.10 35.12 3 1.272 96.70 1.32 1.16 37.27 4 1.4 97.89 1.47 1.22 39.63 5 1.556 99.88 1.63 1.29 42.21 6 1.75 101.87 1.83 1.37 45.07 7 2 104.66 2.06 1.45 48.24 8 2.333 108.24 2.32 1.54 51.64 9 2.8 112.22 2.65 1.65 55.49 10 3.5 117.39 3.02 1.78 59.37 注：l1=31.25 mm，FREQ=20 000 Hz。 
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表 2 l1对变幅杆性能参数的影响
Table 2. Effect of l1 on performance parameters of horn
样本编号 l1/mm l2/mm Mp φ xm/mm 1 1.99 139.67 2.94 1.705 82.46 2 3.97 138.08 2.95 1.695 80.95 3 5.92 136.49 2.97 1.716 78.86 4 7.85 134.88 2.98 1.711 77.44 5 15.14 128.92 3.04 1.746 71.37 6 21.50 124.14 3.06 1.741 67.02 7 26.85 120.56 3.03 1.767 62.51 8 31.25 117.39 3.02 1.780 59.37 9 34.86 115.00 2.98 1.792 56.58 10 37.82 113.01 2.94 1.794 54.49 11 40.27 111.02 2.93 1.806 52.97 12 42.32 109.83 2.88 1.801 51.42 13 44.05 108.64 2.85 1.801 50.23 14 47.36 106.25 2.79 1.822 47.55 15 49.70 104.66 2.74 1.825 45.74 16 51.43 103.46 2.70 1.826 44.40 17 52.75 102.27 2.68 1.834 43.60 18 55.93 99.88 2.60 1.843 41.09 19 57.55 98.69 2.56 1.859 39.37 20 58.53 97.89 2.53 1.867 38.47 注：N=3.5，FREQ=20 000 Hz。
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表 3 00Cr17Ni14Mo2材料参数
Table 3. 00Cr17Ni14Mo2 material parameters
参数 数值 密度ρ/(kg·m－3) 8 000 弹性模量E/Pa 2.06×1011 泊松比μ 0.28
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表 4 N对动力学分析的影响
Table 4. Effect of N on kinetic analysis
样本编号 N FREQ/Hz Mp σmax/MPa xm/mm 1 1.077 20 431 1.14 23.99 34.46 2 1.167 20 355 1.25 25.416 36.45 3 1.272 20 318 1.36 26.926 38.56 4 1.4 20 330 1.50 26.341 41.05 5 1.556 20 273 1.66 27.002 43.51 6 1.75 20 275 1.86 28.745 45.97 7 2 20 239 2.08 30.578 48.80 8 2.333 20 180 2.35 32.287 51.98 9 2.8 20 250 2.66 34.035 55.71 10 3.5 20 330 3.02 34.65 59.49 注：l1=31.25 mm。
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表 5 l1对动力学分析的影响
Table 5. Effect of l1 on kinetic analysis
样本编号 l1/mm FREQ/Hz Mp σmax/MPa xm/mm 1 1.99 20 518 3.00 35.85 81.25 2 3.97 20 489 3.02 35.85 79.84 3 5.92 20 474 3.02 35.81 77.79 4 7.85 20 455 3.04 36.01 76.46 5 15.14 20 449 3.07 35.93 70.57 6 21.50 20 414 3.07 35.76 66.35 7 26.85 20 352 3.05 35.17 61.91 8 31.25 20 330 3.02 34.65 59.05 9 34.86 20 296 2.98 33.94 55.78 10 37.82 20 282 2.94 33.32 53.68 11 40.27 20 311 2.90 32.74 51.98 12 42.32 20 275 2.87 32.35 50.42 13 44.05 20 260 2.83 31.87 49.23 14 47.36 20 263 2.76 30.88 46.58 15 49.70 20 254 2.70 30.35 44.54 16 51.43 20 251 2.66 29.65 43.18 17 52.75 20 276 2.63 29.25 42.14 18 55.93 20 295 2.54 28.91 39.59 19 57.55 20 316 2.50 28.58 37.87 20 58.53 20 359 2.47 28.15 36.82 注：N=3.5。
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表 6 N对相对误差的影响
Table 6. Effect of N on relative error
样本编号 N FREQ相对误差Δ1/% Mp相对误差Δ2/% xm相对误差Δ3/% 1 1.077 2.16 4.59 4.01 2 1.167 1.78 4.17 3.79 3 1.272 1.59 3.03 3.46 4 1.4 1.65 2.04 3.58 5 1.556 1.37 1.84 3.08 6 1.75 1.38 1.64 2.00 7 2 1.20 0.97 1.16 8 2.333 0.90 1.29 0.66 9 2.8 1.25 0.38 0.40 10 3.5 1.65 0 0.20 注：l1=31.25 mm。
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表 7 l1对相对误差的影响
Table 7. Effect of l1 on relative error
样本编号 l1/mm FREQ相对误差Δ1/% Mp相对误差Δ2/% xm相对误差Δ3/% 1 1.99 2.59 2.19 1.47 2 3.97 2.44 2.20 1.37 3 5.92 2.37 1.83 1.36 4 7.85 2.28 1.97 1.27 5 15.14 2.25 0.90 1.12 6 21.50 2.07 0.39 1.00 7 26.85 1.76 0.63 0.96 8 31.25 1.65 0.01 0.54 9 34.86 1.48 0.03 1.41 10 37.82 1.41 0.01 1.49 11 40.27 1.56 0.89 1.87 12 42.32 1.38 0.46 1.94 13 44.05 1.30 0.55 1.99 14 47.36 1.32 1.06 2.04 15 49.70 1.27 1.34 2.62 16 51.43 1.25 1.41 2.75 17 52.75 1.38 1.88 3.35 18 55.93 1.47 2.28 3.65 19 57.55 1.58 2.51 3.81 20 58.53 1.79 2.28 4.29 注：N=3.5。
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表 8 新型复合变幅杆参数
Table 8. New composite horn parameters
参数 数值 l1/mm 31.25 l2/mm 117.39 xm/mm 59.37 Mp 3.02 φ 1.780
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表 9 变幅杆优化设计结果
Table 9. Results of horn design optimization
参数 优化前 优化后 l1/mm 31.25 32 l2/mm 117.39 120.51 l3/mm 4.61 4.39 FREQ/Hz 30 352 20 111 Mp 3.05 3.12 σmax/MPa 35.170 34.527
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