Influence of equivalent stiffness form from stern bearing to transverse vibration of shafting

Table 1. Structure and material parameters of shafting model for verification^[16]
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Table 1. Structure and material parameters of shafting model for verification^[16]
参数轴段
L₁ L₂ L₃ L₄ L₅
轴段截面直径D_i /mm 390 498
轴段长度L_i /m 2.9 3.6 1.55 3.6 2.9
轴段杨氏模量E/Pa 2.1×10¹¹
轴段密度ρ /(kg·m⁻³) 7 850

Table 2. Convergence and accuracy of the improved Fourier series

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Table 2. Convergence and accuracy of the improved Fourier series

固有频率/Hz							文献[16]
M_i = 4	M_i = 6	M_i = 8	M_i = 10	M_i = 12	M_i = 14	M_i = 16	文献[16]
7.72	7.72	7.71	7.71	7.71	7.71	7.71	7.71
42.70	42.60	42.52	42.51	42.50	42.50	42.50	42.49
55.47	55.13	55.10	55.05	55.04	55.03	55.03	55.01
87.64	87.51	87.26	87.25	87.21	87.21	87.21	87.19
108.66	107.62	107.42	107.35	107.32	107.31	107.31	107.27
130.32	129.48	129.34	129.30	129.28	129.27	129.27	129.25
177.19	175.40	175.33	175.32	175.30	175.29	175.29	175.28
238.80	235.43	235.31	235.27	235.27	235.26	235.26	235.25
317.45	302.77	302.56	302.51	302.50	302.49	302.49	302.47
433.17	374.69	372.81	372.73	372.72	372.72	372.72	372.71

Table 3. Comparison of natural frequency accuracy under equi-valent continuous distributed stiffness of stern bearing
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Table 3. Comparison of natural frequency accuracy under equi-valent continuous distributed stiffness of stern bearing
固有频率/Hz
一阶二阶三阶四阶五阶六阶七阶
本文模型 7.97 42.51 55.03 87.35 107.51 129.37 175.48
FEM模型 7.97 42.41 54.96 86.96 107.00 128.67 173.42

Table 4. Equivalent continuous distributed stiffness of stern bearing under different inclination angles of journal

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Table 4. Equivalent continuous distributed stiffness of stern bearing under different inclination angles of journal

α /(°)	等效刚度/(N·m^-1)	拟合曲线函数
α=0		−0.0546xoi6+6.5542 xoi5−332.7649xoi4+9.1433e3xoi3−1.4701e5xoi2+1.3621e6 xoi+1.1696e4
α=0.004		−0.1507xoi6+15.9029 xoi5−673.9896xoi4+1.4853e4xoi3−1.8690e5 xoi2+1.5750e6 xoi−8.1024e4
α=0.008		−0.0038xoi8+0.5434 xoi7−31.3866 xoi6 +949.1562xoi5−1.6053e4xoi4+1.5161e5 xoi3−7.6815e5xoi2+2.5870e6xoi−2.8425e5

Table 5. Exciting amplitude and stiffness at different revolution speeds of propeller
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Table 5. Exciting amplitude and stiffness at different revolution speeds of propeller
参数螺旋桨转速/(r·min⁻¹)
100 150 200 250
激励力幅值/N 111 250 444 649
各转速对应的刚度/(N·m⁻¹) 2.5×10⁸ 2×10⁸ 1.5×10⁸ 1.25×10⁸

Table 6. Vibration displacement level response at the front stern bearing（n＝100 r/min）
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Table 6. Vibration displacement level response at the front stern bearing（n＝100 r/min）
振动位移级响应/dB
轴频叶频 2倍叶频
转速对应刚度(2.5×10⁸ N/m) 229.937 4 302.393 206.658 5
基准刚度(5×10⁸ N/m) 228.085 2 254.834 197.1011

Table 7. Vibration displacement level response at the front stern bearing （n＝150 r/min）
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Table 7. Vibration displacement level response at the front stern bearing （n＝150 r/min）
振动位移级响应/dB
轴频叶频 2倍叶频
转速对应刚度(2×10⁸ N/m) 247.257 9 239.983 9 203.905 6
基准刚度(5×10⁸ N/m) 244.766 6 225.839 4 174.098 5

Table 8. Vibration displacement level response at the front stern bearing（n＝200 r/min）
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Table 8. Vibration displacement level response at the front stern bearing（n＝200 r/min）
振动位移级响应/dB
轴频叶频 2倍叶频
转速对应刚度(1.5×10⁸ N/m) 260.340 9 234.384 4 202.872 2
基准刚度(5×10⁸ N/m) 257.174 8 209.841 4 222.708 3

Table 9. Vibration displacement level response at the front stern bearing（n＝250 r/min）
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Table 9. Vibration displacement level response at the front stern bearing（n＝250 r/min）
振动位移级响应/dB
轴频叶频 2倍叶频
转速对应刚度(1.25×10⁸ N/m) 271.845 5 232.619 7 236.120 6
基准刚度(5×10⁸ N/m) 269.825 3 150.449 231.8207

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Huihui ZHOU, Tianyun LI, Xiang ZHU, Rui NIE, Qingsheng LI. Influence of equivalent stiffness form from stern bearing to transverse vibration of shafting[J]. Chinese Journal of Ship Research, 2023, 18(1): 231

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Paper Information

Category: Ship Structure and Fittings

Received: Apr. 9, 2021

Accepted: --

Published Online: Mar. 18, 2025

The Author Email:

DOI:10.19693/j.issn.1673-3185.02346

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Structure and material parameters of shafting model for verification[16]

Table 1. Structure and material parameters of shafting model for verification[16]

Table 2. Convergence and accuracy of the improved Fourier series

Table 2. Convergence and accuracy of the improved Fourier series

Table 3. Comparison of natural frequency accuracy under equi-valent continuous distributed stiffness of stern bearing

Table 3. Comparison of natural frequency accuracy under equi-valent continuous distributed stiffness of stern bearing

Table 4. Equivalent continuous distributed stiffness of stern bearing under different inclination angles of journal

Table 4. Equivalent continuous distributed stiffness of stern bearing under different inclination angles of journal

Table 5. Exciting amplitude and stiffness at different revolution speeds of propeller

Table 5. Exciting amplitude and stiffness at different revolution speeds of propeller

Table 6. Vibration displacement level response at the front stern bearing（n＝100 r/min）

Table 6. Vibration displacement level response at the front stern bearing（n＝100 r/min）

Table 7. Vibration displacement level response at the front stern bearing （n＝150 r/min）

Table 7. Vibration displacement level response at the front stern bearing （n＝150 r/min）

Table 8. Vibration displacement level response at the front stern bearing（n＝200 r/min）

Table 8. Vibration displacement level response at the front stern bearing（n＝200 r/min）

Table 9. Vibration displacement level response at the front stern bearing（n＝250 r/min）

Table 9. Vibration displacement level response at the front stern bearing（n＝250 r/min）

Table 1. Structure and material parameters of shafting model for verification^[16]

Table 1. Structure and material parameters of shafting model for verification^[16]