# 推进轴系纵向高承载准零刚度隔振器的研究

(1.福州大学金属橡胶与振动噪声研究所,福建 福州 350116; 2.福州大学 机械工程及自动化学院, 福州 350116)

## 1 准零刚度隔振器布置方案

Figure 1 Schematic diagram of parallel connection of disc spring and coil spring

Figure 2 Schematic diagram of longitudinal low frequency vibration isolation of propulsion shafting

## 2 轴系纵向动力学分析

### 2.1 动力学方程建立与求解

Figure 3 Shafting-quasi-zero stiffness isolator dynamic model

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(2)

(3)

(4)

### 2.2 求解有效性的验证

Figure 4 Analytical solutions compared with numerical solutions

### 2.3 系统力传递率曲线

Figure 5 Force transmission rate curve

## 3 准零刚度隔振器参数对系统稳定性的影响

(5)

(6)

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(8)

### 3.1 非线性刚度对系统稳定性的影响

Figure 6 Amplitude-frequency response and stability diagram of different nonlinear stiffness

### 3.2 碟簧与螺旋弹簧的设计

Figure 7 Schematic diagram of disc spring

(9)

(10)

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(12)

Figure 8 Single disc spring load-displacement curve

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(14)

Figure 9 Quasi-zero stiffness isolator load-displacement curve

### 3.3 阻尼比对系统稳定性的影响

Figure 10 Amplitude-frequency response and stability diagram of different damping ratios

## 4 隔振性能分析

Figure 11 System force transmission rate curve in different excitation force amplitude conditions

## 5 结论

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# Research on Longitudinal High Load-bearing Quasi-zero Stiffness Isolator for Propulsion Shafting

REN Zhiying1,2, QIU Tao1,2, LIU Niuniu1,2, BAI Hongbai1,2, YAO Jiecheng1,2, LIANG Yi1,2

(1.School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China; 2.Institute of Metal Rubber, Vibration and Noise, Fuzhou University, Fuzhou 350116, China )

Abstract: Aiming at the problem of longitudinal low-frequency vibration isolation of ship propulsion shafting, a high-load quasi-zero stiffness isolator was designed based on disc spring with negative stiffness characteristics and positive-stiffness coil spring in parallel. The dynamic equation of the shafting-quasi-zero stiffness vibration isolation system was established. Through the harmonic balance method, the steady-state response of the system was solved, and the validity of the solution was verified by numerical calculation. For the problem of system response stability, firstly, the influence of nonlinear stiffness of quasi-zero stiffness isolator and external excitation force amplitude on response stability were studied，and combined with the longitudinal static deformation of the shafting, the nonlinear stiffness was determined. Then the specific structural and mechanical parameters of the disc spring and the coil spring were obtained through static analysis. Finally, the influence of damping ratio of quasi-zero stiffness isolator and external excitation force amplitude on the response stability of the system were analyzed, the damping ratio was determined. The results showed that when the nonlinear stiffness and damping ratio were taken as 1×1012 N/m3 and 0.05, respectively, the main resonance of the system no longer jumps, and the solution of the steady-state response of the system was stable within 200 Hz. In the meantime, even with a load of 10 000 N, the quasi-zero stiffness isolator could still effectively isolate the vibration in the range of 10 Hz to 200 Hz.

Keywords: propulsion shafting; low frequency vibration isolation; disc spring; quasi-zero stiffness; stability

doi：10.13705/j.issn.1671-6833.2022.04.019