摘 要

本文结合往复式压缩机在诸如汽车、冶金、钢铁、石化工业中应用广泛的现况，以及目前往复式压缩机正在向着多列、多级、超高压、大型化的方向发展的趋势。随着压缩机列数的增多，轴系的增长，刚度减小、轴系转动惯量增加，直接导致了压缩机的固有频率的降低。压缩机曲轴在高速运行时，一旦转速在临界转速范围内，就会发生轴系共振现象，因此很容易引起轴系断裂。结合我国现在海洋平台的发展现况，分析压缩机的扭转振动，对于提供给海洋平台的压缩机具有非常重要的意义。

本文简要介绍了压缩机的组成和工作原理，并以2701压缩机为例，精心对比分析不同计算方法的优劣，经过对比分析后建立了往复式压缩机的扭振集中质量模型。其次在集中参数模型的基础上对轴系系统进行固有频率计算，并得到相对振幅。再次分析了压缩机所受到的激发力矩，并对轴系进行受迫振动分析，得到轴系各段的应力和扭矩。最后对轴系的自由振动和受迫振动结果进行分析，以及对比理论的正确性。

Matlab是一款可以用于数值计算的高级技术计算语言和交互环境，因为其对矩阵处理的便利性，因此选用该软件作为语言实现本论文中的算法和计算过程。首先在excel中输入工况参数，利用Matlab对其进行读取，建立集总参数模型。根据固有频率理论，建立振动微分方程，利用求特征值和特征向量的算法求得各阶次固有频率和对应振幅。根据激发力矩理论计算激发力矩，进行傅立叶调谐近似计算。最后根据受迫振动理论，求得各轴端的应力和扭矩。

本文的特色：利用自编程序简化压缩机曲轴轴系的计算方法，以实现满足海洋平台工程对压缩机的需求。

关键词：压缩机；集总参数；扭振分析；自编代码。

Abstract

Combined with reciprocating compressor in such as automobile, metallurgy, steel, petrochemical industry widely used in the current situation, and the current reciprocating compressor to multi-column, multi-stage, ultra-high pressure, large-scale development. With the increase of the number of compressor columns, the increase of the shaft system, the stiffness decreases and the rotary inertia of the shaft system increases, which directly leads to the reduction of the natural frequency of the compressor. At high speed, once the speed is within the critical speed range, the shafting resonance phenomenon will occur, so it is easy to cause shafting fracture. It is very important to analyse the torsional vibration of the compressor for the offshore platform.

In this paper, the composition and working principle of the compressor are briefly introduced, and the torsional vibration lumped mass model of the reciprocating compressor is established by taking 2701 compressor as an example. Secondly, on the basis of the model, the natural frequency of the shafting is calculated and the relative amplitude is obtained. The excitation torque of the compressor is analysed again, and the forced vibration of the shaft system is analysed to obtain the stress and torque of each section of the shaft system. Finally, the results of free vibration and forced vibration of shafts are analysed, and the correctness of the theory of comparison is given.

Matlab is a high-level technical computing language and interactive environment that can be used for numerical calculation. Because of its convenience in matrix processing, this software is selected as the language to realize the algorithm and calculation process in this paper. Firstly, the operating parameters were input in excel and read by Matlab to establish lumped parameter model. Then, according to the theory of natural frequency, the differential equation of vibration is established, and the algorithm of eigenvalue and eigenvector is used to obtain the natural frequency and corresponding amplitude of each order. The excitation moment is calculated according to the excitation moment theory and the Fourier tuning approximation is calculated. Finally, according to the theory of forced vibration, the stress and torque at each end of the shaft are obtained.

The feature of this paper is to simplify the calculation method of compressor crankshaft shafting by self-programming and meet the requirement of offshore platform engineering for compressor.

Key words： compressor； centralized parameter； torsional vibration analysis； self-coding

目 录

第1章 绪 论 1

1.1论文来源及背景 1

1.1.1论文研究背景 1

1.1.2研究意义 2

1.2国内外往复式压缩机研究现状 2

1.2.1国内外压缩机研究现状 2

1.2.2国内外轴系扭振分析方法研究现状 3

1.3研究思路与研究内容 4

第2章 压缩机轴系模型建立和基本参数求解 6

2.1集中质量弹簧模型建立 7

2.2弹性参数的当量转化 9

2.3惯性参数的当量转化 10

2.4计算参数导入 11

第3章 压缩机曲轴的自由振动分析 12

3.1自由振动理论 12

3.2自由振动计算实现 13

第4章 压缩机曲轴激励力矩 14

4.1气体力 14

5.2往复惯性力 17

4.3激励力矩 19

4.4激发力矩计算 20

第5章 压缩机的强迫振动分析 21

5.1临界转速 21

5.2激振功 21

5.3阻尼功 22

5.4共振振幅及扭振应力计算 22

5.5临界转速和受迫振动计算 24

第6章 各部分计算分析及验证理论 26

6.1验证理论 26

6.2计算结果参照实际限制对比 27

结论 28

参考文献 29

附录 31

附录A 自由振动振型图 31

附录B 激发力矩图 37

附录C 代码展示 39