汽轮机、燃气轮机相关国际标准背后的力学问题

Mechanical Problems in the Relative International Standards about Steam and Gas Turbines

国际标准是先进技术的结晶,既有很好的理论基础,同时也是对行业实践的总结,得到了广泛认可。然而,这些标准通常仅给出了简单结论性的概念和表达式,没有给出其背后的原理和机理,如果不能对其深入理解,将影响标准的使用和作用发挥。以国际标准ISO10814"机械振动-机器不平衡敏感度和不平衡灵敏度"为例,将复杂转子系统在共振附近等效为单自由度系统,推导出了模态灵敏度的计算公式,解释了其物理含义。从频响函数角度给出了基于奈奎斯特图法试验确定某个共振转速下模态灵敏度的理论依据。采用半功率点法,推导出了基于波德图法试验确定某个共振转速的模态灵敏度的计算公式。计算了某1 000MW机组的临界转速和对应的模态灵敏度,计算结果表明该转子系统的各阶临界转速均处于中等敏感度机器灵敏度的A区,即灵敏度很低,具有较好的动力学特性。本文工作对相关国际标准的理解和灵活应用有参考价值。

The international standards are the combination of advanced technologies. It is based on a good foundation of theory and is a summary of the modem industry practice. It is widely accepted. However, these standards only provide simple conclusions and formulae, don＇ t explain the mechanical principles behind them. The application of the international standards could be limited if they are not well understood. In this paper, the ISO 10814 ＂Mechanical vibration-susceptibility and sensitivity of machines to unbalance＂ is taken as an example. We simplify the complicated rotor system into an equivalent single degree of freedom system, derive the formula for calculating the modal sensitivity and explains its physical meaning. From the aspect of frequency-response function, the theoretical basis of the method for determining the modal sensitivity at certain resonant speed using Nyquist diagram is given. A formula is derived to calculate the modal sensitivity of a certain resonant speed based on the bode diagram using the half power point method. The critical speeds and the modal sensitivity of a 1 000MW turbine unit are calculated. The result shows that the critical speeds of this rotor system are in a area of modal sensitivity for moderate susceptibility machine, which means the rotor bearing system isn＇ t sensitive to unbalance. The paper will be helpful for the comprehension and flexible application of the international standards.