Variable structure and dynamics properties of mixing rotor due to thermal expansion
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摘要:
航空发动机、汽轮机等大型旋转机械多运行在复杂多变的高温环境中,机组主转子系统在工况下因热膨胀而产生结构变化,进而影响运行特性。首先,考虑盘鼓混合式旋转构件与转轴相比具有高刚度特点,将其结构简化并建立单厚盘转子动力学模型;其次,针对热膨胀引发的系统变结构特征,以曲线拟合结合Hermite插值法描绘出圆柱厚盘窜动到任意位置时的转轴弯曲情况,根据弯曲轴所储存的弹性势能运用数值方法折算出对转盘所提供的恢复力及转轴的弯曲恢复刚度;最后,通过数值分析热膨胀诱发的轴向窜动对厚盘转子系统进动频率、临界角速度和振动响应幅值等动力学特性的影响,验证了热膨胀诱发的转轴窜动因素是影响厚盘转子系统动力学特性的主要因素之一。
Abstract:According to complex and changeable high-temperature environments of large rotating machinery, such as aero engines or steam turbines, the main rotor system of the unit has a variable structure due to thermal expansion under operating conditions, which could also affect the operation characteristics. First, considering high stiffness of turntable-drum mixing, compared with the rotating shaft, the structure is simplified and a single-thickness disk rotor dynamic model is established. Second, aimed at the variable structure characteristics of the system caused by thermal expansion, Hermite interpolation method and curve fitting method are used to depict the bending condition of rotating shaft when the thickness table is at any position, and then bending restoring force provided to disk and the bending restoration stiffness of the shaft are calculated by using numerical methods, basing on elastic potential energy stored in the bending.Finally, through numerical analysis of precession frequency, critical angular velocity and response amplitude of thick disk rotor system, it is verified that axial movement induced by thermal expansion is one of the main factors that affect the dynamics properties of thick disk rotor system.
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Key words:
- mixing rotor system /
- thermal expansion /
- thick disk /
- bending potential energy /
- bending stiffness
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表 1 厚盘转子系统参数
Table 1. Parameters of rotor system with thick disk
参数 数值 弹性模量E/(N·m-2) 2.058×1011 泊松比μ 0.28 材料密度ρ/(kg·m-3) 7 800 转盘质量m/kg 100 转盘半径R/m 0.12 转轴半径Rl/m 0.03 偏心量ε/m 0.3×10-4 比例阻尼系数β1,β2 0.2×10-3 转轴总长l0/m 1.5 轴段长l10/m 0.6 轴段长l20/m 0.9 表 2 弯曲恢复刚度受T1W的影响
Table 2. Bending restoration stiffness affected by T1W
T1W/K krr/(107N·m-1) kθθ/(106N·m-1) krθ/(106N·m-1) 248 3.770 6 5.869 3 -4.078 4 356 3.751 7 5.863 7 -4.058 2 428 3.739 2 5.860 0 -4.044 7 482 3.729 8 5.857 3 -4.034 7 536 3.720 5 5.854 5 -4.024 6 572 3.714 3 5.852 7 -4.018 0 608 3.701 8 5.850 9 -4.011 3 表 3 弯曲恢复刚度受T2W的影响
Table 3. Bending restoration stiffness affected by T2W
T2W/K krr/(107N·m-1) kθθ/(106N·m-1) krθ/(106N·m-1) 1 472 3.692 6 5.862 4 -3.985 6 1 652 3.701 8 5.850 9 -4.011 3 1 742 3.715 8 5.845 1 -4.024 2 1 796 3.720 5 5.841 7 -4.031 9 1 868 3.726 7 5.837 2 -4.042 2 2 012 3.739 2 5.828 1 -4.062 9 2 192 3.754 9 5.816 8 -4.088 8 表 4 弯曲恢复刚度受转盘厚度的影响
Table 4. Bending restoration stiffness affected by disk thickness
b/m krr/(107N·m-1) kθθ/(106N·m-1) krθ/(106N·m-1) 0.05 3.754 9 5.070 7 -2.553 2 0.08 3.754 9 5.500 7 -3.474 5 0.1 3.754 9 5.816 8 -4.088 8 0.12 3.754 9 6.156 5 -4.703 0 0.15 3.754 9 6.710 4 -5.624 3 0.2 3.754 9 7.751 6 -7.159 9 0.22 3.754 9 8.209 3 -7.774 1 表 5 临界角速度受T1W的影响
Table 5. Cirtical angular velocity affected by T1W
T1W/K ω1/s-1 ω2/s-1 ω3/s-1 248 566 620 2 219 392 564 618 2 218 482 563 617 2 218 608 562 615 2 217 表 6 临界角速度受T2W的影响
Table 6. Cirtical angular velocity affected by T2W
T2W/K ω1/s-1 ω2/s-1 ω3/s-1 1 472 561 614 2 220 1 652 562 615 2 217 1 832 563 616 2 214 2 192 565 619 2 209 d0/m ΩA-max/s-1 Axr/(10-4m) 0.04 291 4.175 7 0.05 455 2.736 9 0.06 658 1.928 3 T1W/K ΩA-max/s-1 Axr/(10-4m) 302 459.2 2.717 9 572 456.5 2.739 4 932 452.9 2.768 2 T2W/K ΩA-max/s-1 Axr/(10-4m) 1 832 453.7 2.758 0 2 192 455.2 2.737 0 2 732 459.8 2.733 0 -
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