Transient Response of Control Stage Blade Disk due to Partial Admission by a Reduced Method

Partial admission can improve the thermal efficiency of steam turbines at low loads, but a non-uniform flow in circumference will be caused inevitably at the same time. That makes control stage blade subject to complex load, leading to the high cycle fatigue. Therefore, it is important to calculate and accurately analyze transient response of control stage blade disk due to partial admission. However, the large number of degrees of freedom of the practical control stage blade disk will lead to an extremely high computational cost when the finite element method is used. A strategy for reducing the number of degrees of freedom based on the component modal synthesis (CMS) method is presented. CMS method is used to generate a super-element of one group of 4 blades. The cyclic symmetric property is used to generate super-elements for other groups of blades through circumferential rotation and coordinate transformation. The total number of degrees of freedom is reduced to 1.21% of the original DOF. When the rotating blades enter and leave the arc of admission under partial admission conditions, they are subject to the effect of shock loading. The length of the effect of shock loading depends on the rotating blade pitch and the peak of effect of shock loading depends on stage pressure ratio. The displacement response of control stage blade disk under different shock coefficients (1.6, 2.5, 4) is calculated. This paper analyses the vibrations of blade disk under high frequency force caused by nozzles under partial admission conditions. The results show that compared to the shock coefficient of 1.6 the maximum displacement response increased by 27.3% and 72.6% for shock coefficients 2.5 and 4. In addition, a beat phenomenon is found in displacement response of blade disk under high frequency force. The FFT of the response and excitation and the ZZENF of blade disk indicate that the composite vibration of 6050Hz, 6000Hz and 4900Hz these 3 kinds of harmonic vibrations is the main reason of the beat phenomenon.