Abstract
The object of this investigation was to study mathematically the effect of the deck band on the natural frequency of turbine blades in a group which are mounted on the rim of a turbine wheel rotating with a constant speed.For the purpose of obtaining the result the method of combination of two kinds of frequencies, one of which is that for an elastic body without rotation and the other is that for the same body when the effect of the flexural rigidity is neglected, was employed. The section of each blade was assumed to be uniform throughout its length in order to avoid the complexity of the problem. The series of blades in a group was considered as endless. The deflection vibrations of blades in one group are mainly in the direction of the least moment of inertia of the blade section.When the density, Young's modulus and the effective breadth of the deck band are respectively equal to those of the blades, the values of (ρ1P'2/E1K12) 4/1l1, where the effect of the rotation is neglected, are shown in the table below.a1/a2 1/10 1/2 1 2 4 6 9l1/l2=10 5 1.72 - 2.13 1.98 2.226 2.10 2.22 2.19 2.09 1.97 1.97 1.90 1.90 -In this a1, and a2, are effective areas of blade and deck band, l1, and l2 their respective efective lengths, and ρ1, E1, K1 are the density, Young's modulus, the effective radius of gyration of the section of a blade, while p'/2π is the natural frequency under the assumed condition of the problem.When the conditions concerning densities, Young's moduli and breadths are similar to those of the preceding case and the effect of the flexural rigidity is neglected, the values of l1/R corresponding to different p''2/ω2 and l2a2/l1a1 are shown in the following table.p''2/ω2 3 6 10 15 21l2a2/l1a1=0 1/40 1/20 1/10 1/5 1.736.719.698.678.617.410.291.285.280.263.250.151.1615.160.153.149.136.082.104.102.009.097.090.052.073.071.069.968.061.038In this table ω is the angular velocity of the wheel in radian and p''/2π is the natural frequency of blade under the assumed condition.The effectiveness of the deck band on the, stiffness of turbine blades, excepting the prevention of the mutual impact of blades, was discussed from theoretical point of view and the method of application of the present result to practical problems was shown by the introduction of the formula indicating the actual natural frequency of the blade, namelyp/2π=1/2π√p'2+p''2.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
