軸系捩振動のために推進器翼に加はる荷重
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概要
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The Author ever stated that the torque fluctuation of the intermediate shaft must be considered when calculating the strength of propeller. The present paper expains the relation between torque fluctuation and bending moment at the root of blade of propeller by its own inertia. The wave form of one complete period on film which is recorded by Author's torsionmeter can be expressed as follows : Δ-Δ_m=Σγ_nsin (nω_0t+φn), where Δ=displacement of image from zero line (cm), Δ_m=mean displacement of image from zero line (cm), n=wave number of the component of harmonics included in one period, ω_0=2πN/60 for 2-cycle engine, =πN/60 for 4-cycle engine, N=revolutions of shaft per miuuite, γ_n=amplitude of the component (cm), φ_n=phase angle of the component. Assuming the positions of nodes of forced vibration to be the same as those of free vibrations, fathermore neglecting the inerlia of shaft, the formula for amplitude of shaft at propeller position referred to any one of the mode of vibration is θ_L=1/(Ip^2)Σqγ_nsin (nω_0t+φn), where L=virtual moment of inertia of propeller (g. cm^2), p/2π=natural frequency per second for the mode of vibration under consideration, q=torque per unit displacement of image (dyne, cm^<-1>). Practically, it is enough for this purpose only to consider the vibration with one node. The angular displacement, angular speed and angular acceleration of propeller are φ=(2πN)/(60)t-1/(Ip^2)Σqγ_nsin (nω_0t+φn), ω=(2πN)/(60)-1/(Ip^2)Σnω_0qγ_ncos (nω_0t+φn), α=1/(Ip^2)Σ(nω_0)^2qγ_nsin (nω_0t+φn). Assuming that the distribution of virtual mass along the blade is similar to the distribution of actual mass of blade and the boss is sphere, the virtual moment of propeller and the bending moment at root of a blade are I=zk'p^1∫^<R0>_<Rr>AR^2dR+p^2π/(60) (2Rr)^5,M=-α・k'p^1[∫^<R0>_<Rr>AR^2dR-Rr∫^<R0>_<Rr>ARdR], where z=number of blades, k'p_1=virtual density of blade (g. cm^<-3>), p_3=density of boss (g. cm^<-3>), 2Rr=dia. of boss, 2R_0=dia of propeller, A=sectional area of blade at a rad. R. k' is larger than unity. M is the vector quantity whose direction coincides with axis of propeller shaft. Assuming that the contour of blade is elliptic and sectional form of blade at any radius is parabolic, the above formu'as can be simplified as follows : I=((1+ε)z)/6k'p_1γβ(2R_0)^5φ_2(cr), M=-(φ(Cr))/((1+e)z)Σ((nω_0)/p)^2qγ_nsin (nω_0t+φn), =-716(φ(Cr))/((1+ε)z)・(S.H.P)/(zN)Σ(N/(N_nc))^2(qγn)/(Qm)sin (nω_0t+φn), where ε=ratio of moment of inertia of boss to virtual moment of inertia of blades, γ=blade thickness ratio, ηγ=thickness ratio of blades at tip, β=max. blade width ratio, φ_1 (Cr)=∫^1_<cr>c^2 (1-c+ηc)√<c-c^2>dc, φ_2 (Cr)=Cr∫^1_<cr>c(1-c+ηc)√<c-c^2>dc, φ (Cr)=1-(φ_2 (Cr))/(φ_1 (Cr)), C=R/R_0,Cr=Rr/R0=boss ratio, Nnc=critical speed of shaft for nth component, Qm=mean torque transmitted through shaft, (qγn)/(Qm)=(γ_n)/(Δm)=torque fluctuation for nth component. On designing a propeller, unknown factors in the formula for M are qγn/Q_m and φn. However, as it is sufficient to know the peak value of bending moment at root of blade, so the following simplified formula may be used. M=-716(φ(cr))/((1+ε)z)(S.H.P.)/(zN)Σ(N/(Ncn))^2(qγn)/(Qm) Reasonable value for qγn/Qm will be able to estimate from the records of torsionmeter which are printed in previous paper.
- 1941-09-30
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