From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Technical page detailing frequency calculations for one-node vibration in a six-cylinder diesel crankshaft.
| Identifier | ExFiles\Box 132\1\ scan0113 | |
| Date | 18th March 1939 | |
| RM{William Robotham - Chief Engineer} DIESEL CRANKSHAFT VIBRATION 375 Six-Cylinder Engine f₂ = 51500 cycles per min. Frequency Calculation One-Node Vibration ωa² = 29,090.909 rad²-sec.⁻² TABLE II Figs. 13-14-15. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |---|---|---|---|---|---|---|---|---|---|---| | Cyl. Mass No. | d | l | I Eq. 14 | Iω² | ϵ Eq. 9 | Iω²ϵ | ΣIω²ϵ | M = GJ/l Eq. 3 | ΣIω²ϵ/M | S Eq. 13 | | 1 | 3 | 7 | 0.22 | 6.4 x 10⁶ | 1.0000 | 6.40 x 10⁶ | 6.40 x 10⁶ | 13.7 x 10⁶ | 0.4664 | ±20850 | | 2 | 3 | 7 | 0.22 | 6.4 x 10⁶ | 0.5336 | 3.41 x 10⁶ | 9.81 x 10⁶ | 13.7 x 10⁶ | 0.7160 | 32000 | | 3 | 3 | 7.5 | 0.22 | 6.4 x 10⁶ | -0.1824 | -1.16 x 10⁶ | 8.65 x 10⁶ | 12.8 x 10⁶ | 0.6757 | 28300 | | 4 | 3 | 7 | 0.22 | 6.4 x 10⁶ | -0.8581 | -5.50 x 10⁶ | 3.15 x 10⁶ | 13.7 x 10⁶ | 0.2299 | 10500 | | 5 | 3 | 7 | 0.22 | 6.4 x 10⁶ | -1.0880 | -6.97 x 10⁶ | -3.82 x 10⁶ | 13.7 x 10⁶ | -0.2788 | 12420 | | 6 | 3 | 9 | 0.22 | 6.4 x 10⁶ | -0.8092 | -5.17 x 10⁶ | -8.99 x 10⁶ | 10.7 x 10⁶ | -0.8401 | 29000 | | FLY | ... | ... | 10.00 | 290.9 x 10⁶ | 0.0309 | 8.99 x 10⁶ | 0 | ... | ... | ... | where s = 10,850, the maximum stress for one deg. of deflection (see Table I, col. 12); A is the amplitude of vibration (Equation 12), and C, the hysteresis constant, which is equal to 2100. According to Doctor Dorey, the hysteresis constant C varies with the composition of the steel, being equal to 1250 for 3 per cent nickel steel and to 1100 for carbon steel. It is interesting to note that when the material is stressed beyond the critical range, carbon steel with a hysteresis constant of 1100 has a higher vibration quality than high-tensile steel. However, in Diesel engines, with their high explosion pressures, the stresses in the crank arms must be kept within the permissible limits without undue increase in the thickness of the arms, which would result in lengthening the crankshaft and the cylinder block, and would add considerably to the weight and size of the engine, so it is advisable to use alloy steels. Normal Elastic Curve To find the maximum stress at the node of the crankshaft and the stress at any other section of the shaft during free vibration, it is necessary to determine the normal elastic curve (see Fig. 6 and Tables I and II). The normal elastic curve represents the value of the angular amplitude ϵ at the centers of the various crank-train masses and of the flywheel. These amplitudes are indicated in Fig. 6. The amplitude of the mass of cylinder No. 1 may have any arbitrary value, and is usually taken as ϵ = one radian. The angular amplitude at cylinder No. 2 then is ϵ₂ = ϵ₁ - (I₁ω²/M₁)ϵ₁ and that at cylinder No. 3, ϵ₃ = ϵ₂ - (ω²/M₂)(I₁ϵ₁ + I₂ϵ₂), etc. (9) where I₁ is the moment of inertia of mass No. 1 in lb.-in-sec.²; ωa², is the phase velocity in rad.²-sec.⁻² (Equation 5); M₁, the torsional rigidity or stiffness of shaft, in lb.-in. per radian (Equation 3); ϵ₁ = 1 radian, the angular amplitude at cylinder No. 1. Example: Angular amplitude at cylinder No. 2 (Equation 9) (see Table I, cols. 6 and 10) Figure 7 Graph with axes ENERGY and AMPLITUDE, showing curves for ENERGY STORED PER CYCLE BY TORQUE and ENERGY DISSIPATED IN HYSTERESIS DAMPING. Figure 6 NORMAL ELASTIC CURVE—SIX CYLINDER ENGINE Top diagram shows ONE NODE VIBRATION curve. Bottom diagram shows TWO NODE VIBRATION curve. Automotive Industries March 18, 1939 | ||