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).
Analysis of one-node frequency and maximum vibration stresses at resonance speed for a six-cylinder engine crankshaft.
| Identifier | ExFiles\Box 132\1\ scan0116 | |
| Date | 18th March 1939 | |
| 378 DIESEL CRANKSHAFT VIBRATION Six-Cylinder Engine TABLE III ONE-NODE FREQUENCY MAX. VIBRATION STRESSES AT RESONANCE SPEED WITH HYSTERESIS DAMPING f₁ = 18440 cycles per min. ω₁² = 3,700,000 rad²-sec.⁻² Firing Order : 1-4-2-6-3-5 I.M.E.P. = 100 lb. per sq. in. | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | |---|---|---|---|---|---|---|---|---|---| | Harmon Order K | Critical Speed R.P.M. f : K | P Fig. 9ab | Σe Table V | PΣe | A Eq. 12 | Q 10850 × A | γ Eq. 8 | S 1-4-2-6-3-5 | A max. Eq. 12 | | 3 | 6200 | 25.00 | 4.0810 | 102.000 | ±0.051000 | ±555.00 | 90.0 | ±50000 | ±4.60 | | 3½ | 5300 | 20.00 | 0.5000 | 10.000 | 0.005000 | 54.20 | 286.0 | 15600 | 1.43 | | 4 | 4600 | 15.00 | 0.2500 | 3.750 | 0.001900 | 20.60 | 466.0 | 9900 | 0.89 | | 4½ | 4100 | 10.10 | 1.4500 | 14.500 | 0.007300 | 80.00 | 236.0 | 19000 | 1.72 | | 5 | 3720 | 8.00 | 0.2500 | 2.000 | 0.001000 | 10.85 | 656.0 | 7250 | 0.66 | | 5½ | 3350 | 6.00 | 0.5000 | 3.000 | 0.001500 | 16.33 | 525.0 | 8600 | 0.79 | | 6 | 3000 | 4.65 | 4.0814 | 19.000 | 0.009500 | 103.00 | 210.0 | 21600 | 2.00 | | 6½ | 2840 | 3.50 | 0.2500 | 1.750 | 0.000900 | 9.80 | 700.0 | 6860 | 0.63 | | 7 | 2640 | 2.80 | 0.5000 | 0.700 | 0.000350 | 3.80 | 1100.0 | 4200 | 0.38 | | 7½ | 2460 | 2.50 | 1.4500 | 3.630 | 0.001800 | 19.50 | 470.0 | 9200 | 0.85 | | 8 | 2300 | 1.60 | 0.2500 | 0.400 | 0.000200 | 2.17 | 1470.0 | 3200 | 0.30 | | 8½ | 2170 | 1.50 | 0.5000 | 0.750 | 0.000380 | 4.15 | 1030.0 | 4300 | 0.39 | | 9 | 2050 | 0.90 | 4.0814 | 4.080 | 0.002100 | 22.78 | 446.0 | 10200 | 0.94 | | 9½ | 1940 | 1.10 | 0.5000 | 0.450 | 0.000220 | 2.40 | 1600.0 | 3880 | 0.35 | | 10 | 1840 | 0.90 | 0.2500 | 0.170 | 0.000085 | 0.92 | 2200.0 | 2000 | 0.19 | | 10½ | 1760 | 0.70 | 1.4500 | 0.870 | 0.000440 | 4.80 | 955.0 | 4600 | 0.42 | | 11 | 1680 | 0.60 | 0.2500 | 0.125 | 0.000060 | 0.65 | 2620.0 | 1700 | 0.16 | | 11½ | 1600 | 0.50 | 0.5000 | 0.200 | 0.000100 | 1.08 | 2000.0 | 2160 | 0.20 | | 12 | 1530 | 0.33 | 4.0814 | 1.300 | 0.000650 | 6.50 | 840.0 | 5500 | 0.50 | The outside diameter of the flywheel rim is 15 in., the inside diameter 10 in., the weight 95 lb., and the square of the radius of gyration, m² = (D² + d²)/8 = 40.6. Therefore, the moment of inertia of the flywheel is I₇ = W × m² / 386 = 95 × 40.6 / 386 = 10 lb.-in.-sec.² The torsional stiffness of the crankshaft is calculated by means of Equation (3) (see also Fig. 11) M₁ = M₂ = M₄ = M₅ = GJ / l₁ = (12 × 10⁶ × 8) / 7 = 13.7 × 10⁶ M₃ = GJ / l₃ = (12 × 10⁶ × 8) / 7.5 = 12.8 × 10⁶ M₆ = GJ / l₆ = (12 × 10⁶ × 8) / 9 = 10.7 × 10⁶ M₇ = GJ / l₇ = (12 × 10⁶ × 8) / 26.75 = 3.6 × 10⁶ (15) We now have a six-cylinder crankshaft reduced to the system illustrated in Fig. 11, with calculated inertias of 0.22 lb.-in.-sec.² for the moving mass of each cylinder, with a flywheel inertia of 10 lb.-in.-sec.², and torsional rigidities of the shaft units as calculated in Equation (15). For the purpose of calculating the natural frequencies this system is replaced by: (a) A two-mass system (Fig. 10), one mass representing the six crank units, with a moment of inertia I = 1.32 lb.-in.-sec.², the other representing the flywheel, with a moment of inertia of 10 lb.-in.-sec.² This is for the first mode of vibration with one node. (b) A three-mass system (Figs. 13, 14, and 15), for second-mode vibration with two nodes. The third, fourth, and higher modes of vibration are of no particular interest in our case. The natural frequency of the two-mass system is according to Equation (5) ω₁² = M₇(I + I₇) / II₇ = (3.6 × 10⁶(1.32 + 10)) / (1.32 × 10) = 1800 rad/sec. ω₁² = 3,300,000 rad²-sec.⁻² mass system with one node according to Equation (2) is f₁ = 9.55 √(M₇(I + I₇) / II₇) or f₁ = 9.55 √((3.6 × 10⁶(1.32 + 10)) / (1.32 × 10)) = 17200 cycles per minute The phase velocity of the two- Part Two of this treatise by O.{Mr Oldham} Malychevitch will be concluded in AUTOMOTIVE INDUSTRIES in the issue of March 25. March 18, 1939 Automotive Industries | ||