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 crankshaft vibration with calculations for moment of inertia and stress.
| Identifier | ExFiles\Box 132\1\ scan0115 | |
| Date | 18th March 1939 | |
| DIESEL CRANKSHAFT VIBRATION 377 Where crank arms of special form are used, it is advisable to divide them up into simple geometrical bodies A, B, and C, find the center of gravity, weight and moment of inertia of each, and then make use of the rule that the moment of inertia of a body around any axis parallel to an axis through its center of gravity is equal to its moment of inertia around the axis through its center of gravity plus the product of its weight by the square of the distance between the two axes. The outside axis in this case is the crankshaft axis. The moment of inertia of the crank arm is I_6 = 15.442 / 386 = 0.04 lb.-in.-sec.² The various moments of inertia for the moving parts of the six-cylinder engine add up as follows: Rotating parts 6 x 0.046 = 0.2760 Reciprocating parts 6 x 0.0393 = 0.2358 Journals, front and interm. 5 x 0.008 = 0.0400 Journals, center and rear 2 x 0.0116 = 0.0232 Crank cheeks 12 x 0.04 = 0.4800 Pins 6 x 0.0384 = 0.2304 Total moment of inertia = 12.86 This makes the moment of inertia per cylinder 12.86 / 6 = 0.22 lb.-in.-sec.² ... (14) The equivalent length of the whole crankshaft is L = 3 x 7 + (1.7 to 2) d_1 = 26.75 in. The moment of inertia of the front and intermediate crank journals, each of which has a diameter d_2 of 3 in., a length l of 1.4 in., a weight W of 2.76 lb., and a squared radius of gyration m² = d_2²/8 of 1.12, is found to be I_1 = Wm² / 386 = (2.76 x 1.12) / 386 = 0.008 lb.-in.-sec.², 386 representing the gravitational constant in in.-sec.² For the rear and center main journals d_2 is 3 in.; l, 2.03 in.; W, 4 lb., and m², 1.12, so that the moment of inertia of each of these journals is I_2 = (4 x 1.12) / 386 = 0.0116 lb.-in.-sec.² For the crankpin d is 2.5 in.; l, 1.83 in.; W, 2.42 lb., and m² = d²/8 + r² = 5.84. I_3 = (2.42 x 5.84) / 386 = 0.0384 lb.-in.-sec.² The reciprocating parts have a weight W of 6 lb. and an equivalent radius of rotation r of 2.25 in.; hence their moment of inertia I_4 = Wr² / 2g = (6 x 5.06) / (2 x 386) = 0.0393 lb.-in.-sec.² Figures 10, 11 and 12 Figures 13, 14 and 15 Automotive Industries FIGURE LABELS: FIG. 10: L=26.75, d=3", NODE, I=1.32 LB. IN. SEC.², I₇=10 LB. IN. SEC.² FIG. 11: NORMAL ELASTIC CURVE, CYLINDERS, NODE, M₁, M₂, M₃, M₄, M₅, M₆, M₇, d=3", I₁=0.22, I₂, I₃, I₄, I₅, I₆, I₇=10, L₁=7, L₂=7, L₃=7.5, L₄=7, L₅=7, L₆=9. Curve values: 1.0000, 0.9405, 0.8255, 0.6497, 0.4477, 0.2180, -0.0905. FIG. 12: VIBRATION STRESS, 10850 LB./SQ. IN. PER 1° DEFLECTION AT CYLINDER NO. 1. Y-axis: LB. PER SQ. IN. Values: ±2000, 6000, 10000. Chart text: ω²=3700000 RAD² SEC², f₁=18440 VIB. PER MIN. FIG. 13: Lₐ=21.5, Lₑ=16, d=3", I=0.66, L_Ma, M_b, Iₐ=0.66 LB.-IN.-SEC.², I₇=10 LB.-IN.-SEC.² FIG. 14: NORMAL ELASTIC CURVE, CYLINDERS, NODE, NODE, M₁, M₂, M₃, M₄, M₅, M₆, CYL. I=0.22, I₂, I₃, I₄, I₅, I₆, I₇=10, L₁=7, L₂=7, L₃=7.5, L₄=7, L₅=7, L₆=9. Curve values: 1.0000, 0.5336, 0.1824, -0.8581, -1.0880, -0.8092, 0.0309. FIG. 15: VIBRATION STRESS, 32000 LB.-SQ.-IN. PER DEG. DEFLECTION AT CYL. NO. 1. Y-axis: LB. PER SQ.-IN. Values: ±0, 10000, 20000, 30000, 40000. Chart text: f₂ = 51500 V/m, ω₂²=29090909 RAD² SEC². | ||