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).
Treatise on engine crankshafts, focusing on torsional vibration analysis and stress calculations.
| Identifier | ExFiles\Box 132\1\ scan0119 | |
| Date | 25th March 1939 | |
| 403 Part Two Engine Crankshafts Completing this treatise, Part One of which appeared in the March 18 issue of AUTOMOTIVE INDUSTRIES Table 5 HARMONIC ORDER 1/2 - 2 1/2 - 3 1/2 5 1/2 - 6 1/2 - 8 1/2 9 1/2 - 11 1/2 1 - 2 - 4 - 5 7 - 8 - 10 - 11 1 1/2 - 4 1/2 7 1/2 - 10 1/2 3-6 9-12 FIRING ORDER 1-4-2-6-3-5 PHASE DIAGRAM | VECTOR DIAGRAM [Diagram for ω/2] | [Vector Diagram Σε=0.5] [Diagram for 2ω] | [Vector Diagram Σε=0.25] [Diagram for 1 1/2 ω] | [Vector Diagram Σε=1.45] [Diagram for 3ω] | [Vector Diagram Σε=4.0814] CYL. NO. | FIRING ANGLE 1 | 0° 2 | 120 3 | 240 4 | 360 5 | 480 6 | 600 f₁ = 9.55 x 1923 = 18,440 cycles per min. The vibration amplitude in col. 6 represents a normal elastic curve EE (Fig. 11) with one node near the flywheel. The phase velocity for two-note vibration (Figs. 13, 14, and 15, and Equation 17), was found to be ωs² = 19,734,000 rad²-sec.⁻², and the corresponding second natural frequency, f₂ = 42,400 cycles per min. Proceeding in the same manner we calculate the normal elastic curve for two-node vibration (Table II, col. 6). Having the data for the normal elastic curves for one- and two-node vibration (Tables I and II, col. 6), we can determine the vibration stress in each section of the shaft for a deflection of 1 deg. at cylinder No. 1 by means of Equation (13), which is represented in col. 12 of Tables I and II, and graphically in Figs. 12 and 15. The vibration stresses are a maximum at the nodes, their values being s = 10,850 lb. per sq. in. for one-node vibration, and s = 32,000 lb. per sq. in. for two-node vibration. For two-node vibration the frequency f = 51,500 cycles per min., and for a maximum engine speed of 3000 r.p.m. the lowest harmonic order that can come into resonance is the 51,500/3000 = 17th, which is of no practical importance. Therefore, we will omit any further consideration of possible two-node vibration and proceed with the calculation of vibration stresses at resonance in one-node vibration. If there should be a possibility of resonance with harmonic orders of less than the twelfth, the stresses due to two-node vibration should be investigated. Table V is a phase and vector diagram for six-cylinder four-stroke engines. The firing angles are shown in the last column, and the phase angle of any harmonic order is the product of the firing angle by the number of the order. In the phase diagrams 180 deg. corresponds to 360 deg. of crankshaft revolution. The vector diagram is developed from the phase diagram. The values of the normal elastic curve given in Table I, col. 6, for each cylinder serve as the lengths of the corresponding vectors. The resultant of the force polygons gives the vector sum Σε for the various harmonic orders. Inserting the values Σ ε from Table V in Table III, col. 16, and multiplying by the harmonic torque P, we have the resultant harmonic components of all cylinders (col. 17). The maximum stresses (col. 19) at the node are the product of amplitude A by the maximum stress per degree of deflection at No. 1 cylinder given in col. 12 of Table I; s = 10.850 lb. per sq. in. The stress in the crankshaft opposite cylinder No. 4, for example, can be found by multiplying amplitude A by s = 9100, etc. The maximum vibration stress S in lb. per sq. in., at the crankshaft node (Table III, col. 21) at resonance speed with hysteresis damping is the product of the magnification factor 8 (Table III, col. 20; also Equation 8) by Q (Table III, col. 19). After plotting the values S (Table III, col. 21) on Fig. 16 for each harmonic order and critical speed at resonance speed with hysteresis damping, we have the magnitudes of torsional vibration stresses in lb. per sq. in. for the six-cylinder crankshaft with the firing order 1-4-2-6-3-5. We see that the only important critical is due to the sixth harmonic order, at 3000 r.p.m., and the stress induced by it is much above the safe stress and near the critical stress of 30,000 lb. per sq. in.; therefore, it is not advisable to run the engine at that speed in continuous service. Critical speeds of the 9 and 7 1/2 order occur at 2000 and 2500 r.p.m. of the engine, but the stresses induced by them are within the critical stress limit. The stresses are based on the equivalent shaft diameter of 3 in., and it is obvious that if a smaller shaft were used, the stresses would be greater. For the firing order 1-5-3-6-2-4 the maximum stresses are the same for the major critical speeds, and differ only for the minor critical speeds; nevertheless, it must be kept in mind that the change in firing order of the engine may affect the torsional stresses and endanger the life of the shaft, especially in the case where the minor critical speeds are of importance. With an increase of the speed of the engine up to 6000 r.p.m., the stresses reach prohibitive figures; therefore, if it is required to run the engine at a higher speed for Automotive Industries March 25, 1939 | ||