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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 diesel crankshaft vibration for a four-cylinder engine, including diagrams and a table of stress values at resonance.

Identifier  ExFiles\Box 132\1\  scan0121
Date  25th March 1939
  
DIESEL CRANKSHAFT VIBRATION
405

deg. for the 10 order critical. Values of Amax. are plotted in Fig. 20.
We note that the important critical for the four-cylinder engine is that corresponding to the sixth harmonic, at 4350 r.p.m., which is outside the operating speed range of the engine.
The calculated stresses are based on a shaft of 3 in. diameter, the same as for the six-cylinder engine; so, comparing Fig. 20 with Fig. 16, we find that the distribution of stress is more favorable in the four-than in the six-cylinder, which is due to the fact that the crankshaft length is less in the former. This does not mean, however, that for the same bore and stroke the crankshaft can be made of smaller diameter in the four-cylinder engine. The inherent roughness of the four-cylinder engine, due to the unbalanced secondary inertia force, often calls for a much heavier flywheel for tractor and industrial installations, and the larger flywheel increases the vibration stresses. The moment of inertia of the flywheel should not be more than 50 times the inertia of the moving parts of the individual cylinder.
Examining the normal elastic curve, we see that the amplitude of vibration of the flywheel is comparatively small, and we, therefore, cannot expect any noticeable change in frequency to result from increasing the moment of inertia of the flywheel above normal. In comparing the shafts of the six- and four-cylinder engines, the former will show up to advantage because the moment of inertia of its rotating masses is smaller.
It is important to note that the operating speed of both engines is kept well below the critical speeds of the first to fourth harmonic orders. The reason for this is that at these critical speeds the inertia

FIGURES 17, 18, and 19

FIG 17
L=19
M5 NODE
I=0.88 LB. IN. SEC.²
I5=11.5 LB. IN. SEC.²

FIG 18
NORMAL ELASTIC CURVE
E
1.0000
0.8800
d=3"
0.6460
0.3400
-0.0550
E
NODE
M1 M2 M3 M4
CYLINDERS
I1=0.22
I2
I3
I4
I5=11.5
L1=7
L2=7.5
L3=7
L4=8

FIG 19
LB. PER SQ. IN.
±0
5000
10000
15000
ω²=7500000 RAD²SEC⁻²
f=26148 CYCLES PER MIN.
20000
VIBRATION STRESS
15,300 LB. PER SQ. IN. PER 1° DEFLECTION AT CYLINDER NO. 1

Four-Cylinder Engine
f = 26148 cycles per min.
One-Node Frequency
MAX. VIBRATION STRESSES AT RESONANCE SPEED WITH HYSTERESIS DAMPING
ω² = 7,500,000 rad²-sec.⁻²
TABLE VI
Firing Order : 1-2-4-3
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 VII | PΣe | A Eq. 19 | Q 15300 x A | γ Eq. 8 | S | A° max. Eq. 19 |
| 4½ | 6537 | 15.00 | 2.8460 | 42.600 | ±0.015000 | ±229.50 | 139 | ±32000 | ±2.10 |
| 4¾ | 5800 | 10.10 | 0.6875 | 6.875 | 0.002400 | 36.70 | 346 | 12600 | 0.83 |
| 5 | 5250 | 8.00 | 0.1860 | 1.500 | 0.000500 | 7.65 | 780 | 5950 | 0.39 |
| 5½ | 4750 | 6.00 | 0.6875 | 4.140 | 0.001400 | 21.40 | 458 | 9800 | 0.64 |
| 6 | 4350 | 4.65 | 2.8460 | 13.200 | 0.004600 | 70.40 | 253 | 17800 | 1.16 |
| 6½ | 4000 | 3.50 | 0.6875 | 2.400 | 0.000840 | 12.85 | 600 | 7700 | 0.50 |
| 7 | 3750 | 2.80 | 0.1860 | 0.520 | 0.000180 | 2.75 | 1620 | 4450 | 0.29 |
| 7½ | 3500 | 2.50 | 0.6875 | 1.710 | 0.000600 | 9.20 | 700 | 6400 | 0.42 |
| 8 | 3280 | 1.60 | 2.8460 | 4.550 | 0.001600 | 24.50 | 430 | 10500 | 0.69 |
| 8½ | 3100 | 1.50 | 0.6875 | 1.030 | 0.000400 | 6.12 | 840 | 5120 | 0.34 |
| 9 | 2900 | 1.10 | 0.1860 | 0.200 | 0.000070 | 1.07 | 2100 | 2200 | 0.15 |
| 9½ | 2750 | 0.90 | 0.6875 | 0.620 | 0.000200 | 3.06 | 1220 | 3660 | 0.24 |
| 10 | 2614 | 0.70 | 2.8460 | 2.000 | 0.000700 | 10.70 | 655 | 7000 | 0.46 |
| 10½ | 2500 | 0.60 | 0.6875 | 0.410 | 0.000140 | 2.14 | 1500 | 3200 | 0.21 |
| 11 | 2380 | 0.50 | 0.1860 | 0.093 | 0.000032 | 0.49 | 3000 | 1470 | 0.10 |
| 11½ | 2280 | 0.40 | 0.6875 | 0.270 | 0.000090 | 1.38 | 2000 | 2760 | 0.18 |
| 12 | 2170 | 0.33 | 2.8460 | 0.940 | 0.0000330 | 5.05 | 940 | 4750 | 0.31 |

Automotive Industries
  
  


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