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).
Calculation table for torsional vibrations in 12-cylinder Vee engines, showing coefficients for various harmonic orders and engine Vee angles.
| Identifier | ExFiles\Box 138\1\ scan0009 | |
| Date | 1st January 1932 | |
| 12 CYL. VEE ENGINES - TORSIONAL VIBRATIONS 1932 HS.{Lord Ernest Hives - Chair}533 (Diagram showing Z and β) (β = p(2π - α)) Z = 2 Sin(pπ - β/2) TABLE: ORDER | α = 30° | α = 45° | α = 60° | α = 65° | α = 80° | α = 90° | *W/N Θ Z N | *W/N Z N | *W/N Θ Z N | *W/N Θ Z N | *W/N Θ Z N | *W/N Θ Z N 1 1/2 | 1.255 135 .77 .97 | 1.111 1.40 | 1.414 82.5 1.77 1.5 | 1.89 60 1.730 2.18 | 60 1.730 2.18 | 45 1.78 2.24 2 | .16 300 1.732 .28 | 1.414 .23 | 1.0 16 .16 | 2.30 .84 .14 | 200 .348 .06 | 180 0 0 2 1/2 | .682 105 1.22 .83 | 1.663 1.13 | 1.932 17.5 1.32 1.98 | 1.35 340 1.97 1.34 | 340 1.97 1.34 | 315 1.78 1.21 3 | _4.33_ _270_ _1.42_ _615_ | .765 3.31 | 0 0 | 165 .26 1.12 | 120 1.0 4.33 | 90 1.42 6.15 3 1/2 | .682 75 1.58 1.07 | 1.961 1.34 | 1.932 312.5 1.32 1.84 | 1.26 260 1.284 .88 | 260 1.284 .88 | 225 .77 .52 4 | .16 240 1 .16 | 0 0 | 1.0 16 | 100 1.28 .20 | 40 1.88 .30 | 0 2 .32 4 1/2 | _1.255_ _45_ _1.77_ _2.22_ | 1.961 2.46 | 1.414 247.5 1.78 1.11 | 1.39 180 0 0 | 180 0 0 | 135 .77 .97 5 | .16 210 .52 .08 | .765 .12 | 1.732 35 .25 .77 | .12 320 .684 .11 | 320 .684 .11 | 270 1.42 .23 5 1/2 | .652 15 2 1.36 | 1.663 1.13 | .517 182.5 .35 .04 | .03 100 1.284 .87 | 100 1.284 .87 | 45 1.78 1.21 6 | _4.33_ _180_ _0_ _0_ | 1.414 6.12 | 2.0 330 8.66 1.94 | 8.40 240 1.0 4.33 | 240 1.0 4.33 | 180 0 0 6 1/2 | .68 345 2 1.36 | 1.111 .76 | .517 117.5 .35 .04 | .71 20 1.970 1.34 | 20 1.970 1.34 | 315 1.78 1.22 7 | .16 150 .52 .08 | 1.848 .30 | 1.732 265 .28 1.76 | .28 160 .348 .05 | 160 .348 .05 | 90 1.42 .23 7 1/2 | 1.255 315 1.77 2.22 | .39 .49 | 1.414 52.5 1.77 1.80 | 2.26 300 1.732 2.16 | 300 1.732 2.16 | 225 .77 .97 8 | .16 120 1 .16 | 2.0 .32 | 1.0 200 .16 .76 | .03 80 1.42 .23 | 80 1.42 .23 | 0 2 .32 8 1/2 | .682 285 1.58 1.07 | .39 .27 | 1.932 347.5 1.32 1.99 | 1.36 220 .684 .46 | 220 .684 .46 | 135 .77 .52 9 | _4.33_ _90_ _1.42_ _6.15_ | 1.848 8.00 | 0 135 0 .76 | 3.30 0 2 8.66 | 0 2 8.66 | 220 1.42 6.14 9 1/2 | .682 250 1.22 .83 | 1.111 .76 | 1.932 282.5 1.32 1.58 | .11 140 .684 .46 | 140 .684 .46 | 45 1.78 1.21 10 | .16 60 1.732 .28 | 1.414 .23 | 1.0 70 .16 1.84 | .30 280 1.42 .22 | 280 1.42 .22 | 180 0 0 10 1/2| 1.255 220 .77 .97 | 1.663 2.08 | 1.414 217.5 1.77 .65 | .82 60 1.732 .216 | 60 1.732 .216 | 315 1.78 .224 11 | .16 30 1.92 .29 | .765 .12 | 1.732 5 .28 2 | .32 200 .348 .05 | 200 .348 .05 | 90 1.42 .22 11 1/2| .682 190 .26 .17 | 1.961 1.34 | .517 152.5 .35 .48 | .33 340 1.970 1.34 | 340 1.970 1.34 | 225 .77 .53 12 | _4.33_ _0_ _2_ _8.66_ | 0 0 | 2.0 300 8.66 1.732 | 7.50 120 1.0 4.33 | 120 1.0 4.33 | 0 2 8.66 THE COLUMNS MARKED * WOULD IF MULTIPLIED BY THE MAGNITUDE OF THE APPROPRIATE HARMONIC OF THE GAS AND INERTIA TORQUE BE AN EXACT CRITERION OF THE SEVERITY OF THE TORSIONAL PERIODS. AS THEY STAND THEY ARE DIRECTLY COMPARABLE ALONG THE HORIZONTAL LINES BUT NOT ALONG THE VERTICAL COLUMNS. THIS TABLE SHOWS THEREFORE THE RELATIVE IMPORTANCE OF ONE PARTICULAR VIBRATION WHEN THE VEE ANGLE OF THE ENGINE IS VARIED. THE IMPORTANT VIBRATIONS ARE UNDERLINED. W/N IS A NON-DIMENSIONAL COEFFICIENT DEPENDING ON THE DEFLECTION CURVE OF THE CRANKSHAFT. Θ IS THE ANGLE OF LAG OF ONE BANK OF CYLINDERS BEHIND THE OTHER. Z IS THE COMBINED EFFECT OF BOTH BANKS. ALL CALCULATIONS BASED ON “LIBERTY” CRANKSHAFT IN FIRING ORDER. | ||