Stress analysis of the Model W-1 engine (Power Plant Section report)

              Auburn University Libraries
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File D52.41 /W-1 /4 IA f f(!~OK · ELD REPORT, SERIAL No. i 131
Vol. V
(AVIATION)
PUBLISHED BY THE CHIEF OF AIR SERVICE, WASHINGTON, D. C.
March 1, 1924
STRESS ANALYSIS OF THE MODEL
W-1 ENGINE
(POWER PLANT SECTION REPORT)
Prepared by H. CAMINEZ and C. W. ISELER
Engineering Division, Air Service
McCook Field, Dayton, Ohio
March 17, 1923
No. 447
Ralph Brown Draughon
LI BRA.RY
WASHINGTON
GOVERNMENT PRINTING OFFICE
1924
MAY 1 3 2013
Non·Depoitmv
Auburn Un\versltv
CERTIFICATE: By direction of the Secretary of War, the matter contained herein is published as administrative
information and is required for the proper transaction of the public business.
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STRESS ANALYSIS OF THE M0DEh 7:.W-1 .EN . INE.
-.._'-._:;;../
OBJECT.
The object of this report is to give a complete stress
analysis of the Model W-1 engine.
PROCEDURE.
The method of stress analysis given in Engineering
Division Report, Serial No. 2038, has been followed.
The equations used herein are numbered to correspond
to the equations in the a bove-mentioned report from
which they are derived.
The Model W-1 engine was designed to develop 800
horsepower at 1,800 revolutions per minute with a
mechanical efficiency of 88 per cent. The stress analy­sis
is made on a basis of the designed rating, together
with the engine characteristics and dimensions given
in the following table:
ENGINE CHARACTERISTICS.
Brake horsepower_ _ _ _ _ _ 800
Revolutions per minute ____ ___ _____ _______ __ 1,800
Number of cylinders_ __ ___ ___ ___ __ _______ ___ 18
Cylinder arrangement___________ ____ 3 banks at 40°
Bore _ ____ ________ ____ ___ ----- - ___ inches__ 5. 5
Stroke:
Center bank cylinders ______ ______ do ____ 6.50
Side bank cylinders _ _______ _____ _ do_ _ 6 . 685
Piston displacement per cylinder:
Center bank cylinders ____ _ cubic inches __
Side bank cylinders. ______ _____ __ do __ _ Total piston displacement_ ·- ____ ______ do ___ Compression ratio ___ ___ _____ ________ _____ _
Mechanical efficiency ___ _____ ___ __ per cent __
Method of numbering cylinders:
{
O O O O O 0-R
Propellerend __ ____ 0 0 0 0 0 0-C
· 0 0 0 0 0 0-L
65432i
. {1L--6C-1R-5L--2C-5R
Firing order ._ ___ 3L--4C-3R-6L--1C-6R
2L--5C-2R-4L--3C-4R
154.4
158.8
2 ,832
5.4
88
Piston area _____ __ ___________ square inches __ 23. 76
Connecting rod length, center to center (master
rod)---- -~---- - -- - s - - - -- -- ----- -inches__ 13
Rod, stroke ratio ___ -- - - - -______ ___ _________ 2:1
Link rod length, center to center ____ .inches_ .10. 156
Reciprocating and centrifugal weights:
. Piston, complete with rings and pin
---- - - -- - - - - - - - - ------- - ----Pounds_ 5.4
Articulated connecting rod, asse!llbled
-- ------ - - - -- - --------------Pounds _ 16.2
. Master rod assembled with link pins
Link rod assembled ____________ pounds__ 3.0
Lower end _____ __ ________ __ . do_ 1. 5
Upper end _________________ .do____ 1. 5
Total _reciprocating weight per cylinder (center)
--- - --- - - - - - ---- -- - - ------ · _ __ pbunds__ 7.4
Total centrifugal weight per crank pin ___ do ___ • 11. 2
Total length of piston ______ ___ ______ inches__ 5}
Effective bearing length of piston ___ ___ do____ 3 .41
Effective bearing area of piston_ square inches__ 18. 73
Crank pin bearing:
• Diameter ____ _____________ _ . __ inches__ 3
Effective length _____ ____________ _ do ____ 2-h
Bearing area ___ __ __ ______ square inches__ 7. 31
Crankshaft bearing:
Diameter ___ _____ ____________ __ inches __ 3 .125
Effective length-
Center ___ _____ ___ _______ __ __ do ____ 3 .594
Intermediate and end _____ ___ do ___ _ 2.094
Bearing area-
Center ___ ___ _______ square inches __ 11 . 68
Intermediate and end_· __ ______ do____ 6 .81
Crankshaft:
Length of crank pin ___ ___ ____ __ _ inches _
Diameter of bore in crank pin ____ _ do ___ _
Diameter of bore.in journaL __ ___ _ do ___ _
Width of crankcheek (at top of journal)
________ __ ___ _____ ____ __ __ inches __
Thickness of crankcheek __ _____ __ .do __ _ Distance between journal centers ___ do __ _ Piston pin:
Outer diameter ______ ____ ___ ___ .inches _
Inner diameter ___ " __ ______ _____ _ do __ _ Length ____ _____ ________ __ ______ do ___ _
Length of bearing in connecting rod.do __ _ KINEMATICS OF THE ENGINE.
41
Ii
8
li
1
4ti
2-h
In the Model W engine three cylinders operate on a
common crank pin. An articulated connecting rod
construction is employed. The master connecting
rods operate in the center cylinders, the link connecting
rods in the siq_e cylinders. Figure 1 represents dia­grammatically
the arrangement, in which
OA, OB, and OC = center lines of cylinders .
L0 = length of master connecting rod =
i3 inches: ..
L1 = length of link . connecting rod -10-h
inches .
- - ----- - - - --- --- - ---- -------Pounds _
Lower end __ ~_-- -- - - ------- _do ___ _
Upper end~ _______ _ --~ ____ __ do ___ 10.2
8.2
2.0
(1)
0 = crankshaft center.
D =crank pin center.
E and F=link'pin.center (fixed in.master rod) .
R =OD =crank radius =3i inches.
M = DE and DF =link radius =2ti- inches.
a =angle between center and side
cylinders= 40°.
0 1 and 0 2 =angle of crank rotation from top
center position of side and center
cylinders, respectively.
c/>1 and c/>2 =angle between connecting rod and
cylinder center line in side and
center cylinders, respectively.
a1 and a2 =travel of piston from top center in
side and center cylinders, respec­tively.
{
-angle between link radius, ED, and
,t, side cylinder axis. ·
=link radius angle.
t3 = link pin angle.
Determination of angle t3
In order to prevent heavy explosion pressures in
the side cylinders from producing large bending
stresses in the master rod, the link pin angle t3 is so
chosen that the link radius is in line with the center
line of the link rods when the link rod piston is at top
dead center position. The value of t3 to satisfy this
condition is given by the following equation:
t3 = a+sin-1 (f. sin a)
t3 =40°+sin-1 (l sin 40°) =49° 15'
Determination of link rod length L •.
2
In the preliminary layout of the piston travel it was
found that the total piston travel in the link rod cylin­ders
was greater than that in the master rod cylinders.
This is due to the distorted motion of the link pin
as shown in Figure 2. In order that the compres­sion
ratio be the same in all cylinders, a larger com­pression
volume must be obtained in the side cylinders
than in the center cylinders. For reasons of manu­facture
and interchangeability of parts, this is best
obtained by making the distance of the piston in the
side cylinders from the crankshaft center at top dead
center position, distance OA0 (fig. 1), slightly less
than that in the center cylinder, distance OB0 • The
difference between distance OB0 and distanc.e OA 0
provides the additional compression volume in the
side cylinder. This difference is determined by the
difference in length of stroke in the side and center
cylinders and by the compression ratio employed.
Total piston travel, side cylinder= 6.68 inches.
Total piston travel, center cylinder= 6.50 inches.
x = Difference in piston travel= .18 inch.
r = Compression ratio employed = 5.4.
y = Difference between OB0 and OA0 •
X .18 041
y=r-1=5.4-1=· ·
OB0 =R+L.=16.25.
OA0 =OB0 -y =16.209.
L,=OAo-R-M . .,
L, = 10.146 use 10/,- inches.
The link rod length was taken at the nearest thirty­second
of an inch for convenience. With this length
the compression ratio in the side cylinders is computed
to be 5.43. Also, distance OA0 is 16.219 inches.
Piston travel.
The connecting rod angle, per cent piston travel,
and piston travel for any value of the crank angle are
obtained from the following equations:
For the center cylinders­cf,
2 = sin- 1 (. 25 sin 82) (2)
%p.t. = { l -coso,+/;5- .J16-sin262] (4)
'• =6.5X(%p.t.)
For left-hand cylinders-s
1 = 16.219-[ 10.156 coscf,1 +2.813 cos,J;1 +3.25cos 01]
"11 =c/>2+9° 15'
c/>2 =sin-{.25 sin (81 -40°) J
,,_1 • 1[3.25 sin 81 -2.813 sin ,J;1]
"' =sm- 10. 156
(5)
(6)
(7)
(8)
For the right-hand cylinders the same formulas
used for the left-hand cylinder are applicable by
substituting for the angle 83 the angle (360 -83) .
The values of the connecting rod angle, per cent
piston travel, and total piston travel for every 10°
of crank angle are given for the center cylinders in
Table 1 and for the side cylinders in Table 2. From
Tables 1 and 2 curves of piston travel versus crank
angle (fig. 3), per cent piston travel versus crank
angle (fig. 4), and connecting rod angle versus crank
angle (fig. 5) are drawn.
Piston velocity and acceleration.
The linear velocity of the crank pin is:
v0 21rN R
=60 · 12 feet per second. (9)
where R = crank radius, inches.
N =revolutions per minute of crankshaft.
The piston velocity at any crank angle is obtained
from the equation
Vp = v0 X (f v) • (11)
where vP =piston velocity, feet per second.
f v = crank angle factor for piston velocity.
The piston acceleration at any crank angle is
V 2
a= R Xf . (16)
where a =linear acceleration of piston, feet . per
second.
v0 =crank pin -velocity, feet per second.
R =crank radius, feet.
f. =crank angle factor for piston acceleration.
For the center cylinder the crank angle factors for
piston velocity and for piston acceleration are, re­spectively,
f. =sin9+cos9 tancf,
f. =cos9+.25 cos 29
(12)
(18)
The crank angle factor for piston ·velocity and piston
acceleration for the side cylinders are obtained graph­ically;
the velocity factor from the curve of piston
-)
1
r
r
3
travel versus crank angle, and the acceleration factor] - The per cent of its total volume that the piston must
from the curve of piston velocity versus crank angle. I move to displace a volume .equal to the compression
Table 1 gives the crank angle factors for piston volume is
velocity and piston acceleration at every 10 degrees of 1
crank angle for the center cylinder. Curves of piston V.=,-1Xl00%=22.7% (26)
velocity factor versus crank angle and piston accelera­tion
factor versus crank angle for all three cylinder
banks are drawn in Figure 6 and Figure 7.
Centrifugal and inertia forces .
The centrifugal force at the crank pin, due to the
lower end of the connecting rods, is
F0 = .0000284 W0RNi (19)
The inertia force acting in each cylinder in the
direction of the cylinder axis is
F; = - .0000284 W1RN2f • (20)
Referring to Figure 7, it is seen that the piston
acceleration factor is slightly different in the various
cylinder banks, the factor for the side cylinders being
slightly greater at corresponding crank angles. In the
table of dimensions it is seen that the weight of the
upper end of the connecting rod is less in the side
cylinders than in the center cylmders. The increase in
acceleration factor in the side cylinder is compensated
by the decrease in reciprocating weight, so that the
inertia forces ·are considered to be the same as in the
center cylinders at corresponding crank angles. The
inertia force in each cylinder is, therefore, calculated
from the reciprocating weight and the acceleration
factor for the center cylinder, and is
F; = - .0000284 X7.4 X3.25 Xl,8002 Xf. = -2,212fa
The value of F1 at various crank angles is shown in
Table 4 and Figure 9.
Gas pressure forces.
Figure 8 shows the indicator diagram for a cylinder
in which gas pressure in pounds per square-inch gauge
is plotted versus p-er cent piston travel. This diagram -
is calculated from the indicated mean effective pressure
and the compression ratio.
The indicated mean effective pressure necessary to
give 300 brake horsepower at 1,800 revolutions per
minute, with a mechanical efficiency of 88 per cent,
the piston displacement being 2,832 cubic inches, is
. 792,000X800
1• m. e. p.= .88X2,832Xl,800 141.5 <22)
The thqoretical pressure at the end of the expansion
stroke is ,
(p-1) (r-1) i. m. e. P·+ (24)
~ ~-r f ~
where r=compression ratio=5.4
p=exponent of curves=l.30
/=diagram_ factor=.90
p.=initial pressure in cylinder=13 pounds per
square inch absolute.
Pd (L3- l)(5.4-l) x 141.~+ 13= 71.5 pounds
8.95-5.4 .90
per square inch absolute.
The gas pressure, pounds per square inch absolute,
for a given per cent of piston travel xis
P PX( 122.7 )1.30
xi= ,,, x+22.7 for the compression
stroke (27)
P x(· 122.1 )1.30 - _ .
xz=Pd x+22.7 fortheexpans10n (28)
stroke
From the above equations, the gas pressures are ob­tained
for every 10 per cent of piston travel. The re­sults
are given in Table 3. The absolute pressures
are reduced to gauge pressures and the)ndicator dia­gram,
Figure 8, is drawn.
Referring to figure 4, it is seen that the variation in
per cent piston travel at corresponding crank angles for
the three· cylinder banks is small. This variation is
neglected and it is assumed that the per cent piston
travel versus crank angle is the same for all cylinder
banks. The crank angles corresponding to various per
·cents of piston travel, obtained from the mean of the
curves in figure 4, are_ shown-in figure 8.
Resultant force along cylinder axis.
The gas pressure force and the inertia force are ob­tained
at various crank angles. The gas pressure force
is equal to the piston area (23.76 square inches) times
the gas pressure, which is obtained from the indicator
diagram. The inertia force is equal to-2,212 times the
acceleration factor. The resultant force acting aiong
the cylinaer axis is the algebraic sum of the gas and
inertia forces. Table 4 and _ figure 9 show the gas,
inertia, and resultant forces acting throughout a com­plete
cycle.
Piston side pressure.
The piston side thrust due to the force acting along
the cylinder axis is
(30)
Due to the fact that the ·center line of the link con­necting
rod does not pass through the crank pin at all
crank angles, the force in each link rod cylinder exerts a
turning.moment on the master rod about the crank pin.
Referring to figure 1, this turning movement is
T m=F1M sin (it,1 -4>1)=2.813 Fi sin (it,1-4>1)
The reaction due to this turning moment produces
an additional side thrust in the master rod cylinder,
which is
T T
F,1= t_+cos <f,2 = 13 + cos 4>i
The total piston side thrust in the master rod cylin­der
is the algebraic sum of the side thrust due to the
force along _the center cylinder axis and the side thrust
4
due to the turning moments caused by the link con­necting
rods. The cyclic relation of the forces acting
in the three cylinders, which operate on a single crank
pin, must be considered in combining these forces.
In the W-1 engine the firing order is such that when the
center cylinder is at the beginning of its cycle, 0° crank
angle, the left-hand cylinder is at 400° and the right­hand
cylinder at 320°.
Tables 5 and 6 give the piston side thrust in the
cylinder and the turning moment exerted aoout the
crank pin for the left-hand and right-hand cylinders,
respectively. Table 7 gives the piston side thrust in
the center cylinder due to the force along the cylinder
axis, the side thrust due to the link rod turning moment,
and the total piston side thrust. From the above tables
figure 10 is drawn, sl).owing piston side thrust versus
crank angle and figure 11 showing piston side thrust
versus per cent piston travel. From figure 11 the
average side thrust during the power stroke and during
the complete cycle is obtained.
---- ----- --- -' Cenwr. I h~J. I :~~~ Pounds. I Pounds . Pounds.
9i0 980 1,100
846 6~0 984
376 I 335 384
Piston side thrust:
Maximum ..... . ........ .. . ... ..... ..
Mean during power stroke ..... . ... .
Mean during complete cycle .••.....
The piston side pressure, pounds per square inch, is
obtained by dividing the side thrust by the effective
projected bearing area of the piston (18.73 square
inches.):
Center. Left
hand.
Right
hand.
- --------- - ---[---- --------
Pounds Pounds Pounds
Piston side pressure: inch. inch. . in·h.
. _ per square per squarelper squ.are
Maximum...... . . . . ...... .. . . .. . . . · 51. 8 · 52 .. 3 58. 7
ll!ean during power stroke . . .... :-, .. 45. 3 36. 3 i 52. 5
Mean during complete cycle... . .. .. . 20.1 17. 9 I 20. 5 ·
Torque.
The torque due to a single cylinder is
T=FaRf.
·the maximum engine _torque to the mean torque, as
obtained from the curve, is 1.05:1.
Resultant force on crank pin.
The resultant force on the crank pin is obtained
graphically by combining the resultant forces along
the connecting rod axes. with the centrifugal force
due to the lower end of the connecting rod assembly,
as shown in Figure 13. It is assumed that the center
lines of the side rods pass through the crank-pin center,
the distortion due to the articulated rod construction
not being considered.
The forces acting along the connecting rod are cal­culated
for the center cylinder. The force along the
connecting rod of a side cylinder is considered to be the
same as that of the center cylinder at the corresponding
phase of its cycle. Table 9 gives the forces along the
connecting rod axes for every 20 degrees of crank angle,
the crank angle being taken with respect to the center
cylinder. When the center cylinder is at 0° crank
angle, the left-hand cylinder is at 400° in its cycle and
the right-hand cylinder at 320°. Table 9 also gives
the magnitude of the resultant force on the crank pin
and the direction of the resultant with respect to the
engine center line. Figure 14 is a polar diagram of the
forces acting on _the crank pin, the direction of the
forces being shown with respect to the engine axis.
In Figure 15 the direction of the resultant force on the
crank pin is shown with respect to the crank throw.
Figure 16 is a polar diagram showing the force acting
on the connecting rod bearing.
Crank-pin bearingarea=3X2.437=7.31 square inches
. . 1rX3X1800
Rubbmg veloc1ty=-12X
6
0 =23.55 feet per second.
Maximum force on bearing=9,150 pounds.
Mean force on bearing~6,370 pounds.
Maximum bearing pressure=
97_1
3
5
1° = 1,250 pounds per
square inch.
Mean bearing pressure= 6,370 8.70 . d .
7
;
31
= . poun s per
square inch.
Rubbing factor=23.55 X 870=20,500.
Resultant force on crank-shaft bearings.
The resultant forces acting on_ the crank-shaft bear-where
'.l'=torque, pounds per foot.
F, =resultant force along
pounds.
ings are obtained by considering the force on each
cylinder axis, crank pin together with the centrifugal force of the
R=crank radius, feet=0.2708.
crank-pin and crank cheeks equally divided between
the two adjacent crank-shaft bearings. The end bear-f.=
crank angle factor for piston velocity. ing is loaded on only one side by half the force on the
Figure 6 shows the crank angle factor for piston crank pin combined with half the centrifugal fore~ of
velocity for the three cylinder banks. The slight the crank pin and crank cheeks. The same loading is
variation of the three curves is negligible, and the applied on both sides of the _center and intermediate
average value of the velocity factor is taken at various bearings, but the.forces acting on each side of the center
crank angles to determine the single cylinder torque. bearings diffe~ in phase relation by 360°, while in the
Table 8 gives the indicated torque· of a single cylinder case of the intermediate bearing they ·differ in phase
as calculated from the above. equation. The resultant . relation by 240°.
torque of the engine is the algebraic sum of the instan- Bearing area, center bearing=3.125X3.594=11.23
taneous torques of the individual cylinders. Figure 12 1 square inches.
shows the variation 9f torque throughout a cycle (720°) Bearing area, intermediate and end=3.125X2.094=
for a single cylinder and for the engine. The ratio of 6.54 square inches.
' '·-
5
Rubbing velocity irX
3·:;t;~,SOO 24.65 feet per ]
second.
End crank-shaft bearing:
Maximum bearing pressure=
56~:4° = 900 pounds
per square inch.
Mean _b earing pressure = 46 2_00 54
= 642 pounds per
square inch.
Rubbing factor =24.55 X642 = 15,750.
Center' crank shaft bearing: '
. 11,400
Maximum bearing pressure= 11 _23 = 1,015
pounds per square inch.
8 100
Mean bearing pressure= 1i_23 =721 pounds
per square inch.
Ruql;>ing factor = 24.55 X 721 = 17,700.
Intermtidiate crank shaft bearing: .
8 700
Maximum bearing pressure= 6_54
= 1,330
pounds per square inch.
4 880
Mean bearing pressure= 6_54 =745 pounds
per square-inch.
Rubbing factor = 24.55 X 7 45 = 18,300.
Crank pin oil hole location.
A diagram of the comparative wear on the crank pin
was plotted in Figure 20 according to the method
given in the report on "Standard Method of Engine
Calculations." From this diagram it is seen that the
oil hole should be located from 50° to 70° ahead of
the top center position in the direction of rotation, as
shown in Figure 20.
Crank shaft stress analysis.
The crank s!iaft of this engine falls under the classi­fication
given in Case I in the report on "Standard
Method of Engine Calculation," which report gives the
derivation of the equations and the definitioll of the
symbols herein employed. · ·-
Brake horsepower =800 at 1,800 revolutions per
minute.
Ratio of maximum to mean torque, K = 1.05.
Tm 800 = 63,000 X 1 800 X 1.05 = 29,400 pounds per
inch. '
F O = (from· fig. 15) 9,000 pounds.
29,400
F1=3.25 =9,040 pounds.
Fb =-J9;0002+9,04Q2 = 12,750 pounds.
a =4 inches r =3.25 inches
inches.
e =2.062 inches f = 1.375 inches.
Stress in Journal:
(38)
(39)
c=l.687
Mb = .25X12,750X4.0 = 12,750 inches . per
pound. (40)
M0 = .5 X12,750+.5-J2,7502+29,4002 =22,400
inches per pound. (41)
D =3.125 d=l.875.
Z =2.61 iuches1
4.91 inches.2
ZP =5:22 inches.3 A=
(42-44)
Sb = maximum fiber stress.
S
22•400 8 580 . I (4::;) h = _ 2_61 = , per square me 1. v
s. = total shear stress.
s. 29,400 9,000 = 5_22 + 2 x 4.91 =6,550 pounds per
square inch. (46)
Stress in crank pin:
Mb (center section).= i 9,000X4=9,000 inches
per pound. (47)
Mb (end section) =9,040Xl.375=12,400 inches
per pound. (48)
M0 =! 12,400+!-JI2,4002 +29,4002 =22,100
inches per pound. (41)
D =3.0 d = 1.875.
Z =2.24 inches.a Zp=4.48 inches.3 A=
4.31 inches.' (42-44)
Sb =maximum fiber stress.
S =
22
•
100
~9 860 pounds per square
b 2.24 '
inch. (45)
s. =total shear stress.
S = 29•400 + 9,000 = 7 610 pounds per
• 4.48 2X4.31 '
square inch. (46)
Stress in crank cheek:
Mt= 9,040 X 2.062 = 18,600 inches per pound.
(49)
Mb = 9,040 X 1.687 = 15,250 inches per pound.
(50)
b =4.25. t=l.375.
Zp =2.69X4.25XL3752 =2.16 cubic inches.
(51)
Z b 4.252 X 1.375 4 14 b" . h
6
. cu 1c me es. (52)
A = 4.25 X 1.375 = 5.84 square inches.
St= Tensile stress.
S = 15,250 + 9,000 = 4,45~ pou~ds per
t 4.14 2 X5.84 square mch. (54)
s. =Shear stress.
S = 18,600 = 8,~20 pounds per square (55)
• 2.16 mch.
s. = Maximum equivalent stress.
s. =! 4,450+-Jl 4,4502 +8,6202=7,075
pounds per square inch. (56)
CONNECTING ROD STRESS ANALYSIS.
Stress in shank of master connecting rod.
The resultant force along the connecting rod axis
throughout an engine cycle· producing direct compres­sion
or tension in the rod has previously been deter-
6
mined when obtaining crank pin bearing loads and is I (c) Sb'." 1.61 X 1,812 = 2,920 pounds per square
given in Table 9. The turning moment, due to the mch.
link rods producing b~nding stresses in th~ master con- I From the above results it is seen that the predom­necting
rod, has previously been determmed for both inant stress is due to compression and occurs at the
side cylinder banks when obtaining piston side pressure center section of the connecting rod shank. The
and is given in Table 7. The resultant force along the variation of stress throughout a complete engine cycle
connecting rod and the resultant turning moment pro- that occurs in this section is given in Table 10.
duce the predominant stresses in the master connecting The compression stress in the rod due to a force of
rod. Their value at various crank angles is given in 500 pounds per square inch of piston area acting on
Table 10. the rod, is
The master connecting rod is shown in Engineering s. = (500 x 23. 76) 2.23 = 26,500 pounds per square
Division Drawing No. 051025. Using the same nota- inch .
.tions as is given in Figure 22 of report on "Standard The stresses due to the whipping force on the rod
Method of Engine Calculations," the dimensions and were not taken into account in this analysis, being of
properties of the connecting rod are given in Table 11. · a negligible quantity.
The stress in the center section of the rod due to
compression is calculated by means of the following
column formula:
(
1 .000526£2) _ F (! + .000526L,2
\) So=F, A- + I or- r A 41
X y
(65)
The stress in an end section of the rod due to com­pression,
or in any section due to tension, is
S=F' • A
The stress due to the resultant turning moment
caused by the link rods on the master rod is determined
by the equation
S=Mi~
b . L, (71)
The properties of the master connecting rod are
given in Table 11.
Substituting in equation 65 the values of the prop­erties
of the average section of the connecting rod
shank, the stress due to direct··compression is
(..i) S -(-1-+.000526X169) F =2 23 F
.- .562 -198 r • r
The stress due to direct compression in the small
end of the rod is
(b) 1
S0= .492 F, =2.03 F,
The stress due to the turning moment is greatest at
the end section of the rod where the value of Z/x is
least and is
(c) Sb =M, (/3x_0
f79)=1.61 Mi
At the center section, where the compression stress
is greatest, the stress due to the turning moment is
Using the largest value of F, and M,, respectively,
as given in Table 10, the maximum stress due to com­pression;
which occurs at the center section, is
(a) S0 =2.23 X8640 = 19,300 pounds per square
inch.
and the maximum stress due to the turning moment
which occurs at the end section of the rod is
Stress in link connecting rod.
The link connecting rod is shown in Engineering
Division Drawing No. 051032. ·using the same
notation given in figures 22 and 24 of the report on
"Standard Method of Engine Calculations," the
dimensions and properties of the rod are . given in
Table 12.
The maximum stress in the shank of the rod due
to a force of 500 pounds per square inch of piston
area acting on the rod, as obtained by means of
equation 65, is
(
1 .000526 X 104)
S0 =(500X23.76) .492f _160 =28,200
pounds per square inch.
The stress in the fork of the link rod due to a force
of 500 pounds per square inch of piston area acting on
the rod is determined by means of equation 72 (see
report on "Standard Method of Engine Calculations").
S = ( 500 xz23.7Q) [:;~ + .o!;3 (.98- .22-.33 x. 77) ]=
50,900 pounds per square inch. ·
Stress in bearing ·cap.
The stress in the master rod bearing cap, drawing
No. 051025, due to the maximum centrifugal and
inertia loads on the cap is calculated b;y means of the
following equation:
S=Fc-02: C +i) (73)
where S=maximum stress in bearing cap.
F = maximum load on bearing cap.
C=distance between bolt centers=4.31 inches.
A=area of.cap cross-section=.848 inch.
Z = section modulus of area=.058 cubic inch.
Inertia force in center cylinder at top center=2,770
pounds.
Component of inertia force of side cylinders in the
direction of center cylinder axis=2,340 pounds.
Centrifugal force producing load on cap=.0000284X
9.0X3.25 Xl,800 2 =2,690 pounds. (19)
F =2,770+2,340+2,690 =7,800 pounds.
(
.023 X 4.31+ . 5 ) 17 950 d
S =7,800 . 058 . 848 = , poun s per
square inch.
Stress in bearing cap bolts.
The stress in the bearing cap bolts, as determined by
equation 74, is
F
S=nA
where S =tensile stress in bolts.
F = load on bearing cap= s ;200 pounds.
n = number of bearing cap bolts = 4.
(74)
A = minimum cross-sectional area of bolt = .109.
S=4~~~g9=17,900 pounds per square inch.
Piston pin analysi s.
In the following analysis a maximum load of 500
pounds per square inch of piston area is considered as
acting on the pin.
The maximum bearing pressure in the piston pin
bearing of the connecting rod is
p 500X23.76 .
1.375 x2_3i=3,750 pounds per square mch. (77)
The maximum tensile stress in the piston pin is
S =500X23.76 (2X3.7-2.3) 401500 pounds per
t 8X.1835
square inch. (78)
The maximum shear stress in t he piston pin is
500X23.76 .
S , 2 x_702 8,480 pounds per square mch.
VAL VE AN AL YSIS.
Gas veloci ty.
The gas velocity through the valve port, determined
by means of equation 80, is
D2SN
Vi=360 d'n
where D =cylinder diameter =5.5 inches.
S =piston stroke= 6.5 inches.
(80)
N =revolutions per minute of engine = 1,800.
d =diameter of valve port
inlet, d=l.75.
exhaust, d=I.75.
n =number of valves
inlet, n ~2.
exhaust, n =2.
The gas velocity . through the valve annulus on
basis of maximum lift is obtained by means of equa­tion
81.
74174- 24-2
D2 S N
1440 d h n (81)
7
where h =total valve lift
inlet, h = .39 inch.
exhaust, h= .39 inch.
The gas velocity through valve annulus on basis of
mean lift is obtained by means of equation 82.
D2 SN
l'a · 8 q0 d hm n
where q0 =period of valve opening
inlet = 220°
exhaust =235°
hm =mean valve lift
inlet = . 26 inch .
exhaust= .27 inch . •
Inlet valve gas velocity:
v1 = 161 feet per second.
V2 = 180 feet per second.
v, = 221 feet per second.
Exhaust valve gas velocity :
v1 = 161 feet per second.
v2 = 180 feet per second.
v3 = 199 feet per second.
Cam analysis.
(82)
The usual cam formulrn for det ermining valve
lift, velocity, and a cceleration are not applica ble in
this case, for the path of the roller is along an a rc
which does not approximate a straight line t hat
passes through the valve center. The vale lift ,
velocity, and acceleration were obtained by a careful
graphical determination and the results obtained are
shown in Figures 21 and 22.
TABLE 1.- Center cylinder banks.
I
Connect- Piston Piston I Crank ing rod Per cent Piston velocity accelera-anog,
l.e , angle, piston travel, factor tion I ¢ , . travel. S!! , Iv- factor I
---
:·~ I 0
---!~ ---
0 360 I 0 0 0 0 ' 10
10 350 2 29 . 9 . 058 1 . 216 I. 220
20 340 4 54 3. 7 . 241 I . 423 1. 131 I 30 330 7 11 8. 3 .540 . 609 . 991
40 320 9 15 14. 3 . 930 . 768 . 809
50 310 11 2 21. 6 I. 404 . 891 .599 I
60 300 12 30 29. 7 1.930 . 977 . 375
I
70 290 13 35 38.5 2.502 I. 022 . 151
80 230 14 15 47.5 3.088 1. 029 - .061
90 270 14 29 56.4 3. 667 1. 00 - . 250
100 260 14 15 64.9 4. 220 . 941 - .409
110 250 13 35 72. 7 4. 726 . 857 -.534
120 240 12 30 79. 7 5.180 . 755 - .625
130 230 11 2 85. g 5. 58.'i .641 -.686
140 220 9 15 90.9 5. 910 . 518 - .723
150 210 7 11 94. 9 6.168 . 391 - .741
160 200 4 54 97. 7 6. 350 . 261 - . 748
170 190 2 ~I 99.4 6. 460 . 131 - . 750
180 180 0 100 6.500 0 -. 750
I
• For crank angles between 180° and 360°, <1>2 and/ . are negative
I
TABLE 2.-Side cylinder banks.
Crank Crank Connect- Angle,' Per rent Piston
angle, angle, ingrod- piston travel,
,_ 81. 8,., angle,1<1>1. V,1. travel. S1.
. . --. ----- ----- I . ' 0 360 0 0 0 0 0 0
10 350 2 37 2 4 0. 8 0.058
20 340 5 5 4 21 3.6 .244
30 330 7 19 6 46 8.2 .546
40 320 9 18 9 15
14. 1 I .935
50 310 10 53 11 44 21.0 1.402
I 60 300 12 4 14 9 29.0 1. 931
I 70 290 12 50 16 26 37.5 2.507 80 280 13 8 18 30 46.3 3.097
I
I 90 270 12 57 20 17 55. 0 3.682
I 100 260 12 16 21 45 63.5 4.246
I 110 250 11 8 22 50 71. 4 4. 773
I 120 240 9 36 23 30 78.5 5.256
I 130 230 7 41 23 44 84.8 5.659 I
140 220 5 29 23 30 :~11 6 . 027
150 210 3 1 22 50 6.299 I 160 200 0 23 21 45 97.3 6.504 I 170 190 -2 20 20 17 99.2 6.633
16ii 180 -5 3 1s· 30 100 6.685
I 190 170 -7 42 16 26 99.5 6. 657
200 160 -10 12 14 9 98.0 6.550
210 150 ·-12 30 11 44 95.2 6.364
220 140 -14 29 9 15 91.1 6. 091 I 230 130 -16 8 6 46 86. 1 5. 7.59
240 120 -17 21 4 21 80.6 5.345
250 110 -18 6 2 4 , 72.8 4.866
I
260 100 -18 22 0
4~ I 64. 8 4.332
270 90 -18 9 -1 56.2 3. 757
280 80 -17 'J:l -3 1.5 ' 47.2 3.157
290 70 -16 15 -4 20 38.2 2.553
300 60 -14 39 -5 0 29.4 1.966
I 310 ,50 -12 43 -5 14 21. 3 I. 420
320 40 -10 ~, -5 0 H. 2 .946
330 30 -8 -4 20
8.2 1
. 548
I
340 20 -5 -3 15 3. 7 .250
350 10 -2
4t I -1 47 0.9 .056
360 0 0 0 0 0 0
I
• Angle </>a - - </>, and angle ,/;, = - ,/;1•
TABLE 3.
Pressure pounds Pressure pounds
per square inch, per square inch,
Per cent 1.30
absolute. gage.
piston x-Vc ( 122.7 )
travel. x-22. 7 Com- Com- E~pan- J>.res- E~an- J>.res- SlOn, SlOn. s10n. SIOD.
--- --- ---------,
0 22. 7 8.96 640.5 116.5 625.8 101. 8
10 32. 7 5.58 399.0 72.6 384.3 57.9
20 42. 7 3.94 281. 8 51. 2 267. l 36.5
30 52. 7 3.00 214.5 39.0 199.8 24.3
40 62. 7 2.39 170.9 31.1 156.2 16. 4
50 72.7 1.97 140.9 25.7 126. 2 11.0
60 82. 7 1. 67 119.4 21. 7 1 104. 7 7.0
70
92. 7 1
1. 44 103.0
18. 7 1
88.3 4.0
80 102. 7 1.26 90.l I 16.4 75.4 1. 7
90 112. 7 1.12 80.1 14.5 65.4 -.2
100 122. 7 1. 00 71.5 13.0 56.8 1 - 1. 7
'
8
Crank
angle.
Gas
pressure
(pounds
per
square
inch) .
TABLE 4.
Gas
force
(pounds).
Piston
accel.
factor .
I
Resultant
Inertia force
force along
(pounds). cyl. axis
(pounds). ____ , _____________ __ _
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
553400 I
550
560
570
.580
590
600
610
620
630
640
650
660 I
670
680
690
700
710
300
440
468
410
326
256
203
164
134
112
96
85
76
70
60
50
40
30
20
10
4
3
2
1.3
1. 3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1. 3
1. 3
1. 3
1.3
1.3
0
-1. 7
- 1. 7
-1. 7
-1.7
-1.7
-1.7
-1.7
-1. 7
-1. 7
I -1.7
-1. 7
-1.7
-1.7
-1. 7
-1. 7
-1.7
-1.7
-1. 7 I -1
0 ! I
i
1
1
72
118
180
, 1
7, 130
10,450
11,120
9,740
7,740
6,080
4,820
3,900
3, 180
2,660
2,280
2,020
1,810
1,660
1,430 1,Jl&
710
480
240
100
70
50
30
30
30
30
30
30
30
30
30
30
30
30
30
30
0
- 40
-40
-40
-40
-40
-40
-40
-40
- 40
-40
- 40
-40
-40
-40
-40
-40
-40
- 40
-40
-20
0
20
50
100
140
210
310
430
590
830
1,140
1,710
2,800
4,280
1. 250
1. 220
1.131
.991
.809
.599
. 375
. 151
- .061
- .250
- .409
- .534
- .625
- .686
- . 723
- . 741
- . 748
- . 750
- .750
- . 750
- . 748
- . 741
- . 723
- .686
- .625
- . 534
- .409
- .250
- .051
.151
.375
.599
.809
. 991
1. 131
1.220
1. 250
1.220
1.131
. 991
. 809
.599
.375
.151
- .031
- .250
- .409
- .534
- .625
- .686
- • 723
- • 741
- .749
- .750
- .750
- .750
- .749
- .741
I
:J:
- .625
- .534
- .409
- .250
- .061
. 151
.375
.599
.809
.991
1.131
1.220
-2,770 =~;;n
=t~: - 1,330
-830
-330
130
550
910
I, 180
1,390
1,520
1,600
1,640
1,660
1,660
1 660
1;660
1 660
1;640
1,600
1,520
1,390 l,ti&
550
130
-330
-830
-1,330
- 1, 790
- 2,200
- 2,510 =~:~n
=~:;~ =t~: - 1,330
-830
-330
130
550
910
l,lRO
1,390
1,520
1,600
1,640
1,660
1,660
1,660
1,660
1,660
1,640
1,600
1 520
1;390
1, 180
910
550
130
-330
- 830
-1,330
-1, 790
-2,200
-2,510
- 2, 700
4 360
1;,50
8,610
7,,540
5,.11.5.0
4,7i50
3,990
3;570
3,310,
3, 210
3,\90
3,290.
3,200
3,1~0
3,030·
2 830
2;s10
2,370
2 140
1:000
1,760
1, no
1,650
1,550
1,420
1,210
940
580-
1 =ii_
=U~ -2,170
-2,480
- 2,670
-2,740
-2, 700
-2,550
-2,240
=~:~Z -870
- 370
90
510
87!)
1,140
1,350
1,480
1,560 I 1,600
1,620
1,620
1,620
1,620
1,620
1,620
MTc:
1;440 I
1,2SQ I 1 050 ·~, 100 ~~l-J 290 · l,68<! -1
9
TABLE 5.-Left-hand cylinder. TABLE 6.-Right-hand cylinder.
·--
Force I Per along Piston I
Crank cent cylin- side Turning I angle. piston der tan4>,. thrust Sin moment, , travel. axis, (total), (4>,-,f,,) Tm.
F. Ftan 4> _, --- I
0 0 4.360 0 0 0
20 3. 7 8,610 .0945 814 -.0375 -89g I
40 14.2 5,950 .1850 1,100 -.0956 -1,599 1
60 29.4 3,990 .2614 1,040 -.1676 =~·rJ, 80 47.2 3,310 .3143 1,040 -.2453
100 64.8 3,190 .3320 1,060 -.3151 -2:s26 I 120 80.0 3,200 .3124 999 - . 3698 -3,330 I
140 91.1 3,030 .2583 782 - . 4025 -3,432 ,
160 98.0 2,610 . 1799 469 -.4123 -3,025 I
180 100.0 2, 140 .0884 189 -.3996 -2,405 1 200 97.3 1, 760 -. 0067 1 -12 -.3643 -1 804
~ I
90.2 1,650 -.0960 -158 -.3093 -1:435
78.5 1,420 '-.1691 I -240 -.2402 -959 !
260 63.5 940 -.2174 -204 -.1648 -_!: 1 280 46.3 160 -.2330 -37 - . 0935 1 300 29.0 - 800 -. 2138 171 -.0372 !! I 320 14.1 -1, 760 -.1638 288 .0009
I 340 3.6 -2,480 -.0890 221 .0128. -90 1
360 0 -2, 740 0 0 0
218 I
I
380 3. 7 -2,550 .0945 -241 - . 0375
400 14.2 -1,830 .1850 -338 - .0956
420 29.4 -870 . 2614 -227 -.1676 441912 1
•
440 47.2 90 .3143 28 -.2453 -62
460 64.8 870 .3320 289 -.3151
480 80.0 1,350 .3124 422 -.3698 -1-,470741 1
500 91.1 1,560 .2583 403 -.4025 -1, 766
520 98.0 1,620 . 1799 291 -.4123 -1,880
540 100.0 1,620 .0884 143 -.3996 -1,820 I 560 97.3 I, 6i!() -.0067 -11 - . 3643 - 1,660 I
580 90.2 1,600 -.0960 -153 -.3093 - 1,393 1 600 78.5 · ~,t: -.1691 -244 -.2402 -973
620 63.5 - . 2174 -228 -.1648 -487
640 46.3 '44() - .2330 -102 -.0935
- 115 1
I
660 29;0 -240 - . 2138 53 -.0372 25
680 14.1 -6,xl -.1638 Hl6 . 0009 -2
700 3.6 290 -.0890 -26 . 0128 10
/ - j - Force J I
I Crank 1 :;~ along p~fl~n Sin Turning
,
1
angle. / piston ·ca::;i- tan4>,. thrust. (fr-<1>1). mo¥!.:.nt,
traVel. axis, Fa.
___I :-_· _ _ F. ••_ ________
0 I O I 4,360 0 0 0 0
i 20 - 3.6 8,610 .0890 766 -.0128 -311
I 40 1 14.1 5,950 .1638 975 -.0009 -15
I 00
80
I 29.o 3,990 .2138 854 .0372 418
I 46. 3 3,310 . 2330 770 • 0935 870
I 100 . 63.5 3,190 .2174 694 .1648 1,475
, 1
1
2
4
00
1
;:8.5 3,200 .1691 541 .2402 2,162
90.2 3,030 . 0960 291 .3093 2,630
160 97.3 2,610 .0067 18 .3643 2,675
180 l@.O 2,140 -.0884 -189 .3996 2,405
200 9.8.0 1,760 -.1799 -316 .4123 2,040
220 i!l.l , 1,650 -.2583 -427 .4025 1,870
240 80.0 1, 420 -.3124 -444 .3698 1,476
260 64.8 940 -.3320 -312 .3151 833
280 47. 2 160 -. 3143 -50 . 2453 110
300 29. 4 -800 -. 2614 209 .1676 -377
320 14. 2 -1, 760 1-.1850 326 • 0956 -473
g~ 3. J =~:~ , 11,.0945 ·2~ I .037g -26~ '\
380 3.6 -2,550 .0890 -227 -.0128 92
400 14. 1 1-1,830 .1638 -300 - . 0009 5
420 ·29.0 I -870 .2138 -185 . 0372 -9241 /
440 46. 3 90 • 2330 21 . 0935
460 63. 5 870 • 2174 189 .1648 403
480500 78. 5 . 1,350 . 1691 212580 ·. 23402093 912
I 90.2 1,560 .0960 1,356
520 .97.3 1,620 .0067 11 .3643 1,660
-~600 ', 100.0 1,620 -.0884 -143 .3996 1,820
u 98.0 1,620 -.1799 -291 .4123 1,880
.580 91.1 1,600 -.2583 -414 .4025 1, 815
600 80.0 1,440 -.3124 -450 . 3698 1,500
620 64.8 1,050 -.3320 -349 .3151 931
640 47.2 440 -.3143 -138 .2453 304
660 29.4 -240 -.2614 63 .1676 -112
680 14.2 -650 -. 1850 120 I .0956 - 175
l. ___10 0~_3._7~-29- 0 -'---·-09_.4_5-'-- - -2_1~-· 0-375~--3-l ~
'
TABLE 7.- Center cylinder .
. - --.----.--- ---,----.---- -------,------;----,--- -
I
. 1
1.'urnin~:oment,
Crank Pe_r cent Florce Side Side P'r,.sottoanl
ISton a ong tan 4>,. thrust cos c/>'J. thrust, I angle. fravel. cyμnder F. Left- Right- F. side
I aXIS, F.. •· hand hand ••· thrust.
I
' cylinder. cylinder.
, 0 0 .. 4,360 0 0 I 5 -4 1.0000 0 I 0
1
1
: ~u g:i1& J~i ~ig 1
1
- : - 9g :r87sg -~~ i~
60 29. 7 3,990 I . 2217 1 884 403 270 I . 9763 50 , . 934
1 80 47. 5 3;310 . 2540 840 I 912 492 • 9692 105 945
I 100 64. 9 3, 190 2540 810 I, 356 411 . 9692 132 , 942
120 79, 7 3, 200 I . 2217 708 I, 660 -62 . 9763 120 I 828
II 140 90.9 3,030 .1629 493 1,820 -771 , 9870 80 573
160 97. 1 2, 610 . 0851 223 I 1, 880 -1, 404 . 9963 31 260
. 180 100.Q 2,140 0 0 1,815 -1,766 1.0000 3 3
200 97.7 1,760 I .0857 -151 J,500 - 1,880 . 9963 -27 - 178
I ~ rJJ t1gg J~~ =~~~ I ~~ =t~ :i;: II ~g~ I =ir~ 260 64.9 940 . 2540 - 239 - 112 -1,393 .9692 - 112 - 351
I 280 47.5 160 .2540 -41 - 175 -973 .9692 -861 -127
I 300 29. 7 - 800 .2217 177 31 -487 .9763 - 34 143
1 320 14.3 -1,760 .1629 287 0 - 115 .9870 I -9 278
.
'1 340 3. 7 -2, 480 . 0857 1 213 -311 25 . 9963 -2'2 191
360 0 -2, 740 0 0 - 15 -2 1.0000 -1 -1
380 3.7 -2,550 . 0857 219 418 10 .9963 33 -186
J 400 14.3 - 1,830 . 1629 -298 870 0 .9870 66 - 232
• 420 29. 7 -870 . 2217 -193 I, 475 -896 . 9763 44 -149 ! 440 47. 5 90 . 2540 I 23 2,162 - 1, 599 . 0092 41 64
, · 460 64.9 870 .2540 \ 221 2,630 - 1,882 .9692 56 277
I 480 79.7 1,350 .2217 I 299 2, 675 -2,286 .9763 29 328 I
'1 500 90. 9 I, 560 .1629 1 254 2,405 -2, 826 1 . 9870 -32 222
I
520 97. 7 1,620 . 0857 139 2, 040 - 3, 330 . 1)963 -96 43
540 100.0 1;620 0 0 1,870 -3,432 1.0000 -122 -122
560 97. 7 1, 620 . 0857 ! - 139 1, 476 -3, 025 . 9963 -119 -258
580 90. 9 1,600 . 1629 i -261 833 -2, 405 . 9870 -119 -380
I, 600 19.1 . 1,440 .~11 1· - 319 110 -1,804 . . 9763, -121 - «6
620 64.9 1,050 .2540 i -267· ;,; -377 -1,435 .9692' -135 -402
I 640 47. 5 440 . 2540 r -11'2 .. ;,· -473 -959 . 9692 -107 ' -219
Ii 660 1' . 2!J. 7 -240: . 2217. ~ : . -262 -436 . 9763 -52 1 680 14. 3 -650 . 1629 100 o - 42 • 9870 -3 1oa
j 700 3. 7 · 290 .0857
1
-25 92 84 . 9963 13 -12
10
TABLE 8.-Single cylinder torque.
I· I
Piston Force Piston Forre
Crank veloc- along Crank veloc- along
angle. · lty cylln- Torque. angle. ity cylin- Torque.
factor. der der axis. !11ctor. axis.
------ ---- - - - 1- --- ----
0 0 f ,360 0 360 0 - 2, 740 0
10 .22 7,700 462 370 .22 -2, 700 -160
20 .43 8,610 1,003 ; 380 .43 -2,550 -298
30 .62 7,540 1,266 390 .62 -2,240 -377
40 • 78 5 950 1,256 400 • 78 -1,830 -387
50 .90 4:7.50 1,157 410 .90 - 1,370 -333
I
60 .99 3,990 1,069 420 . 99 .;_870 -233
70 1. ()( 3,570 1,005 430 1.04 -370 -103
80 1.0. 3,310 932 440 1. 04 90 24
90 1.02 3,210 887 450 1.02 510 141
100 .96 3,190 830 460 .96 870 228
110 . 87 3; 200 754 470 . 87 ..... I 268
120 . 77 3,200 667 480 . 77 1,350 282
130 .66 3,180 568 490 . 66 1,480 266
140 .54 3,030 443 500 .54 1,560 228
150 .41 2,830 314 510 . 41 1,600 179
160 .28 2,610 195 520 .28 ·~112 2
170 . 14 2,370 90 530
0·
14
1
1,620 62 i 180 0 2,140 0 540 1,620 0 I
190 - .14 1,900 -72 500 -.14 1,620 -62
200 -.28 1,760 -131 560 -.28 1, 620 -122
210 -.41 1,710 -190 570 - . 41 1, 620 I -179
220 -.54 1,650 -241 580 - . 54 1 1, 600 -233
230 -.66 1,500 - 276 590 -.66 1, 540 I -276
240 -.77 1,420 -295 600 -. 77 1 1,440 -301
250 - . 87 1,210 -284 610 -.87 1,280 -301
260 -.96 940 -244 620 - . 96 1, 050 -274
270 -I.02 580 -160 630 -1.02 760 -208
280 -1.04 -100 -46 640 - 1.04 440 -125
290 -1.04 - 300 84 650 -1.04 100 -27
300 - .99 ~soo 214 660 -.99 -240 65
310 - . 90 -1, 300 317 670 -.90 -500 122
320 -.78 -1, 760 371 680 - . 78 - 650 I 137
330 -.62 -2, 170 366 690 -.62 -~, 82
340 - .43 -2,480 290 700 - .43 - 34
350 -.22 -2,670 160 I 710 -.22 1,580 -94
TABLE 9.
I Force along connecting Resultant force onJ
Crank Force rod crank pin. I aWJn_gthle along •
center 1- --.-- --,,-----1-- -.---
respect cylin- D' .
to center der Left Right Magni- irect)On
cylinder. axis. Center. hand. hand. tude. to :~lf.ne I
- --- --- 1
Pounds. • I
0 4,360 4, 360 -1, 850 ,-1, 780 1,350 0
20 8,610 8,640 -890 -2,490 5,050 144
40 5, 950 6,030 90 -2, 740 5,050 102
60 3, 990 4,080 900 -2,560 5,800 94
80 3,310 3,410 1, 380 -1,850 6,400 107
100 3,190 3,290 1,580 -890 6,850 124
120 3,180 3,260 1, 630 90 I 7, 650 142
140 3,030 3,070 1,620 900 8, 250 156
160 2, 610 2,620 1,630 1,380 8,450 168
180 2, 140 2,140 1,620 1,580 8,300 180
200 1,760 1,770 1, 480 1, 630 7, 800 192
220 1, 650 1,670 1,080 1,620 7, 050 205
240 1,420 1,450 450 1,630 6, 250 222
260 940 970 -2!i0 1,620 5, 400 214
280 160 170 -660 1,480 4, 800 271
300 -800 · -820 290 1,080 3, 500 293
320 -1, 760 -1, 780 4,360 450 1, 000 I 37 I
340 - 2, 480 -2,490 8, 640 -250 6, 100 100
360 -2, 740 - 2, 740 6, 030. :-660 5,500 61
380 -2, 500 - 2, 560 4, 080 290 4, 600 50
400 -1, 830 -1, 850 3, 410 . "4,360 1,750 1· 116
420 - 870 - 890 3,290 8,640 7, 100 182
440 90 90 3,260 6, 030 7, 000 , 157
460 870 900 3, o,o 4, 080 8, ooo I 150
480 1,350 1,380 2,620 3,410 8, 650 156
~ 500 1, 560 1,580 2, 1:10 3,290 9,000 164
520 1,620 1,630 1,770 3,260 9,150 175
540 1,620 1, 620 1,670 3,070 9,050 185
560 1, 620 1, 630 1, '\_50 2.620 8, 500 195 I
580 1,600 1,620 9:70 . 2,140 7, 500 207
600 1,440 1,480 170 ·1, 770 6,400 225
620 1,050 1,080 -820 1,670 5,600 249
640 440 450 -1. 780 J.fOO 5,500 I ?78
660 -240 -250 -2, 490 970 6,100 304
680 - 650 -660 -2, 740 _ _170 6,550 _ 323_
700 290 . --290 - 2,"560" -820 ~ 5,400 336
TABLE 10.·
Force Resultant Stress m center section of
along turning master rod shank.
Crank C-On- moment
angle. nectmg on mas-rod
axis, ter con- 8tress Ptress Total F, . nect!ng due to due to rod, M,. F,. M,. stress.
---- - - - - ------ - - --
Pound.,. -·
0 4,360 l 9,720 1 9,720
20 8,640 -181 19,250 206 UH50
40 6,030 24 13,440 27 13~470
60
I
4,080 673 9,090 768 . 9;860
80 3,410 1,404 7,600 1,600 9· 200
100 3,290 1,767 7,340 2,003 i :340
120 3,260 1,598 7,270 1,820 ll,090
140 3,070· 1,019 6,~ 1, 192 8, 050
160 2,620 476 _ 5,St0 543 6,380
180 2,HO 49 4,7~ 56 :<t,820
200 1,770 -380 3,950 433 ;i 350
220 1,670 -:889 3,720 1,015 '4il40
240 1 450 - 1,356 3, 2~0 1,546 ,4~1 70
260 '970 .-1,506 2, 160 1,716 3 880
280 170 -1,148 380 1,309 °I'.690
300 I -820 -456 -1,460 I 520 -1"980
320 -1, 780 -115 - 3,170 131 -3;300
340 - 2,490 -286 - 4, 430 326 -4,750
360 - 2, 740 -17 -4,SRO I 19 -4,900
380 -2,560 428 - 4,560 -188 -5;Q50
400 -1 850 870 - 3,290 992 -{ 280
420 ..:goo 579 -1,580 660 - 2j 240
440 90 563 200 643 -.: 8m
460 900 748 2,010 853 2,860
480 1,380 389 3,080 444 3·'.520
500 1,580 -421 3,520 480 ,r,ooo
520 I 1,630 -1,290 3, 640 1,470 5; 110
540 1, 620 -1,562 3,610 1,782 ·5-;390
560 1,6.'lO -1,5-19 3,640 1,767 5)-410
580 I 1,620 -1,572 3,610 1,790 6' 400
600 1,480 -1,694 3,300 1,931 6~230
620 I 1,080 - 1,812 2,410 2,066 4 480
I
640
I
450 -1,432 l,o:JO 1,632 2:630
660 -250 - 698 -450 796 -1,250
680 -660 - 42 -1, 170 48 - 1,220
700 290 176 650 201 850
I I
TABLE 11.- Master connecting rod (Drawing No.
051025) .
Distance of section from piston pin center =x:
l- - ~ ------- - !-- x= 1._5 _ , X=5.2. x=y.9. I
Dim~nsion B . • . • _ .• ....... . _ 1.125 I :i. 1125
88
• 1.,
2
1~
19
5
Dimens10n C...... ... ... .... .156
Dimension D.... . . ....... . . . . 125 . 125 :t~5
Dimension H. .. . . . . .. . . . . . . . 1. 438 1. 50 1. 5§2
Dimlinsion E •.. . _. _. ... ..... I. 125 1. 125 1. 125
Areaofsection A... .... .. ... .492 . 5tl2 . 632
Moment of inertia L,.. .... .. .160 . 198 . 239
Moment ofinert!a I,...... ... . 0372. . 0-146 . 0521
Section modulus Z . . . . ... .. • 1 . 283 . 352 . 425
Z divided by x... . . . . ...... . .189 . 0678 . 0-178
Length of rod L = 13
Length of rod Li =9.2
TABLE 12.-Link connecting rod (Drawing No. 051032).
Dimension of center section of shank:
B~0
;1.125 C~.156 D=.125
iE=l.125
Area of section A = .492
l\loment of inertia Ix= .160
M,()iuent of inertia.JV= .0372
Length of rod L = 10.2, 'L, = 7.5
Dimensions of section of fork:
x=.22 fJ=50° C=.98
H-=1.5 . E =-,1~7 -K = l.-125
G=.15
Area of section A = .51
Distance Y1 = .33
Distance Yi = .59
Moment of inertia I,.= .0423
H = 1.438
D=.92
FIGURE 1.
\
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F!GVRE 2,
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(
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F IGURE 4,
- , ·,
-- T • I• I I I I~ S, -
I I I I I I • •
cel'lre1e. CY'LI/YOER /, . ) ...
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t-t--++:-,r:-H-+t-t-t-Hl<tt+rt-t-t-t-Ht-H-t-t--t--tTHL. H. CYLINOER. ----
J..4-l-!-l--1-1-4-!-4-1--1-1--il'N-4, -+-++-+-++---+-+-++-+-t ~ . H. C YL If'/ DER. - ·---1-.u...~1-1-1,-1-1--1-+~l-Hl+++++++-+-1-t-1~+++t-t-t-H-i-H
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t.t:,t, .~!~,~~t.t.t.t.t~+~~:i~,t.t.t.t+++-,;,'lf= i'=-t..t..t .ti:+j.~.." =+~~~t.t-.t.:. ;. :..1 ...v .J' ~.• 1 C°: Ml'i K ft !i~l.E
I I "'. I I; I I I I I I I I I I I II I I I I I I II I I
FIGURE 7.
)
1
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1 ,_ ,.
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... 11 I
l IND IC/flT ali!. 0/Aq','!.1'9/'1
' t.. m.e.p. = 141 . .5
-~~ 0 ~ r : .5.40
' , T = I. :3C
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I .- . II I I I I
0 4t) .:. 0 j J .so li,O 70 80 ~o 100 //0 IZO ,, 140 I. t, 160
C!(!/9/'iK ,.,:Jl'it:lL.!:' - oetJ~ees
FIGURE 8.
-
qA.5 PRe~5{)/U: R:JRCe -- - - - - -
I !"I ER. Tl/:> l"Oli!Ce -·--·-·--
Re!J{)LTrr/"/1 FORCE
~
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I,,
I,
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r,
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C " ~-) . ,L I
FIGUR F. 0.
.
ceNreR. Cr'LINDeR.
L. H. CYL!/"/Dc'~ - - - - - - -
. e, .H. CY'L 1/"/De'I<. - ·--·--·-
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PISTOi"/ 5/0e Trlle(}..!JT
- v.,: CRrrliK ~!Y(j/..E
.
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F IGURE 10.
certre~ CYLIIYO~
.. L.H. CYLINO~,li! -----~- ~ . H CYl//YOe'li!..
__ _._. ____
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vs. PIS "TOIY r ,e~VeL .•
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FIGURE 12.
AB ·~Ree ALOl'lt; cr1tm eoQ
BC • FOece At.N'/6 L. H ~co
CD. fi,,?CE 1/Lf)t((j /i! l'i ROO
22
D
C
FIG. 13.- Mcthod of determining resultant force on crank pin.
----
'\/~ ~ ..... ~~
II ' \
I . \
I . \
~' IG. 14.-Polar diagram showing magnitude of force on crankpin and direction with respect to engine axis.
23
1 "
FIG. 16.-Polar diagram showing magnitude of force on crankpln and direction with respect to crank throw.
FIG. 16.- Polar diagram showing magnitude and direction of force on master connecting rod.
24
Fm. 17.- Polar diagrwn of forces on end main crankshaft bearing.
F10. 18.-Polar diagram of forces on center main crankshaft bearing.
-
25
J<'tG. 19.- Polar diagram of forces on Intermediate main crankshaft bearing.
-~-- --------....
FIG. 20.-Diagram showing comparative wear on crankpln.
.-. 1,- Cl
' ,,, ,.. ---
0
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J<'t<>URIC 22.
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