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BOYER, KUIVINEN—STRESS AND DEFLECTION IN RECIPROCATING PARTS OF ENGINES 503
in tension the force due to reciprocating inertia plus the centrifugal
force of the rotating end of the connecting rod (less that
caused by the connecting-rod cap). In other types of engines,
particularly double-acting engines, the actual maximum load
must be determined by a complete analysis of loads for the
entire cycle. The proportion of rotating and reciprocating
portions of the rod can be determined by calculating its center of
gravity or by weighing simultaneously the assembly on two scales.
Crank-bearing bolts are very vital parts of an engine and
failure may cause considerable damage to the balance of the
engine. For this reason, stresses must be conservative and the
material should be the best steel that is obtainable. A factor
of safety of approximately 12 to 13, based on the ultimate strength
of the steel, is recommended in selecting the bolt size for a known
working load. Heat-treated chrome-molybdenum steels of excellent
physical properties, both in ultimate tensile strength and
impact resistance, can be obtained. On assembly, these bolts
should be tightened to give an initial stress of approximately
twice the actual working stress.
It has been suggested that an important part of an engine,
such as a crank-bearing bolt, should be replaced with a new one
after a certain period of service because the bolt “fatigues” and
must be replaced or it will ultimately fail. This should not be
necessary if the engine is so designed that these bolts are not
stressed to the endurance limit of the steel being used. Physical
research on steels has proved that, when repeated stresses, below
the static ultimate strength of the steel, are applied, failure
occurs after a certain number of cycles. However, as various
stresses are applied, there is a stress value below which the repeated
loads can be applied with an indefinite number of cycles
without failure. Research laboratories have accepted 10,000,000
cycles as the point of measurement of the endurance limit.
Therefore, if the stress is at such a value that the specimen will
absorb 10,000,000 or more cycles without failure, it will go on
indefinitely without failure at this stress. As long as the actual
stresses used on the bolt are safely below this value, known as the
“endurance limit,” these stresses therefore could be repeated
indefinitely without failure. The fallacy of the practice of
changing bolts every few years is apparent when considering
that it would be necessary to change them perhaps each week or
each month, depending upon engine speed, in order not to exceed
10,000,000 cycles.
C o n n e c t in g - R o d -B e a r i n g C a p s
Regardless of the shape proposed for the cross section of the
connecting-rod-bearing cap, the cap stress should be determined
by the most severe consideration in order to gain rigidity.
Again, it is not practical to state what definite deflections should
be permitted, because the ideal would be zero and the limiting
value is determined by good performance experience. The
simplest method of gaining rigidity is to consider the cap as a
freely supported curved beam. The supports are at the crankbearing-bolt
center lines and the maximum load applied to the
center of the cap as a concentrated load. The actual total load in
all crank-bearing bolts, obtained from a study of the forces
(inertia forces and others), can be this concentrated load. Again,
I-beam cross sections give the most strength and rigidity with
the least weight.
The bending moment on the beam is the simple beam formula
where M = moment, in-lb; P = load on cap, lb; and X = distance
from nearest bolt to cross section under consideration, in.
The stress caused by moment M in Equation [7] is determined
by using the straight beam-stress formulas and applying a correction
factor K. These K values are given in Fig. 5 for various
types of cross sections.6 Thus, the stress at the section being considered
is
where Sb = bending stress, psi; M = bending moment from
Equation [7]; c = distance from neutral axis to extreme fiber on
side (tension or compression) being considered, in.; I = crosssectional
moment of inertia, in.4; K = correction factor for curvature
of beam and is variable depending upon shape of cross section
and also on jR/ci where R = radius of curvature of path of
neutral axis at point where the cross section is being studied and
ci = distance from neutral axis to extreme fiber on concave side
of curved beam.
Thus, for a connecting-rod cap with a load P on the concave
side we have
compression on the inner fiber in psi, and
tension on the outer fiber, psi. In Equations [8], Ki = correction
factor for inner fiber; K 2 = correction factor for outer fiber; ci
= distance to inner fiber, in.; and c2 = distance to outer fiber, in.
Both Ki and K2 are given in Fig. 5 for the determined value of
R/ci for a definite section shape.
By referring to Fig. 1, a better tie-in of the foregoing method
to solving an actual problem is apparent. Various cross sections
of the cap should be analyzed for stress in the same manner. At
section CC in Fig. 1, note that there is a small radius where a
flat is milled to prevent the head of the crank-bearing bolt from
turning. Even if this radius is made as generous as possible, the
tension stress at this point, as determined previously, should be
6 Fig. 5 is reproduced from Seely’s results in “Handbook of Engineering
Fundamentals,” reference (3), pp. 5-34.