SEPTEMBER 1898.

AND RAILROAD JOURNAL.

295

 
 

Editor “American Engineer!

I am glad of the opportunity to answer the question Mr.
Henderson asks in the above letter discussing the strength of
driving axles.

It is often better to reason from known facts and base our
conclusions upo-n them than to assume certain conditions which
are not so clearly established. It seems more desirable to as-
sume normal conditions for the Working stresses, and keep the
fiber stress at such a low figure as to give an ample margin of
strength to resist the abno-rmal and extraordinary stresses
which may occur from time to time.

In a locomotive having but one pair of drivers the entire
piston thrust must evidently be resisted by the one crank pin
and axle. The bending moment is the thrust of the piston mul-
tiplied by the lever arm; the maximum fiber stress caused by

@___@_,-@._.___-@___

Fig. I.

this force is the bending moment -divided by the modulus of sec-
tion of the axle when worn. o-ut. If the tractive force exceeds
the resistance caused by the adhesion of the wheels, slipping will
take place. In ordinary types of engines having two or more
pairs of drivers, the parallel rods transmit to the other pairs of
wheels a proportional amount, so that each pair has to resist
an equal turning moment. It is a generally accepted prop-o-
sition that an equal force is transmitted to each pair, or that
the maximum turning moment on any pair is equal to the piston
thrust divided by the number of pairs of drivers. This fact
being established-, it follows that the parallel rod prevents the
entire thrust being borne by the main axle and transmits it
equally to all the drivers. If the lost motion is excessive, or if
a lack of parallelism exists between the axles and the crank
pins, slipping will take place at every revolution to adjust the
irregularities. The stress on- the main axle under these con-
ditions will be increased up to the limit of adhesion, an ex-
cess amount probably not exceeding 125 or 30 per cent. of the
normal stress.

When the crank is on the dead center the effect of lost mo-
tion in the rods or driving boxes is felt at its maximum. It is
probable that ordinarily when there is much lost motion in the
parallel rod bearings, the main axle will be also loose enough in
its box to allow the load to be distributed among the drivers as
at other portions of the stroke. There is also a certain amount
of spring or deflectioln in the axle and crank pin, which occurs
before the maximum stress is reached, and assistsmaterially in
equalizing the pressure between the drivers, taking up in a de-

R ‘”"“@‘*”“@ ‘””i‘%

Fig. 2.

gree the lost motion in the rod bearing. The possibility of over-
Strain in the main axle due to excessive slack in: the parallel rod
bearings, Was carefully considered in the suggestion that the
fiber stress should be decreased as the number of axles in-
creases. . .

Mr. Henderson assumes that only the main axle is subjected
to increased stresses due to excessive slack or improper adjust-
ment, whereas, under certain conditions any of the other axles
may be required to resist considerably more than their normal
loading‘. Fig. 1 shows the crank pins of a_ consolidation engine
at the commencement of the stroke, with an equal amoun-t of
slack in- front of all the pins. This is the condition assumed
by Mr. Henderson. It is evident, however, that a slight,1005e-
ness in the main driving-box and spring in the pin and axle will
in most cases, prevent the entire ;piston thrust from being resist-
ed by the main axle. —

Fig. 2 shows the slack on the back of the main, second and
fourth, and in front of the first pair. '. Here the first axle has to
Withstand an overload, unless relieved by looseness in: the boxes
or springing. . . A

In Fig. 3 the slack is back o-f the main, first and second, and
in front of the fourth pair, the latter axle having to withstand
the overload. ’* ‘

Were it a fact that the working stress on the main axle 0*’
a. consolidation engine should be taken as the entire piston
thrust, irrespective of the number of axles, it could be shown
by a. number of instances of engines which have been in service
for 1'5 01' 20 Years, during which time comparatively few
breakages have occurred, in spite of the fact that the assumed
stresses would figure up to 30,000 to 32,000 pounds per square
inch for hammered iron axles, undergoing, roughly speaking,
::out 12 millions of repetitions of alternating‘ loads per

at.

The 9-bilits’ Of Wrought iron to resist repeated changes of
loading is now so well known that it is unnecessary to go into
details, but merely to state that breakages may always be ex-
pected to occur after a few million changes of load at from
3-6:000 t0 25.000 pounds stress per square inch, the former being
for reversing or alternating tension and comp:-'essio.n, and the
latter a load applied and entirely removed, but always acting
in the same direction.

An axle under a freight locomo-tive is subjected to an. alter-
nating stress in which the reversals, although they do not reach
the maximum yet when the engine is moving slowly and cutting
Off Steam 3-1:. say, 80 per cent., do reach 50 or 60 per cent. of the
maximum stress acting in the o-pposite direction. The breaking
stress after two or three million repetitions could, therefore,
reasonably be taken at about 20,000 pounds per square inch for
good wrought iron. -This is the breaking load for this range
of stress as opposed to the static breaking load once applied,
as seen in the testing machine, and known as the ultimate
strength of the material, neither having any margin of strength
or factor of safety, the latter breaking quickly with a single
load steadily applied and not removed until after fracture, and
the other breaking equally as surely, although _not so quickly,
after the required number of changes of load have taken place.

s--s--ss-s

Fig. 3.

Again, the working stress of an axle can be approximately de-
termined by the amount the rear axle of an eight-wheel engine
can withstand, the parallel rod transmitting the force and the
pin and axle being, therefore, entirely unsupported. Here in-
stances can be cited where fractures usually occurred with
iron axles when the stress exceeded 12,000 or 13,000 pounds. It
seems unreasonable, therefore, to consider it _necessary to de-
sign the main axle of a consolidation engine to resist the entire
piston thrust unaided by the parallel rod, and keep the fiber
stress down to, say, 8,000 to 10,000 pounds per square inch, fig-
ures Which would usually be considered the maximum safe
stress for this manner of loading. Taking the higher figure of
10,000 pounds, a mogul, consolidation or 10-wheel engine having
20-inch cylln‘ders, steam pressure 200 pounds and a lever arm of
21 inches (center of main rod to center of frame), would require
an axle of 11 inches diameter when worn down to the limit to
resist the piston thrust alone.

’ For crank pins the support of the parallel rod was duly con-
sidered. On engines having the main rold outside it is com-
paratively small, so that the simplest method is to disregard
it and use a higher Working stress», as suggested in page 125 of
the April number, and shown graphically in Fig. 6, page 164, of
the June number. The distance from the wheel face to the
center of the parallel rod is usually from 2 to 3 inches, mak-
ing the counter-moment small in proportion to. the bending
moment, so that, after ‘all, the real question is whether it is
more desirable to use the higher stress without and the sup-
port of the parallel rod, or the lower stress,-when it is taken into
consideration. " The latter seems to me the morerational, al-
though’ more complicated, method.

Paterson, N. J. F- 3- COLE-

Pneumatic tubes for the ‘transmission of mail between the
New York and Brooklyn Postoffices were put into service -Aug.
1. The tubes pass over the Brooklyn. Bridge, and are provided
with three expansion joints on the structure. The cost of the
plant, including the double-pipe system. W3-S $60,000. and the
annual rental paid to the New York Newspaper and Transpor-
tation Co. for carrying first-class matter is to be $14.000 for 9-
three-years’ lease. The system is similar to that illustrated in
our issue of November, 1897, page 379. . -