Crank Gearsfirst-order inertial for

Crank Gears
first-order inertial force is not completely compensated so
that the free X component does not become too large, and
it is only 50% balanced. Completely balancing the rotating
inertial force Frot and the 50% balance of the oscillating
first-order inertial force is termed a normal
balance—it was used even in the 19th century for drivetrains
of steam locomotives. The mass balancing of
designed passenger car engines is 50% to 60% of the
oscillating inertial force and 80% to 100% of the rotating
inertial force.
(6.85)
(6.86)
Another method for balancing oscillating inertial
force is to use the so-called foot balance in which additional
mass on the large connecting rod eye moves the
conrod center of gravity toward the crank pin.12
The oscillating
first-order inertial force is completely balanced
when two balancing masses revolving in the opposite
direction that are half the oscillating crank gear masses are
symmetrically arranged in relation to the vertical engine
axis. Then the two components in the direction of the
cylinder axis compensate the oscillating inertial force; the
two components perpendicular to the cylinder axis cancel
each other out (Fig. 6-44).
To obtain a balance of the second order, the countermass
must rotate at twice the crankshaft speed (Fig. 6-45).
Fig. 6-44 Complete balance of the inertial forces of the
first order.
Fig. 6-45 Diagram of mass balancing of the second order
in a four-stroke crank gear.
6.1.5.2 Balancing Multicylinder Crank Gears
Automobile engines are built with multiple cylinders, i.e.,
with 3 to 12 (16) cylinders, as three-, four-, five-, and sixcylinder
inline engines and V6, V8, and V12 (V16)
engines, and as VR5 and VR6 engines. Earlier, there was
also a V-4 engine (Ford 12 M). Recently, three-row engines
(W-engines) with 12 cylinders have been developed.
These engines have three-, four-, five-, and six- (eight-)
stroke crankshafts so that with a corresponding arrangement,
the mass effects of the individual throws cancel
each other out (self-balance). For this purpose, the throws
are to be distributed evenly in the peripheral direction and
lengthwise direction:
• With centrally symmetrical shafts (equal to the throw
spacing across the perimeter), the free forces cancel
each other out.
• Centrally and longitudinally symmetrical arrangements
of the throws of a four-stroke engine shaft have
no free forces and torques of the first order; starting
with six strokes, the shafts are completely force-free
and torque-free.
The criteria for the throw sequence are
• No or very low free mass effects. A simple rule of
thumb for throw sequences with favorable mass balances
was presented by O. Kraemer in Refs. [13, 14].
• Additional torque may not arise from mass balancing,
and no additional inertial forces may arise from torque
balancing.
• Even angular ignition spacing.
Free first-order inertial torque can be balanced by a
shaft rotating in the opposite direction at the crankshaft
speed with two countermasses of a corresponding size and
lengthwise spacing (torque differential). The arrangement
in the engine can be freely selected. Gears or chains provide
the drive; frequently the oil pump drive is connected.
To balance torque of the second order, the differential
rotates at twice the crankshaft speed (Fig. 6-46).
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6.1 Crankshaft Drive 67
Fig. 6-46 Torque differential of the Audi V6.
The following holds true for crankshafts of fourstroke
engines:
• Three-stroke shaft: free torque of the first and second
orders occurs. The torque of the first order is
compensated—especially in V-engines—with a
torque differential.
• Four-stroke shaft: In four-cylinder, four-stroke inline
engines, the inertial forces of second order are additive.
These forces are balanced by two oppositely
rotating shafts with countermasses (differential).
Earlier, this was done only with tractor engines since
the engine, the transmission, and rear axle housing
form the bearing element of the vehicle.
Fig. 6-47 Differential for inertial
forces of the second order.
Today, such differentials are also used for passenger
car engines since beginning at 4000 min 1
, the free
second-order inertial forces are noticeable. The vertical
accelerations are guided into the body and cause an
"unpleasant humming."15
Because of the high peripheral speeds of the bearing
pin of this differential—up to 14 m/s—the bearing
and drive must be carefully designed. The balance
shafts are driven by a gear on a crankshaft web where
the tooth face play of the drive must be harmonized to
the shifts and rotational oscillations of the crankshaft
(Figs. 6-47 and 6-48).
Fig. 6-48 Effect of the mass differential in a four-cylinder
inline engine.
By offsetting the height of the balance shafts, an
additional oscillating torque of the second order can