Page 552 - Dynamics of Mechanical Systems

0593_C15_fm Page 533 Tuesday, May 7, 2002 7:05 AM

Balancing 533

TABLE 15.10.2
Engine Balance: Listing of Terms of Eqs. (15.7.8) to (15.7.11) for the Eight-Cylinder Crank Angle
Configuration from Table 15.9.6.
i φφ φ φ (°) cosφφ φφ i sinφφ φφ i cos2φφ φφ i sin2φφ φφ i (i – 1)cosφφ φφ i (i – 1)sinφφ φφ i (i – 1)cos2φφ φφ i (i – 1)sin2φφ φφ i
i
1 0 1 0 1 0 0 0 0 0
2 90 0 1 –1 0 0 1 –1 0
3 270 0 –1 –1 0 0 –2 –2 0
4 180 –1 0 1 0 –3 0 3 0
5 180 –1 0 1 0 –4 0 4 0
6 270 0 –1 –1 0 0 –5 –5 0
7 90 0 1 –1 0 0 6 –6 0
8 0 1 0 1 0 7 0 7 0
Totals 0 0 0 0 0 0 0 0

(Resultant)

FIGURE 15.10.1 FIGURE 15.10.2
A V-type engine. Unbalance primary moments and
their resultants.

A practical difficulty with a straight-eight engine, however, is that it is often too long
to conveniently fit into a vehicle engine compartment. One approach to solving this
problem is to divide the engine into two parts, into a V-type engine as depicted in Figure
15.10.1. The two sides of the engine are called banks, each containing four cylinders.
Because the total number of cylinders is eight, the engine configuration is commonly
referred to as a V-8.
A disadvantage of this engine configuration, however, is that the engine is no longer in
balance, as compared to the straight-eight engine: To see this, consider again the crank
configuration of the straight-eight as listed in Table 15.10.2. Taken by themselves, the first
four cylinders are unbalanced with an unbalanced primary moment perpendicular to the
plane of the cylinders as seen in Table 15.9.6; hence, the second set of four cylinders has
an unbalanced primary moment perpendicular to its plane. With the cylinder planes
themselves being perpendicular, these unbalanced moments no longer cancel but instead
have a vertical resultant as represented in Figure 15.10.2. This unbalance will have a
tendency to cause the engine to oscillate in a yaw mode relative to the engine compartment.
This yawing, however, can often be kept small by the use of motor mounts having high
damping characteristics. Thus, the moment unbalance is usually an acceptable tradeoff in
exchange for obtaining a more compact engine.