I. Introduction
With the recent development of high-speed two-cycle engines the question of balance becomes an important matter for investigation as inertia forces are proportional to the square of the engine speed.
This paper discusses the arrangements of the cylinders and the forms of crankshafts necessary in order that two requirements-explosions at uniform intervals and balancing of inertia forces- may be fulfilled.
II. Balancing of Single-Line Engines
With the exception of 12 cylinders in-line engines, the complete balancing of couples due to inertia forces is generally impossible, but considerably good balancing may be obtained by using proper forms of crankshafts as follows.
When two harmonic balancers, as the Lanchester Anti-Vibrator, may be attached to the engines for the purpose of compensating moments due to primary or secondary harmonic of inertia forces, the forms of crankshafts indicated by the following table are preferable. (chapt. 6. §1.) III. Inertia Forces of Single-Bank Radial Engines.
(In this case, the term single-bank radial engines denotes the c-lines engines where one line has only one cylinder and the angles λ between adjacent cylinders are equal to one another.)
Note: +Rot.: Rotating forces in the same direction as the crankshafts. -Rot.: Rotating forces in the reverse directiou to the crankshafts. S.H.; Simple-harmonically oscillating forces.
We will refer to this table for investigating the methods of balancing of multi-lines engines in section IV.
IV. Balancing of Multi-Lines Engines.
1. 2-Lines Engines (Vee-Type) c=2
§1. Angle of Vee λ=90°
With 90° V-type engines, the primary harmonics of inertia forces and couples may be balanced by attaching suitable counter weights to the crankshafts and the secondary harmonics and couples, if any exists, also by using harmonic-balancers.
§2. Angle of Vee λ=180°
With this case, the secondary harmonics of inertia forces and their moments are both zero, and the primary harmonics of inertia forces and the primary couples may be balanced, if desired, by the aid of harmonic-balncers. (Refer to table 9 in III.)
§3. Angle of Vee λ=60°
The proper use of revolving masses, the rotational speed of which is twice that of crankshafts, will eliminate the secondary harmonics of inertia forces and the secondary couples.
No. of Cylinders N=18 Form of Crankshaft Fig. 51b
2, 3-Lines Engines (W-Type) c=3
§1. Cylinder-Angles λ=60°
As the primary harmonlcs of inertia forces are rotating forces, the primary forces and the primary couples may be balanced by rotating counter masses attached to the crankshaft.
§2. Cylinder-Angles λ=120°
(Refer to table No. 9 in III.)
§3. Cylinder-Angles λ=80°
No. of Cylinders N=18 Form of Crankshaft Fig. 36c. 3, 4-Lines Engines (X-Type) c=4
§1. Cylinder-Angles λ=45°
§2. Cylinder-Angles λ=90°
By using revolving counter masses the balancing of 90° four-lines radial engines is perfect. Consequently the forms of crankshafts must be properly chosen so that the revolving counter masses would be as small as possible.
4, 5-Lines Engines
§1. Cylinder-Angles λ=36°
No. of Cylinders N=20 Form of Crankshaft Fig. 62
§2. Cylinder-Angles λ=72°
(The methods of balancing are similar to the case mentioned in the 4-lines engines having cylinder-angles λ=90°)
5, 6-Lines Engines Cylinder-Angles λ=60°
(The methods of obtaining good balancing are similar to that of 4-lines engines of λ=90°)
6, Multi-Banks Engines Multi-banks engines are composed by putting radial engines into layers as in the cases of the 4-cycle radial engines. Here the rotating masses attached to crankshafts may be reduced in their weights by selecting adequate forms of crankshafts.
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