The multi-cylinder engines with the cylinder centre lines in the same plane and on the same side of the centre line of the crankshaft, are known as In-line engines.

The following two conditions must be satisfied in order to give the primary balance of the reciprocating parts of a multi-cylinder engine:

The following two conditions must be satisfied in order to give the primary balance of the reciprocating parts of a multi-cylinder engine:

1. The algebraic sum of the primary forces must be equal to zero. In other words, the primary force polygon must be close; and

2. The algebraic sum of the couples about any point in the plane of the primary forces must be equal to zero. In other words, the primary couple polygon must close.

We have already discussed, that the primary unbalanced force due to the reciprocating masses is equal to the component, parallel to the line of stroke, of the centrifugal force produced by the equal mass placed at the crank pin and revolving with it. Therefore, inorder to give the Primary balance of the reciprocating parts of a multi-cylinder engine, it is convenient to imagine the reciprocating masses to be transferred to their respective crank pins and to treat the problems as one of revolving masses.

1. For a two cylinder engine with cranks at 180°, condition (1) may be satisfied, but this will result in an unbalanced couple. Thus the above method of primary balancing cannot be applied in this case.

2. For a three cylinder engine with crank at 120° and if the reciprocating masses per cylinder are same, then condition (1) will be satisfied because the forces may be represented by the sides of an equilateral triangle. However, by taking a reference plane through one of the cylinder centre lines, two couples with non-parallel axes will remain and these cannot wanish vectorically. Hence the above method of balancing fails in this case also.

3. For a four cylinder engine, similar reasoning will show that complete primary balance is possible and it follows that 'For a multi-cylinder engine, the primary forces may be completely balanced by suitably arranging the crank angles, provided that the number of cranks are not less than four'.

__Notes:__1. For a two cylinder engine with cranks at 180°, condition (1) may be satisfied, but this will result in an unbalanced couple. Thus the above method of primary balancing cannot be applied in this case.

2. For a three cylinder engine with crank at 120° and if the reciprocating masses per cylinder are same, then condition (1) will be satisfied because the forces may be represented by the sides of an equilateral triangle. However, by taking a reference plane through one of the cylinder centre lines, two couples with non-parallel axes will remain and these cannot wanish vectorically. Hence the above method of balancing fails in this case also.

3. For a four cylinder engine, similar reasoning will show that complete primary balance is possible and it follows that 'For a multi-cylinder engine, the primary forces may be completely balanced by suitably arranging the crank angles, provided that the number of cranks are not less than four'.

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