Reciprocating Balancing Example

A four crank engine has two outer cranks set at 120o

to each other and their reciprocating masses are

400kg each. The distance between the planes of

rotation of adjacent cranks are 450mm, 750mm and

600mm. If the engine is to be in complete primary

balance, find the reciprocating mass and the

relative angular position for each of the inner

cranks. If the length of each crank is 300mm, length

of each connecting rod is 1.2m and speed of

rotation is 240rpm, what is the maximum secondary

unbalance force and the crank position at which this

occurs?

June/July 2011

1 2 3 41

4

Mass 1 =400kg

Mass 4 =400kg

Mass 3=?Mass 2=?

Axis of Crank Shaft

Cylinder axis of Engines 1, 2, 3 & 4

450 750 600

1

2

3

4

120

120

Direction of engine piston

450

750

600

DRAW LAYOUT OF THE ENGINE

Plane

Mass(m)

Radius ofRotation

(r)

Centrifugal force (N)(Actual)

CF ω2

( mr )Dist.

From RP ( l )

Couple ω2

( mrl )

Scaled Force (5)

Scaled Couple (2)

1 400 0.3 75782 120 – 0.45 54 24 27

2 m2 0.3 189.5 m2 0.3 m2 0 0 - 0

3 m3 0.3 189.5 m3 0.3 m3 + 0.75 0.225m3 - -

4 400 0.3 75782 120 + 1.35 162 24 81

Assume that crank-1 makes an angle of 0 with the engine IDC.

SET-UP DATA TABLE

CALCULATE ω AND n

n = 4 ; ω = 25.13 rad/s

Construct Primary Couple Polygon

27

81

97,35

120°

SCALE: 1mm = 2 couple units.

C1 = 27 mm; C2 = 0; C4 = +81 mm

o

d

a

From couple polygon, vector do = 97.35 mm or 97.35 2 = 194.7 couple units.

0.225 m3 = 194.7, orm3 = 865.3 kg

120°

46°

Referring to the couple polygon determine the crank angle of engine-3 to be 46 (CW) from crank-1.

With couple polygon we can determine m3 and the crank position of engine 3 relative to the other two cranks.

Closing side

DETERMINE m3 AND THE CRANK ANGLE

24

24 51,9250,8

Construct Primary Force Polygon

SCALE: 1mm = 5 force units. F1 = 24 mm; F4 = 24 mmF3 = 0.3m3 = 0.3 865.3 = 259.6 force units. 259.6 units to scale would be 259.6 5 = 51.92mm

120°

46°

161°

o

c

a

b

Closing side

Closing side = vector co = 50.8mm.50.8 mm 50.8 5 = 254 force units.0.3 m2 = 254 or m2 = 847 kg.Direction of crank-2 is 161 from crank-1

Thus mass 2 and 3, and their crank locations are determined.

DETERMINE m4 AND THE CRANK ANGLE

120°

46°

161°PRIMARY CRANKS

Crank-1 makes 0 with engine I.D.C. Therefore secondary crank-1 makes 2 0 = 0 with IDC




360-322=38

628-360=268=180+88

SECONDARY CRANK POSITIONS

FIXING THE ORIENTATIONS OF SECONDARY CRANKS

24

50,8

52

24

115,51

64°

Plane

CF ω2 Scaled Force (5)

1 120 24

2 254 50.8

3 260 52

4 120 24

SECONDARY CRANK POSITIONS

THE CLOSING VECTOR od

REPRESENTS MAXIMUM

UNBALANCED SECONDARY FORCE

o a

b

c

d

CONSTRUCTION OF SECONDARY FORCE POLYGON

24

50,8

52

24

115,51

64°

The scale used to draw secondary force polygon was 1mm = 5 force units.

Therefore, 115.5mm on the secondary force polygon corresponds to 115.5 5 = 577.5 force units.

Angular velocity ω = 25.13 rad/s

n = l/r = 1.2/0.3 = 4

The maximum unbalanced secondary force = 577.5 ω2 / n = 577.5 25.13 25.13 / 4 = 91175 N.

MAGNITUDE OF MAXIMUM SECONDARY FORCE

SECONDARY FORCE POLYGON

24

50,8

52

24

115,51

64°

Line is engine cylinder axis (Fixed line)

NOTE: Primary and Secondary forces from the reciprocating masses ALWAYS act along the (FIXED) line of cylinder axis.

Therefore for the GIVEN CRANK POSITIONS, the maximum unbalanced secondary force of 91175 N resolved along the fixed cylinder axis will be 91175 cos(64)= 39968 N.

39968 N

Resultant = 91175 N

OBSERVATIONS

Engine axis(Fixed line)

Force Polygon turned 64 in Counter Clockwise sense

DETERMINE CRANK ANGLE WHEN THE SECONDARY FORCE IS MAXIMUM

But the crank positions for secondary forces/couple is known to be twice the actual crank angles (2). Therefore, maximum secondary forces occur on the engine when the crank positions are 32 CCW from the given position.

POSITION OF THE CRANKS AS GIVEN IN THE PROBLEM

32

CRANK POSITION WHEN SECONDARY FORCE IS MAXIMUM

DETERMINE CRANK ANGLE WHEN THE SECONDARY FORCE IS MAXIMUM

1 The pistons of a 4-cylinder vertical inline engine reach their uppermost position at 90o interval in order of their axial position. Pitch of the cylinder = 0.35m, crank radius = 0.12m, length of CR = 0.42m. The engine runs at 600 rpm. If the reciprocating parts of each engine have a mass of 2.5kg, find the unbalanced primary and secondary forces and couples. Take the central plane of the engine as reference plane. (June/July 2013)

2 The cranks and connecting rods of a 4-cylinder in-line engine running at 1800 rpm are 60mm and 240mm each respectively and the cylinders are spaced 150mm apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90o in an end view in the order 1-4-2-3. The reciprocating mass corresponding to each cylinder is 1.5kg. Determine, (i) Unbalanced primary and secondary forces, (ii) Unbalanced primary and secondary couples with reference to central plane of the engine. (Dec.2012)

3 A four crank engine has two outer cranks set at 120o to each other and their reciprocating masses are 400kg each. The distance between the planes of rotation of adjacent cranks are 450mm, 750mm and 600mm. If the engine is to be in complete primary balance, find the reciprocating mass and the relative angular position for each of the inner cranks. If the length of each crank is 300mm, length of each connecting rod is 1.2m and speed of rotation is 240rpm, what is the maximum secondary unbalance force? (June/July 2011)

4 The stroke of piston in a six-cylinder two stroke engine is 320mm and the connecting rod is 800mm ling. The cylinder lines are spaced at 500mm. The cranks are at 60o apart and the firing order is 1-4-5-2-3-6. The reciprocating mass per cylinder is 100 kg and the rotating part is 50kg per crank. Determine the out of balance forces and couples about the mid plane is the engine rotates at 200 rpm. (Dec 06)

A four cylinder vertical engine has cranks 1m long. The planes of rotation of 1st, 3rd and 4th cranks are 2.5m, 3.5m and 5.5m respectively from that of the 2nd crank. The corresponding weights of reciprocating parts are 300kg, 800kg and 500kg respectively. Find the weights of the reciprocating parts for the 2nd cylinder and the relative angular positions of the cranks in order that the engine may be in complete primary balance. If each connecting rod is 4.5m long and the speed is 150 rpm, find the maximum unbalanced secondary force and couple, and the crank position at which they occur.

140

137,5

37,5

Primary Couple Polygon

30

57,59

80

50

30°

Primary Force Polygon

78°86° 150°

Actual Crank Positions

156° 172°

Secondary Crank Positions

30

57,6

80

50 98,82

50°

Secondary Force Polygon

7°

18,75

68,75

70

151,9

6

Secondary Couple Polygon

Reciprocating Balancing Example

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