This document discusses balancing of reciprocating masses in inline multi-cylinder engines. It defines primary and secondary balancing and the conditions required for complete balancing. Primary balancing requires balancing of primary forces and couples, while secondary balancing requires balancing secondary forces and couples. The document provides an example problem calculating the mass and angular position of cylinders to achieve primary balancing in a four cylinder inline engine.

1. Branch : Mechanical Engineering
Div: 6C-1
Name: Saahil Kshatriya
Enrolment Number: 150120119164

2. Content
 Introduction
 Condition for Completebalancing
 Primary Balancing of inline Multi-cylinder Engines
 Secondary Balancing of inline multi-cylinder Engines
 Balancing of four cylinder inline engines

3. Introduction
 Reciprocating parts of any machine is subjected to continuous
acceleration and retardation.
 Inertia acted opposite to the acceleration of part.
 This inertia force is disturbing or unbalanced dynamic force acting
on reciprocating part.
 Eliminate the unbalanced force by using suitable balancing masses.
 The balancing of reciprocating masses is divided into :
•
•
•
Balancing reciprocating massesin single cylinder engine
Balancing reciprocating massesin multi cylinder inline engine
Balancing reciprocating massesin V-engine

4. Balancingreciprocating masses in
Multi-cylinder inline engine
The multi-cylinder engine having the axes of all the engine of all the cylinders in the same plane and on
thesamesideof theaxis of thecrank shaft, areknown asinline engine.
In the multi-cylinder engines unbalanced force and couples are acting.
Themulti-cylinder engine have twoinner crank and twooutercrank.
Fortheinner crank angle =θ˚
Fortheoutercrank angle =180+ θ˚
Theunbalanced forces due toreciprocating massof each
Cylinder are ;[Primaryforce , Fp=mω 𝟐r cosθ ][secondaryforce= mω r{𝟐 cos2θ
𝒏
}

5. Condition for complete balancing
Primary balancing
 Primaryforces mustbe balanced.
∑mω2r cosθ= 0
 Primarycouple mustbe balanced.
∑mω2r l cosθ= 0
Secondary balancing
 Secondary forces mustbebalanced.
𝒏
∑ mω 𝟐r{cos 2θ}
 Secondary couple mustbe balanced.
𝒏
∑ mω 𝟐rl{cos2θ}

6. Analytical method for primary balancing
Forcompleteprimarybalancing, theanalytical solutionis;
∑ mr cosθ= 0
∑ mrl cosθ= 0
∑mr sinθ= 0
∑ mrl sinθ= 0
Analytical methodfor secondary balancing
∑ mrcos 2θ= 0 ∑ mrsin2θ=0
𝑛 𝑛
∑ mrlcos 2θ= 0 ∑ mrlsin2θ= 0
𝑛 𝑛

7. EXAMPLE : A four cylinder vertical engine has crank 150 mm long . The planes of rotation of first ,
secondandfourthcrankare400mm, 200mm and200mmrespectivelyfromthe thirdcrankandtheir
reciprocatingmasesare50kg,60kg and50 kg respectively.Findthemassof the thirdreciprocatingpart
and their relative angular position of the cranks in order that the engine may be in complete primary
balance.
Sol.:- Given , r1 = r2 = r3 = r4 = 150 mm = 0.15m ; m1 = 50 kg, m2 = 60 kg, m4 = 50 kg;
1 2 3 4
-ve R.P +ve
200 mm 200 mm
400mm
(a) Position of plane
In order to give the primary balance of the reciprocating parts of a multi-cylinder engine, the
problem may be treated as that of revolving masses
with the reciprocating masses transferred to their respective crank pins.

8. Plane Mass Radius Cent.
Force/ω 𝟐
Dist. From
plane 3
Couple/ω 𝟐
1 50 0.15 7.5 -0.4 -3
2 60 0.15 9 -0.2 -1.8
3( R.P) m3 0.15 0.15m3 0 0
4 50 0.15 7.5 0.2 1.5
a’
b’
o’
-1.81.5
-3
(b). Couple polygon
1
2
3
4
(c). Angular position of crank

9. 7.5
9
By measurement we find the angle between crank 2 and crank 1 is 160˚ in anticlockwise.
θ2 = 160˚
And angle between crank 4 and crank 1 is 26˚ in anticlockwise.
θ4 = 26˚
In order to find the mass of the third cylinder (m3) and its angular position, draw the force
polygon, to some suitable scale.
7.5
0.15m3 From the fig. , 0.15 m3 = 9 kg-m
m3 = 60 kg.
and θ3 = 227 ˚