1. CONNECTING ROD AND EQUIVALENT
Chapter 11 Engine Balance INRODUCTION All forces and moments are balanced to prevent noise and vibrations. Static and dynamic balance are considered. Static balance: Shaft (not rotating) does not turn if it is at any angle (position). Dynamic balance: Shaft in rotation and all forces and moments are balanced.
CONNECTING ROD AND EQUIVALENT

2. Static balance G = Centre of gravity m1 r1 = m2 r2 m = m1 + m2 m1 = rotating mass of a part of the connecting rod and the crankshaft web. m2 = reciprocating mass of a part of the connecting rod and the piston assembly (piston, rings, pin.. etc.) r1= distance between centre of gravity and centre of big end r2= distance between centre of gravity and centre of small end

3. CRANKSHAFT BALANCE Static balance Bxa = m1 r B = balance mass m1 = rotating mass of a part of the connecting rod and the crankshaft web a=distance between centre of crankshaft and centre of balance mass r=distance between centre of rotating mass (m1) and centre of crankshaft

4. Dynamic balance Resultant forces and moments equal zero
Dynamic balance Resultant forces and moments equal zero. Centrifugal force=m1r2 ω= angular speed of crankshaft

6. Chapter 11: Mechanical Design Consideration
Engine Balance and Pistons arrangement
INTRODUCTION
Once the type and the size of engine have been determined, the number and disposition of the cylinders have to be decided. Very often the decision will be influenced by marketing and packing consideration, as well as whether or not the
engine needs to be manufactured with existing machinery.
The disposition and number of the cylinders
The main constraints influencing the number and disposition of the cylinders are:
1. The number of cylinders needed to produce a steady output
2. The minimum swept volume for efficient combustion
3. The number and disposition of the cylinders for satisfactory balancing
4. The number of cylinders needed for an acceptable variation in the torque output.
For a four-stroke engine with five or more cylinders, there can always be a cylinder generating torque. Figure 11.1 shows the variation in the instantaneous torque associated with different numbers of cylinders. A six cylinder four-stroke engine is of course equivalent to a three-cylinder two-stroke engine.

8. The most common engine types are the straight or in-line, the V shape and the horizontal opposed. See figure 11.2

9. V shape engines form a very compact power unit, a more compact arrangement is the H configuration (in effect two horizontally opposed engines with the crankshafts geared together), but this is an expensive and complicated arrangement that has had limited use. Whatever the arrangement, it is unusual to have more than six or eight cylinders in a row because torsional vibrations in the crankshaft then because much more troublesome. In multi-cylinder engine configurations other than the in line format, it is advantageous if a single crankpin can be used for connecting rod to each bank of cylinders. This makes the crankshaft simpler, reduces the number of main bearing, and facilitates a short crankshaft that will be less prone to torsional vibrations.
None the less, the final decagon on the engine on the engine configuration will also be influenced by marketing, packing, and manufacturing constraints.
In deciding on an engine layout there are two interrelated aspects: the engine balance and the firing interval between cylinders. The following discussions will be related to four stroke engines, since these only have a single firing stroke in each once every two revolutions. An increases in the number of cylinders leads to smaller firing intervals and smother running, but above six cylinders the improvements are less noticeable. Normally the crankshaft is arranged to give equal firing intervals, but this is not always the case. Sometimes a compromise is made for better balance or simplicity of construction, for example, consider a twin cylinder horizontally opposed four stroke engine with a single throw crankshaft the engine is reasonably balanced but firing intervals are 180o, 540o , 180o etc.

10. When calculating the engine balance, the connecting rod is treated as two masses concentrated at the center of the big -end and the center of the little-end see figure 11.3.
For equivalence
m1 = m1+ m2
m1 r1 = m2 r (11.1)

11. The mass m2 can be considered as part of the mass of the piston assembly (piston, rings, gudgeon pin. etc.) and be denoted by mr , the reciprocating mass. The crankshaft is assumed to be in static and dynamic balance (figure 11.4). For static balance Mr = Ba, where B is the balance mass. For dynamic balance the inertia force from the centripetal acceleration should act in the same plane, this is of importance for crankshaft since they are relatively long and flexible.
As a simple example, consider a planar crankshaft for an in line four cylinder engine, as shown diagrammatically in figure 11.5 by taking moments and resolving at any point on the shaft, it can be seen that there is no resultant moment or force from the individual centripetal forces mr ω2
The treatment of the reciprocating mass is more involved if the connecting rod were infinitely long the reciprocating mass would follow simple harmonic motion, producing a primary out of balance force. However, the finite length of the connecting rod introduces higher harmonic forces.

13. Figure 11.6 shows the geometry of the crank-slider mechanism, when there is on offset between the little-end (or gudgeon pin or piston pin) axis and the cylinder axis. The little end
position is given by:
X= r cos ϴ + l cos ϴ (11.2)
Inspection of figure 11.6 indicates that
r sine ϴ = l sine Ф
And recalling that cos Ф = √(1-sine2Ф), then
X=r(cos ϴ+l/r√{1-(r/l)2sin2ϴ}) (11.3)
The binomial theorem can be used to expand the square root term:
X=r{cos ϴ+l/r[1-1/2(r/l)2 sin2 ϴ -1/8(r/l)4 sin4 ϴ+…]} (11.4)
The power of sine ϴ can be expressed as equivalent multiple angles:
Sin2 ϴ =1/2 – 1/2 cos 2ϴ
Sin4 ϴ = 3/8-1/2 cos 2ϴ +1/8 cos 4ϴ (11.5)
Substituting the results from equation 11.5) into (11.4) gives
X=r{cos ϴ +1/r[1-1/2(r/l)2(1/2-1/2cos 2ϴ) -1/8(r/l)4 (3/8 -1/2 cos 2ϴ+1/8cos 4ϴ)+…]} (11.6)
The approximate position of the little end is thus:
x≈ r{cos ϴ+ l/r[1-1/2(r/l)2(1/2-1/2 cos 2ϴ]} (11.7)
Equation (11.7) can be differentiated once to give the piston velocity, and a second time to give the piston acceleration (in both cases the line of action is the cylinder axis):

14. Ẋ≈ rω(sin ϴ + ½ r/l sin 2ϴ) (11.8)
Ẍ≈ rω2(cos ϴ + r/l cos 2ϴ) (11.9)
This leads to an axial force
Fr ≈ mrω2 r(cos ϴ + r/l cos 2ϴ) (11.10)
Where fr = axial force due to the reciprocating mas
mr=equivalent reciprocating mass
ω= angular velocity, dϴ/dt
r = crankshaft throw
l = connecting rod length
cos ϴ = primary term
cos 2ϴ = secondary term.
In other words there is primary force in amplitude with crankshaft rotation and a secondary force varying at twice the crankshaft speed, these forces act along the cylinder axis. Referring to figure 11.5 for a four cylinder in line engine it can be seen that the primary forces will have no resultant force or moment.

15. By referring to figure 11.7, it can be seen that the primary forces for this four cylinder engine are 1800 out of phase and thus cancel. However, the secondary forces will be in phase, and this causes a resultant secondary force on the bearings. Since the resultant secondary force have the same magnitude and direction there is no secondary moment, but a resultant force of
4mrω2 r2/l cos 2ϴ
For multi cylinder engines in general, the phase relationship between cylinders will be more complex than the four cylinder in line engine. For cylinder n in a multi cylinder engine:
Fr,n ≈ mr,nω2r[cos(ϴ +an) + r/l cos (2ϴ+2an)] (11.12)
Where an is the phase separation between cylinder n and the reference cylinder.
It is then necessary to evaluate all the primary and secondary forces and moments, for all cylinders relatively to reference cylinder, to find the resultant forces and moments

16. There are five reasons to perform an engine balance.
a) Control peak combustion pressures – assuring safe operation within manufacturer’s specifications
b) Proportionately distribute the horsepower load across the power cylinders – minimizing unbalanced crankshaft torsion forces
c) Reduce misfires and cycle-to-cycle variability - minimizing fuel consumption
d) Minimize excessive stresses on engine components created by high peak
firing pressures and detonation – maximizing reliability and availability.
e) Control combustion temperatures – stabilizing exhaust emissions

17. The mechanical balance of a piston engine is one of the key considerations in choosing an engine configuration.
Analysis of reciprocating engine balance refer to primary balance and secondary balance.
Due to the presence of the number of reciprocating parts, like piston, connecting rod, etc. which move once in one direction and then in other direction, vibration develops during operation of the engine. Excessive vibration occurs if the engine is unbalanced. It is, therefore, necessary to balance the engine for its smooth running. The vibration may be caused due to design factors or may result from poor maintenance of the engine. In order to minimize the vibration, attention must be given to the following parameters:
(a) Primary balance (b) Component balance (c) Firing interval (d) Secondary balance.

18. Primary Balance
When a piston passes through TDC and BDC, the change of direction produces an inertia force due to which the piston tends to move in the direction in which it was moving before the change. This force, called the primary force, increases with the rise of the engine speed, and unless counteracted produces a severe oscillation in the vertical plane, i.e., in line with the Direction of primary force for single cylinder

19. Direction of primary force for single cylinder.
Single-cylinder. Figure 1 illustrates the primary inertia forces developed in a –single-cylinder cylinder engine. The diagram shows the direction and magnitude of the force for one revolution of the crankshaft, in which the upward direction has been considered as positive. Thus at TDC,the deceleration of the reciprocating masses (piston assembly and one-third of the connecting rod) produces an upward force on the engine.
At BDC a similar force is also generated but the direction of the force is downwards. The effect of these two forces is such that when the engine is running it oscillates up and down at a frequency equal to the engine speed, causing vibration. This vibration of the engine can be reduced by

20. adding counter-balance masses at A and B to exert an outward force with the rotation of the crankshaft.
Also by varying these two masses, the outward force can be made to equalize the inertia forces F1 and F2. It may be noted that in positions other than the dead centers the counter-balance masses themselves produce an out-of-balance force. This is un- desirable because it only shifts the plane of vibration from the vertical to the horizontal. There- fore, the counter-balance mass used on a single-cylinder engine is set to balance only half the reciprocating mass.
As a result, vibration in the vertical and horizontal planes is expected in a single cylinder engine. To withstand this vibration all nuts and bolts used on vehicles propelled by single- cylinder engines should be adequately locked.

21. The crankshaft throws are arranged so that forces acting on pistons
Four-cylinders
The crank throw layout on a four-cylinder in-line engine and the direction
of the primary forces are shown in Fig. 2. Primary balance is achieved in this arrangement,
because the forces on the two pistons at TDC equal the forces on the pistons at BDC.
The crankshaft throws are arranged so that forces acting on pistons
1 and 2 develop the opposite turning moment (couple) on the shaft axis to that produced by the
forces on pistons 3 and 4. The opposing couples introduced by this crankshaft layout prevent
the rocking action of the engine and consequently minimize fore and aft vibration of the engine.
Counter-balance masses are added to the crankshaft to reduce the bending action on the
crankshaft produced by the couples, and the high load on the center main bearing. Also, five
main bearings are used to support the crankshaft, instead of the three commonly used in the
past, so that a stiffer construction is obtained which is essential for the high-speed operations
of modern engines.
Primary forces for four cylinders.

22. Three-cylinders
Consideration of balancing of a three-cylinder in-line unit is useful
because it is used as a ‘straight’ in-line engine and also it forms the back unit for both the in-line six and V-six cylinder engines. Figure 2 illustrates the crankshaft layout and the primary forces when piston 1 is at TDC. In this case the crank throws are set at 120 degrees; therefore the large force at each of the dead centers is balanced by the two smaller forces on the other two pistons. These smaller forces are caused due to acceleration or deceleration of the piston as it approaches or leaves the end of the stroke.
Primary forces for three cylinders.

23. Component Balance
To minimize vibration, all components that rotate at high speeds must be balanced. This is specifically important for large heavy components such as a flywheel and clutch assembly. Even though these two parts are balanced individually within allowable limits, the mating of each part with the crankshaft axis is essential so that they ‘run true’
Ideally the balancing of both the crankshaft and flywheel assembly as one unit is desirable because it avoids the ‘build-up of tolerances’. Vibration occurs when ‘heavy spots’ of each part are positioned so that they all act in the same direction.
All parts that move in this manner should have nearly equal weight.
Balance of components should cover both static balance and dynamic balance. The static balance can be carried out by placing the shaft and/or component on two horizontal ‘knife-edges’, so that when released the heaviest part moves to the bottom. Dynamic balance requires expensive equipment, which rotates the part at high speed and indicates the extent and location of the heavy spots. Imbalance is normally corrected by removing metal by drilling one or more holes in the component at the heavy point.

24. Firing Interval
The angle turned by the crankshaft between power strokes of a multi-cylinder engine should be regular to achieve maximum smoothness. Also if the more cylinders are fired during the 720 degrees period of the four-stroke cycle, the lower is the variation in the output torque, and the smoother is the flow of power.

25. Secondary Balance
The inertia forces considered during the study of primary balance are based on a piston
movement, called simple harmonic motion (SHM). This type of reciprocating movement is
illustrated in Fig. 3A. Let a point P travels at a constant speed around a circle of diameter
AB, and another point N moves in a straight path from A to B. The point N is said to move in
simple harmonic motion if it always keeps at the foot of the perpendicular NP. The velocity of
point N varies as it travels across AB and this is represented by the graph (Fig. 3B).
When the movement of an engine piston is compared with SHM, it can be seen that during
the first 90 degrees rotation of the crank from TDC, the piston covers a greater distance and
within the range degrees it covers a smaller distance in the given time (Fig. 3C) This
causes the following situations:

26. (a) The piston travels more than half the stroke during movement of the crank from TDC to the 90 degrees position.
(b) Considering the piston initially at TDC, the relative piston velocity for each 90 degrees of crank movement is fast, slow, slow, and fast.
(c) The piston dwell, which is the angular period where piston movement is small in relation to crankshaft motion, at BDC is much greater than at TDC.
(d) The inertia force at TDC is much greater than at BDC.
This last point demands for the engine balance if vibration is to be reduced. The study of
engine balance requires the analysis of secondary balance, which involves the difference
between actual piston movement and the ideal SHM.

27. Figure 4 presents the primary force produced by SHM, and also the secondary force
required to be added or subtracted to correspond the actual motion. It is observed that the frequency of the secondary force is twice the speed of the crankshaft.The information provided by this graph can be used to obtain the direction of the secondary force and this has been added to the diagram of the engine 'shown in Fig. 4 The result indicates a four-cylinder in-line engine has very good primary balance but has poor secondary balance. This imbalance produces a vibration in the vertical plane at a frequency twice the speed of the crankshaft. In the past this vibration has been tolerated and soft rubber engine mountings have been used to prevent transmission of the engine vibration to the remainder of the vehicle.
Direction of primary and secondary forces.

28. In the three- and six-cylinder in-line units, and V-six, the secondary forces balance out, and this is one reason why the six-cylinder in-line engine was used extensively in the past. Nowadays four-cylinder in-line units for engines up to about 2 liters capacity are preferred, because of promising economy resulting from lower frictional losses. When it is combined with the use of simpler engine management systems, a higher power to weight ratio can be obtained. In addition, the short and stubby crankshaft used on a four-cylinder unit does not produce severe torsional vibration problems associated with longer shafts.

29. Questions 1. What is meant by engine balance?
2. What are the classification of engine according to the piston
arrangement?
3. What are the different parameters in engine vibration?
4. What are the two main causes of engine vibration?
5. With the help of a sketch explain the primary balance in one cylinder engine.
6. With the help of a sketch explain the primary balance of 4 cylinder
engine.
7. Explain how the crankshaft and the flywheel are balanced
With the help of a sketch of 4 cylinder engine explain the direction of primary and secondary forces.