62 Questions
What is the main reason for balancing rotating and reciprocating parts in machines?
To minimize dynamic forces
Why do improperly balanced rotating parts lead to unpleasant vibrations?
They set up dynamic forces
What is the purpose of attaching a second mass to counteract the centrifugal force of the first mass on a rotating shaft?
To balance and prevent vibrations
How is the process of balancing rotating masses achieved?
By making the centrifugal force of both masses equal and opposite
What is the purpose of balancing a single rotating mass by another mass in the same plane?
To minimize pressure on main bearings
Why is it essential to balance rotating parts in high-speed machines?
To minimize dynamic forces and dangerous vibrations
To balance the system of masses rotating in the same plane, what condition must be satisfied?
Sum of horizontal components of the centrifugal forces must equal sum of vertical components
In the context of balancing multiple masses, what does tanθ represent?
Resultant centrifugal force
What is a graphical method used for in balancing rotating masses?
To determine the magnitude and position of the balancing mass
What does resolving centrifugal forces horizontally and vertically help in determining?
The magnitude of the resulting force
In balancing multiple masses, what is the role of the balancing mass?
It balances out the resultant centrifugal force
What condition signifies static balance in a rotating mass system?
The plane of the disturbing mass lies on one end of other planes
What is the key factor ensuring that a shaft remains in equilibrium in a rotating mass system?
Centrifugal forces on all masses are equal
What is the purpose of taking moments about specific points in a rotating mass system?
To determine dynamic forces at bearing points
In a rotating mass system, what does 'l1' represent?
Distance between planes A and L
What does equation (i) represent in balancing a rotating mass system?
Condition for static balance
What is the main purpose of introducing balancing masses in the same plane of rotation as the disturbing mass?
To decrease the bending moment on the shaft
In dynamic balancing, what condition must be satisfied for the net dynamic force acting on the shaft to be zero?
The line of action of three centrifugal forces must be the same
What is the significant drawback of using a single balancing mass in the same plane as the disturbing mass?
It produces a net dynamic force on the shaft
In which type of balancing are two balancing masses placed in different planes parallel to the disturbing mass?
Dynamic balancing
What is necessary for static balancing to be achieved in a system?
The centre of masses must not lie on the axis of rotation
What happens if the plane of the disturbing mass lies in between the planes of two balancing masses?
The system achieves perfect balance
What could be a potential consequence of introducing only one balancing mass in the same plane as that of the disturbing mass?
A couple that rocks the shaft is generated
What is necessary for dynamic balancing to be achieved in a system?
The algebraic sum of moments about any point must not be zero
In which case does a single disturbing mass need to be balanced by two balancing masses?
When a couple that rocks the shaft is generated
What condition is required for static and dynamic balancing to be achieved?
The algebraic sum of moments about any point must be zero
In the context of balancing reciprocating masses, the unbalanced force is also known as:
Shaking force
What is the purpose of balancing reciprocating masses in an engine?
To eliminate shaking force and couple
What is the magnitude of the balancing mass (m) required to balance reciprocating masses?
$40$ kg-m
What represents the resultant force in magnitude and direction according to the polygon law of forces?
The closing side
In balancing reciprocating masses, which term describes the force required to accelerate the reciprocating parts?
$FR$
What does the horizontal component of $FB$ (i.e., $FBH$) balance according to the text?
$FI$
How do reciprocating masses affect engine operation?
By creating shaking forces
What is the effect of reciprocating parts on engine operation?
Generation of shaking force and couple
What term describes the force acting on the crankshaft bearing or main bearing in an engine mechanism?
$FBH$
'$m$', representing the balancing mass, should be equal to which calculated value to achieve balance?
$40$ kg-m
What is the purpose of balancing the reciprocating masses in the mechanism described?
To eliminate the shaking force and shaking couple
Which force is denoted as FU in the text?
Reciprocating force
In a reciprocating engine, what is considered equivalent to balancing the primary unbalanced force?
Balancing an external mass at radius b
What is the maximum value of the vertical component of the centrifugal force in a reciprocating engine?
$B \cdot 2 \cdot b \sin(\theta)$
What is the positioning difference between inside cylinder locomotives and outside cylinder locomotives?
Location relative to driving wheels
When is the primary unbalanced force completely balanced in a reciprocating engine?
$B \cdot b = m \cdot r$
What is the purpose of having cranks placed at right angles to each other in locomotives?
To provide uniformity in turning moment diagram
Which locomotive type transmits effort to only one pair of wheels?
Single locomotive
What is the ratio 'n' defined as in the text regarding reciprocating engines?
l / r
What are the two types of locomotives classified based on cylinder placement?
Inside and outside cylinder locomotives
What is the effect of an unbalanced primary force along the line of stroke?
Production of a swaying couple
What is the maximum magnitude of the unbalanced force perpendicular to the line of stroke known as?
Hammer blow
What is the resultant unbalanced force due to the two cylinders along the line of stroke known as?
Tractive force
When is the tractive force maximum or minimum?
$135°$ or $315°$
In multi-cylinder in-line engines, what must be equal to zero for primary balance of reciprocating parts?
Primary forces polygon must close
How can the primary unbalanced force due to reciprocating masses be balanced in multi-cylinder engines?
By transferring reciprocating masses to their crank pins
What is the imaginary crank length for secondary forces in multi-cylinder in-line engines?
$r / 4n$
What angle is each imaginary secondary crank inclined to the line of stroke in multi-cylinder engines?
$2θ$
In multi-cylinder engines, what is considered equivalent to the secondary disturbing force due to reciprocating mass?
Centrifugal force produced by equal mass at crankpin
What must be equal to zero for balancing secondary forces in multi-cylinder in-line engines?
Secondary disturbing forces polygon must close
What must be satisfied to give a complete secondary balance of an engine?
The algebraic sum of the secondary forces must be equal to zero and The algebraic sum of the couples about any point in the plane of the secondary forces must be equal to zero
What is the direct crank OC?
The crank that rotates uniformly at radians per second in a clockwise direction
What is the reverse crank OC'?
The image of the direct crank when seen through a mirror placed at the line of stroke
What does replacing the mass (m) of reciprocating parts with two masses (each m/2) at C and C' do?
Balances the primary forces due to mass (m) at P
How do the secondary direct and reverse cranks OD and OD' rotate?
OD rotates at 2p rad/s clockwise, OD' rotates at 2p rad/s anticlockwise
What is OD = OD' equal to when considering secondary effects?
$r/4n$
Study Notes
Balancing of Reciprocating Masses
- The purpose of balancing the reciprocating masses is to eliminate the shaking force and a shaking couple.
- The shaking force and a shaking couple vary in magnitude and direction during the engine cycle, causing vibrations.
- The reciprocating masses are only partially balanced in most mechanisms.
Primary and Secondary Unbalanced Forces of Reciprocating Masses
- The primary unbalanced force may be considered as the component of the centrifugal force produced by a rotating mass m placed at the crank radius r.
- The primary force acts from O to P along the line of stroke.
- Balancing of primary force is considered as equivalent to the balancing of mass m rotating at the crank radius r.
Partial Balancing of Unbalanced Primary Force in a Reciprocating Engine
- A mass B is placed diametrically opposite to the crank pin C to balance the primary force.
- The centrifugal force due to mass B has a horizontal component that acts in the opposite direction of the primary force.
- The primary force is completely balanced if B·b = m·r, but the centrifugal force produced due to the revolving mass B has a vertical component that remains unbalanced.
Balancing of Locomotives
- Locomotives have two cylinders with cranks placed at right angles to each other to have uniformity in turning moment diagram.
- The two cylinders are classified as inside cylinder locomotives and outside cylinder locomotives.
- The locomotives may be single or uncoupled, or coupled.
Balancing of a Single Rotating Mass by a Single Mass Rotating in the Same Plane
- A disturbing mass m1 is attached to a shaft rotating at rad/s.
- A balancing mass m2 is attached in the same plane of rotation as that of disturbing mass m1, such that the centrifugal forces due to the two masses are equal and opposite.
Balancing of a Single Rotating Mass by Two Masses Rotating in Different Planes
- Two balancing masses m1 and m2 are placed in two different planes, parallel to the plane of rotation of the disturbing mass m.
- The net dynamic force acting on the shaft is equal to zero, and the net couple due to the dynamic forces acting on the shaft is also equal to zero.
Balancing of Several Masses Rotating in the Same Plane
- The magnitude and position of the balancing mass can be found out analytically or graphically.
- The centrifugal forces exerted by each mass on the rotating shaft are resolved horizontally and vertically, and their sums are found.
- The balancing force is equal to the resultant force, but in the opposite direction.### Partial Balancing of Reciprocating Parts of Two Cylinder Locomotives
- Partial balancing of reciprocating parts results in unbalanced primary force along the line of stroke and perpendicular to the line of stroke.
- Unbalanced primary force along the line of stroke causes:
- Variation in interactive force along the line of stroke
- Swaying couple
- Unbalanced primary force perpendicular to the line of stroke causes:
- Variation in pressure on the rails
- Hammering action on the rails
- Hammer blow (maximum magnitude of unbalanced force)
Variation of Tractive Force
- Tractive force is the resultant unbalanced force due to the two cylinders, along the line of stroke.
- Unbalanced force along the line of stroke for cylinder 1 = 2(1- c)m.2.r cos
- Unbalanced force along the line of stroke for cylinder 2 = (1- c)m.2r cos(90° +)
- Tractive force, FT = (1- c)m.2.r(cos - sin)
- Tractive force is maximum or minimum when = 135° or 315°
Balancing of Primary Forces of Multi-cylinder In-line Engines
- A multi-cylinder engine with cylinder centrelines in the same plane and on the same side of the crankshaft centreline is known as an In-line engine.
- Two conditions must be satisfied for primary balance of reciprocating parts of a multi-cylinder engine:
- Algebraic sum of primary forces must be equal to zero (primary force polygon must close)
- Algebraic sum of couples about any point in the plane of primary forces must be equal to zero (primary couple polygon must close)
Balancing of Secondary Forces of Multi-cylinder In-line Engines
- Secondary disturbing force due to reciprocating mass arises when the connecting rod is not too long.
- Secondary forces can be considered equivalent to the component, parallel to the line of stroke, of the centrifugal force produced by an equal mass placed at the imaginary crank of length r / 4n and revolving at twice the speed of the actual crank (i.e. 2).
- Each imaginary secondary crank with a mass attached to the crankpin is inclined to the line of stroke at twice the angle of the actual crank.
Explore the importance of balancing rotating and reciprocating parts to prevent dynamic forces, increased loads, stresses, and vibrations. This chapter discusses techniques for achieving balance in machines and engines.
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