Balancing of Rotating Masses Quiz and Flashcards

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Questions and Answers

What is the main reason for balancing rotating and reciprocating parts in machines?

To cause dangerous vibrations

To increase the loads on bearings

To minimize dynamic forces (correct)

To reduce stress in various members

Why do improperly balanced rotating parts lead to unpleasant vibrations?

They minimize stress in various members

They set up dynamic forces (correct)

They increase the efficiency of the machine

They reduce the loads on bearings

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 (correct)

To bend the shaft even more

To increase loads on bearings

To double the vibrations

How is the process of balancing rotating masses achieved?

By making the centrifugal force of both masses equal and opposite Signup and view all the answers

What is the purpose of balancing a single rotating mass by another mass in the same plane?

To minimize pressure on main bearings Signup and view all the answers

Why is it essential to balance rotating parts in high-speed machines?

To minimize dynamic forces and dangerous vibrations Signup and view all the answers

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 Signup and view all the answers

In the context of balancing multiple masses, what does tanθ represent?

Resultant centrifugal force Signup and view all the answers

What is a graphical method used for in balancing rotating masses?

To determine the magnitude and position of the balancing mass Signup and view all the answers

What does resolving centrifugal forces horizontally and vertically help in determining?

The magnitude of the resulting force Signup and view all the answers

In balancing multiple masses, what is the role of the balancing mass?

It balances out the resultant centrifugal force Signup and view all the answers

What condition signifies static balance in a rotating mass system?

The plane of the disturbing mass lies on one end of other planes Signup and view all the answers

What is the key factor ensuring that a shaft remains in equilibrium in a rotating mass system?

Centrifugal forces on all masses are equal Signup and view all the answers

What is the purpose of taking moments about specific points in a rotating mass system?

To determine dynamic forces at bearing points Signup and view all the answers

In a rotating mass system, what does 'l1' represent?

Distance between planes A and L Signup and view all the answers

What does equation (i) represent in balancing a rotating mass system?

Condition for static balance Signup and view all the answers

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 Signup and view all the answers

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 Signup and view all the answers

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 Signup and view all the answers

In which type of balancing are two balancing masses placed in different planes parallel to the disturbing mass?

Dynamic balancing Signup and view all the answers

What is necessary for static balancing to be achieved in a system?

The centre of masses must not lie on the axis of rotation Signup and view all the answers

What happens if the plane of the disturbing mass lies in between the planes of two balancing masses?

The system achieves perfect balance Signup and view all the answers

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 Signup and view all the answers

What is necessary for dynamic balancing to be achieved in a system?

The algebraic sum of moments about any point must not be zero Signup and view all the answers

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 Signup and view all the answers

What condition is required for static and dynamic balancing to be achieved?

The algebraic sum of moments about any point must be zero Signup and view all the answers

In the context of balancing reciprocating masses, the unbalanced force is also known as:

Shaking force Signup and view all the answers

What is the purpose of balancing reciprocating masses in an engine?

To eliminate shaking force and couple Signup and view all the answers

What is the magnitude of the balancing mass (m) required to balance reciprocating masses?

$40$ kg-m Signup and view all the answers

What represents the resultant force in magnitude and direction according to the polygon law of forces?

The closing side Signup and view all the answers

In balancing reciprocating masses, which term describes the force required to accelerate the reciprocating parts?

$FR$ Signup and view all the answers

What does the horizontal component of $FB$ (i.e., $FBH$) balance according to the text?

$FI$ Signup and view all the answers

How do reciprocating masses affect engine operation?

By creating shaking forces Signup and view all the answers

What is the effect of reciprocating parts on engine operation?

Generation of shaking force and couple Signup and view all the answers

What term describes the force acting on the crankshaft bearing or main bearing in an engine mechanism?

$FBH$ Signup and view all the answers

'$m$', representing the balancing mass, should be equal to which calculated value to achieve balance?

$40$ kg-m Signup and view all the answers

What is the purpose of balancing the reciprocating masses in the mechanism described?

To eliminate the shaking force and shaking couple Signup and view all the answers

Which force is denoted as FU in the text?

Reciprocating force Signup and view all the answers

In a reciprocating engine, what is considered equivalent to balancing the primary unbalanced force?

Balancing an external mass at radius b Signup and view all the answers

What is the maximum value of the vertical component of the centrifugal force in a reciprocating engine?

$B \cdot 2 \cdot b \sin(\theta)$ Signup and view all the answers

What is the positioning difference between inside cylinder locomotives and outside cylinder locomotives?

Location relative to driving wheels Signup and view all the answers

When is the primary unbalanced force completely balanced in a reciprocating engine?

$B \cdot b = m \cdot r$ Signup and view all the answers

What is the purpose of having cranks placed at right angles to each other in locomotives?

To provide uniformity in turning moment diagram Signup and view all the answers

Which locomotive type transmits effort to only one pair of wheels?

Single locomotive Signup and view all the answers

What is the ratio 'n' defined as in the text regarding reciprocating engines?

l / r Signup and view all the answers

What are the two types of locomotives classified based on cylinder placement?

Inside and outside cylinder locomotives Signup and view all the answers

What is the effect of an unbalanced primary force along the line of stroke?

Production of a swaying couple Signup and view all the answers

What is the maximum magnitude of the unbalanced force perpendicular to the line of stroke known as?

Hammer blow Signup and view all the answers

What is the resultant unbalanced force due to the two cylinders along the line of stroke known as?

Tractive force Signup and view all the answers

When is the tractive force maximum or minimum?

$135°$ or $315°$ Signup and view all the answers

In multi-cylinder in-line engines, what must be equal to zero for primary balance of reciprocating parts?

Primary forces polygon must close Signup and view all the answers

How can the primary unbalanced force due to reciprocating masses be balanced in multi-cylinder engines?

By transferring reciprocating masses to their crank pins Signup and view all the answers

What is the imaginary crank length for secondary forces in multi-cylinder in-line engines?

$r / 4n$ Signup and view all the answers

What angle is each imaginary secondary crank inclined to the line of stroke in multi-cylinder engines?

$2θ$ Signup and view all the answers

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 Signup and view all the answers

What must be equal to zero for balancing secondary forces in multi-cylinder in-line engines?

Secondary disturbing forces polygon must close Signup and view all the answers

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 Signup and view all the answers

What is the direct crank OC?

The crank that rotates uniformly at radians per second in a clockwise direction Signup and view all the answers

What is the reverse crank OC'?

The image of the direct crank when seen through a mirror placed at the line of stroke Signup and view all the answers

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 Signup and view all the answers

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 Signup and view all the answers

What is OD = OD' equal to when considering secondary effects?

$r/4n$ Signup and view all the answers

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.

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Description

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.

Balancing of Rotating Masses

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