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Questions and Answers
What is the main reason for balancing rotating and reciprocating parts in machines?
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?
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?
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?
How is the process of balancing rotating masses achieved?
What is the purpose of balancing a single rotating mass by another mass in the same plane?
What is the purpose of balancing a single rotating mass by another mass in the same plane?
Why is it essential to balance rotating parts in high-speed machines?
Why is it essential to balance rotating parts in high-speed machines?
To balance the system of masses rotating in the same plane, what condition must be satisfied?
To balance the system of masses rotating in the same plane, what condition must be satisfied?
In the context of balancing multiple masses, what does tanθ represent?
In the context of balancing multiple masses, what does tanθ represent?
What is a graphical method used for in balancing rotating masses?
What is a graphical method used for in balancing rotating masses?
What does resolving centrifugal forces horizontally and vertically help in determining?
What does resolving centrifugal forces horizontally and vertically help in determining?
In balancing multiple masses, what is the role of the balancing mass?
In balancing multiple masses, what is the role of the balancing mass?
What condition signifies static balance in a rotating mass system?
What condition signifies static balance in a rotating mass system?
What is the key factor ensuring that a shaft remains in equilibrium in a rotating mass system?
What is the key factor ensuring that a shaft remains in equilibrium in a rotating mass system?
What is the purpose of taking moments about specific points in a rotating mass system?
What is the purpose of taking moments about specific points in a rotating mass system?
In a rotating mass system, what does 'l1' represent?
In a rotating mass system, what does 'l1' represent?
What does equation (i) represent in balancing a rotating mass system?
What does equation (i) represent in balancing a rotating mass system?
What is the main purpose of introducing balancing masses in the same plane of rotation as the disturbing mass?
What is the main purpose of introducing balancing masses in the same plane of rotation as the disturbing mass?
In dynamic balancing, what condition must be satisfied for the net dynamic force acting on the shaft to be zero?
In dynamic balancing, what condition must be satisfied for the net dynamic force acting on the shaft to be zero?
What is the significant drawback of using a single balancing mass in the same plane as the disturbing mass?
What is the significant drawback of using a single balancing mass in the same plane as the disturbing mass?
In which type of balancing are two balancing masses placed in different planes parallel to the disturbing mass?
In which type of balancing are two balancing masses placed in different planes parallel to the disturbing mass?
What is necessary for static balancing to be achieved in a system?
What is necessary for static balancing to be achieved in a system?
What happens if the plane of the disturbing mass lies in between the planes of two balancing masses?
What happens if the plane of the disturbing mass lies in between the planes of two balancing masses?
What could be a potential consequence of introducing only one balancing mass in the same plane as that of the disturbing mass?
What could be a potential consequence of introducing only one balancing mass in the same plane as that of the disturbing mass?
What is necessary for dynamic balancing to be achieved in a system?
What is necessary for dynamic balancing to be achieved in a system?
In which case does a single disturbing mass need to be balanced by two balancing masses?
In which case does a single disturbing mass need to be balanced by two balancing masses?
What condition is required for static and dynamic balancing to be achieved?
What condition is required for static and dynamic balancing to be achieved?
In the context of balancing reciprocating masses, the unbalanced force is also known as:
In the context of balancing reciprocating masses, the unbalanced force is also known as:
What is the purpose of balancing reciprocating masses in an engine?
What is the purpose of balancing reciprocating masses in an engine?
What is the magnitude of the balancing mass (m) required to balance reciprocating masses?
What is the magnitude of the balancing mass (m) required to balance reciprocating masses?
What represents the resultant force in magnitude and direction according to the polygon law of forces?
What represents the resultant force in magnitude and direction according to the polygon law of forces?
In balancing reciprocating masses, which term describes the force required to accelerate the reciprocating parts?
In balancing reciprocating masses, which term describes the force required to accelerate the reciprocating parts?
What does the horizontal component of $FB$ (i.e., $FBH$) balance according to the text?
What does the horizontal component of $FB$ (i.e., $FBH$) balance according to the text?
How do reciprocating masses affect engine operation?
How do reciprocating masses affect engine operation?
What is the effect of reciprocating parts on engine operation?
What is the effect of reciprocating parts on engine operation?
What term describes the force acting on the crankshaft bearing or main bearing in an engine mechanism?
What term describes the force acting on the crankshaft bearing or main bearing in an engine mechanism?
'$m$', representing the balancing mass, should be equal to which calculated value to achieve balance?
'$m$', representing the balancing mass, should be equal to which calculated value to achieve balance?
What is the purpose of balancing the reciprocating masses in the mechanism described?
What is the purpose of balancing the reciprocating masses in the mechanism described?
Which force is denoted as FU in the text?
Which force is denoted as FU in the text?
In a reciprocating engine, what is considered equivalent to balancing the primary unbalanced force?
In a reciprocating engine, what is considered equivalent to balancing the primary unbalanced force?
What is the maximum value of the vertical component of the centrifugal force in a reciprocating engine?
What is the maximum value of the vertical component of the centrifugal force in a reciprocating engine?
What is the positioning difference between inside cylinder locomotives and outside cylinder locomotives?
What is the positioning difference between inside cylinder locomotives and outside cylinder locomotives?
When is the primary unbalanced force completely balanced in a reciprocating engine?
When is the primary unbalanced force completely balanced in a reciprocating engine?
What is the purpose of having cranks placed at right angles to each other in locomotives?
What is the purpose of having cranks placed at right angles to each other in locomotives?
Which locomotive type transmits effort to only one pair of wheels?
Which locomotive type transmits effort to only one pair of wheels?
What is the ratio 'n' defined as in the text regarding reciprocating engines?
What is the ratio 'n' defined as in the text regarding reciprocating engines?
What are the two types of locomotives classified based on cylinder placement?
What are the two types of locomotives classified based on cylinder placement?
What is the effect of an unbalanced primary force along the line of stroke?
What is the effect of an unbalanced primary force along the line of stroke?
What is the maximum magnitude of the unbalanced force perpendicular to the line of stroke known as?
What is the maximum magnitude of the unbalanced force perpendicular to the line of stroke known as?
What is the resultant unbalanced force due to the two cylinders along the line of stroke known as?
What is the resultant unbalanced force due to the two cylinders along the line of stroke known as?
When is the tractive force maximum or minimum?
When is the tractive force maximum or minimum?
In multi-cylinder in-line engines, what must be equal to zero for primary balance of reciprocating parts?
In multi-cylinder in-line engines, what must be equal to zero for primary balance of reciprocating parts?
How can the primary unbalanced force due to reciprocating masses be balanced in multi-cylinder engines?
How can the primary unbalanced force due to reciprocating masses be balanced in multi-cylinder engines?
What is the imaginary crank length for secondary forces in multi-cylinder in-line engines?
What is the imaginary crank length for secondary forces in multi-cylinder in-line engines?
What angle is each imaginary secondary crank inclined to the line of stroke in multi-cylinder engines?
What angle is each imaginary secondary crank inclined to the line of stroke in multi-cylinder engines?
In multi-cylinder engines, what is considered equivalent to the secondary disturbing force due to reciprocating mass?
In multi-cylinder engines, what is considered equivalent to the secondary disturbing force due to reciprocating mass?
What must be equal to zero for balancing secondary forces in multi-cylinder in-line engines?
What must be equal to zero for balancing secondary forces in multi-cylinder in-line engines?
What must be satisfied to give a complete secondary balance of an engine?
What must be satisfied to give a complete secondary balance of an engine?
What is the direct crank OC?
What is the direct crank OC?
What is the reverse crank OC'?
What is the reverse crank OC'?
What does replacing the mass (m) of reciprocating parts with two masses (each m/2) at C and C' do?
What does replacing the mass (m) of reciprocating parts with two masses (each m/2) at C and C' do?
How do the secondary direct and reverse cranks OD and OD' rotate?
How do the secondary direct and reverse cranks OD and OD' rotate?
What is OD = OD' equal to when considering secondary effects?
What is OD = OD' equal to when considering secondary effects?
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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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