*BALANCING AND UNBALANCING CLASS NOTES FOR MECHANICAL ENGINEERING

 

BALANCING AND UNBALANCING

 CLASS NOTES FOR MECHANICAL

ENGINEERING

FORCES

  • There are many different forces like
  • (i) contact force
  • (ii) gravity force
  • (iii)inertia force
  • (iv) wind force
  • (v) fluid pressure force
  • (vi) static force
  • (vii) thermal force
  • (viii) centrifugal
  • (ix) frictional force
  • (x) pushing force
  • (xi) pulling force
  • (xii) seismic force
  • (xiii) snow force
  • (xiv) normal force
  • (xv) tangential force

 

Without a force no action like dancing, cycling, playing sports. Even a stationary object is under the action of its weight.
  1. The unit of force is Newton (N).
  2. Firstly 1 Newton = accelerating an object of mass of 1 kg  at 1 m/s2
  3. Secondly 1 pound force =4.448 N
  4. 1 kg force= 9.81 N
  5. A force has both magnitude and direction and hence is a vector quantity like velocity/acceleration/displacement.
  6.  A line of certain length and an arrow placed at one end represents a vector. The length of the line represents the magnitude of the force and the  arrow used to show the direction. 

FUNCTIONS OF A FORCE

  1.  Makes a stationary body to move
  2.  Accelerate a moving body
  3.  Retard a moving body
  4.  Stop motion
  5.  Change direction
  6.  Cause deformation
  7.  Remove deformation
  8. All or any one or two forces which act on objects.
  9. When forces act in pairs, either balanced or unbalanced.

BALANCED FORCE

  1. Balanced forces do not cause change in position or deformation or motion.
  2. They are equal in magnitude and opposite in direction and there is no net force.

UNBALANCED FORCE

  1. An unbalanced force always causes a change in motion or position or deformation.
  2. Find the net force when unbalanced force act in opposite directions.
Net force magnitude  is the vector difference between the two forces.
  1. Direction of the net force will be the direction of the largest force.
  2. Under balanced forces, the object doesn’t move.
  3. Under unbalanced force, the object acts in one of  the following ways:
  4.  Begin to move
  5.  Stop moving
  6.  Changes direction
  7.  Speeds up
  8.   Slows down

FUNCTIONS OF THE UNBALANCED FORCE

Under unbalanced force, the object acts in one of the following ways:
  1. Begins to move

  2. Stop moving

  3. Change direction

  4. Speeds up

  5. Decreases Speed

CAUSES OF UNBALANCING

Unbalancing causes by the followings:

  1. Eccentric rotating masses
  2. Eccentric reciprocating masses
Eccentricity causes the followings:
  1. additional stresses in the body and the material will fail at a lower load
  2. Causes unwanted vibrations

GRAPHICAL DEFINITION OF UNBALANCING

Unbalancing is due to non coinciding of mass axis (inertia axis) and axis of rotation. The perpendicular  distance between the two axes if parallel is eccentricity.

TYPES OF UNBALANCING

  • Static Unbalance
  • Static unbalancing is due to mass axis (inertia axis) and axis of rotation do not coincide. These axes are parallel and at some distance from each other.
  • Couple unbalance
  • Couple unbalancing is due to mass axis (inertia axis) and axis of rotation do not coincide. These axes intersect at the center of gravity of the rotor
  • Dynamic unbalance
  • Dynamic unbalancing is due to mass axis (inertia axis) and axis of rotation do not coincide. These axes intersect somewhere but not at the center of gravity of the rotor. These are neither parallel nor intersecting.
         Dynamic unbalancing has the combined effect of static and couple unbalances.

Undesirable Effects of Unbalancing

  1. Causes vibration
  2. Produces noise
  3.  Decreases machine life
  4. Reduces bearings life.
  5. Creates unsafe working environment
  6. Causes increase in wear and tear
  7.  Increase in repair and maintenance
  8. Does undesirable psychological effects
SYMBOL USED FOR UNBALANCING—————U
MAGNITUDE OF UNBALANCING
U =m r                g mm
UNITS OF UNBALANCING——— g mm
UNBALANCING OF ROTORS
BALANCE QUALITY
OR

BALANCE TOLERANCE

OR

HOW MUCH OF AN UNBALANCE IS ACCEPTABLE

 ANSI (AMERICAN NATIONAL STANDARDS INSTITUTE) gives the answer to the above question.
Standard for Balance Quality of Rotating Rigid Bodies is ANSI S 2.19-1975. These standards make recommendations to the permissible residual unbalance.  These are function of the maximum service speed of a particular rotor.
ANSI standards assigns balance quality “grades” to different rotors of
(i) various types
(ii) sizes
(iii)service speeds.
All these are based on experimental and experience based data. Various sources provide such data.

BALANCING

SYMBOL USED FOR BALANCE QUALITY—-G

MAGNITUDE OF BALANCE QUALITY

Balance quality “G”
Equal to the product of the permissible residual specific unbalance ‘e’( eper) & rotational speed (ω) of the rotor.
G =eper x ω = Constant
where
eper = permissible residual specific unbalance per unit mass  = e
ω = angular velocity
This constant G is a balance quality grade. Use Balance Grades to specify the allowable residual unbalance for rotating machinery. The ISO 1940 standard defines balance grades for different classes of machinery. A rotor named as G 4.2 will vibrate at 4.2 mm/s.
G = e x ω mm/s
UNITS OF MAGNITUDE OF BALANCE QUALITY —-mm/s
Specific unbalance is unbalance per unit mass of the rotor
e = U/ M
where “U” is in g mm and “M” is in g.
By substitution, we get
G = (U / M) x ω
On substitution, G = U ( 2 x π x RPM )/ (60 M)
On simplification, we get unbalance
U = 9.54 x M x G
Methods of Removing/decreasing  unbalancing
 Achieve it by
  1.  Adding mass
  2.  Removing mass
  3. By changing the position of mass

BALANCING MACHINE

A balance machine help to correct the unbalance. Measures the existing vibration and gives the corrected method to apply.
Important Formulas
F = U x ω²
e = U /m
Where F = Force due to Unbalance
U = Unbalance
ω = Angular Frequency
e = Eccentricity
m = mass

 Methods of  correcting unbalance

(a) Mass removal
(b) Mass addition
(c) Mass shifting
(d) Mass centering
There are balancing machines to measure the vibrations (unbalance) and suggest the way to remove the unbalance.
BALANCING
Balancing means
  1. Firstly eliminate partially or completely the resultant unbalanced forces to reduce vibrations.
  2. Secondly eliminate partially or completely the resultant unbalanced couples to reduce vibration
  3. Thirdly eliminate partially or completely the resultant unbalanced forces and couples to reduce vibrations.
  •  Principle of Rigid Rotor Balancing
  1. Method of Static Balancing
  2. (i)Single plane balancing
  3. Balancing by a single mass in the same plane of unbalancing. Limited accuracy because of only one plane balancing.
  4. (ii) Method of Dynamic balancing—-Two plane balancing–Two balancing masses in different planes
Balancing of Practical Rigid Rotor
    1.  Two Plane  balancing (by Cradle Machine Method) only for the rigid rotors having no deflection and no deformation
    2.  Multi-plane balancing for the flexible rotors having deflection or deformation or both