Table of Contents

What is Vibration

When elastic bodies such as a spring, a beam, and a shaft are displaced from the equilibrium position by the application of external forces, and then released, they execute a vibratory motion.
This is due to the reason that, when a body is displaced, the internal forces in the form of elastic or strain energy are present in the body. At release, these forces bring the body to its original position.
When the body reaches the equilibrium position, the whole of the elastic or strain energy is converted into kinetic energy due to which the body continues to move in the opposite direction.
The whole of the kinetic energy is again converted into strain energy due to which the body again returns to the equilibrium position.
In this way, the vibratory motion is repeated indefinitely.

Any motion that repeats itself after an interval of time is called vibration or oscillation. The swinging of a pendulum (Fig.) and the motion of a plucked string are typical examples of vibration. The theory of vibration deals with the study of the oscillatory motion of bodies and forces associated with them.

Elementary Parts of Vibrating system

A means of storing potential energy (Spring or elasticity)
A means of storing kinetic energy (Mass or inertia)
A means by which energy is gradually lost (damper)

The forces acting on the systems are

Disturbing forces
Restoring force
Inertia force
Damping force

Degree of Freedom: The minimum number of independent coordinates required to determine completely the position of all parts of a system at any instant of time defines the degree of freedom of the system. A system with a finite number of degrees of freedom is called a discrete or lumped parameter system, and those with an infinite number of degrees of freedom are called continuous or distributed systems.

The terminology of Vibration :

The following terms are commonly used in connection with the vibratory motions:

(i) Period of vibration or time period: It is the time interval after which the motion is repeating itself. The period of vibration is usually expressed in seconds.
(ii) Cycle: It is the motion completed during a one-time period.
(iii) Frequency: It is the number of cycles described in one second. In S.I. units, the frequency is expressed in hertz (briefly written as Hz) which is equal to one cycle per second.

Types of Vibratory Motion :

(i) Free or natural vibrations:

When no external force acts on the body, after giving it an initial displacement, then the body is said to be under free or natural vibrations. The frequency of the free vibrations is called free or natural frequency.

(ii) Forced vibrations:

When the body vibrates under the influence of external force, then the body is said to be under forced vibrations. The external force applied to the body is a periodic disturbing force created by unbalance. The vibrations have the same frequency as the applied force.
Note: When the frequency of the external force is the same as that of the natural vibrations, resonance takes place.

(iii) Damped vibrations:

When there is a reduction in amplitude over every cycle of vibration, the motion is said to be damped vibration. This is due to the fact that a certain amount of energy possessed by the vibrating system is always dissipated in overcoming frictional resistances to the motion.

Types of Free Vibrations

The following three types of free vibrations are important from the subject point of view:

1. Longitudinal vibrations,

2. Transverse vibrations, and

3. Torsional vibrations.

Consider a weightless constraint (spring or shaft) whose one end is fixed and the other end carrying a heavy disc, as shown in Fig. This system may execute one of the three above mentioned types of vibrations.

(i) Longitudinal vibrations:

When the particles of the shaft or disc move parallel to the axis of the shaft, as shown in Fig. (a), then the vibrations are known as longitudinal vibrations. In this case, the shaft is elongated and shortened alternately and thus the tensile and compressive stresses are induced alternately in the shaft.

(ii) Transverse vibrations:

When the particles of the shaft or disc move approximately perpendicular to the axis of the shaft, as shown in Fig. (b), then the vibrations are known as transverse vibrations. In this case, the shaft is straight and bent alternately, and bending stresses are induced in the shaft.

(iii) Torsional vibrations:

When the particles of the shaft or disc move in a circle about the axis of the shaft, as shown in Fig. (c), then the vibrations are known as torsional vibrations. In this case, the shaft is twisted and untwisted alternately and the torsional shear stresses are induced in the shaft.

Causes of Vibration in Machines

There are various sources of vibration in an industrial environment :
(a) Impact processes such as pile driving and blasting.
(b) Rotating or reciprocating machineries such as engines, compressors, and motors.
(c) Transportation vehicles such as trucks, trains, and aircraft.
(d) The flow of fluids through pipes and without pipes.
(e) Natural calamities such as earthquakes.

Effects of Vibration :

There are various harmful effects of vibration :
(a) Excessive wear of bearings.
(b) Formation of cracks in machines, buildings, and structures, etc.
(c) Loosening of fasteners in mechanical systems.
(d) Structural and mechanical failures in machines and buildings.
(e) Frequent and costly maintenance of machines.
(f) Electronic malfunctions through the failure of solder joints.
(g) Abrasion of insulation around electric conductors, causing soots.
(h) The occupational exposure of humans to vibration leads to pain, discomfort, and a reduction in working efficiency.

Sources of vibration in machine tool

1) Unbalanced of rotating parts
2) Misalignment of coupling and bearing
3) Defective drive
4) Interference in gears
5) Self-induced vibrations because of the cutting process (tool chatter) are generated and
changes its magnitude.
6) Hydraulic forces
7) Aerodynamic forces.
8) Mechanical looseness or insufficient rightness of fasteners.

Following are methods to reduce the vibration in machine tool

1. Change of cutting parameters: Decrease the feed rate, depth of cut and cutting speed
2. Change of tool geometry: Increase of rake angle and method of clamping of the workpiece

3. Change of characteristics of the vibratory system: The following methods can be employed:

(i) Use tuned undamped vibration absorber to counteract forced vibration with a constant frequency.
Example: Electromagnetic imbalance of motion
(ii) Use of stiffener between table and over-arm of a horizontal milling machine, reduction of overheating of the tool in the lathe, use of tighter clamping of the workpiece, use of steady for long slender workpieces, etc.
(iii) Introduction of vibration absorber in the vibratory system especially in boring, milling, and turning operations.

4. Modification of the regenerative effect
(i) The regenerative instability can be destroyed by the use of milling cutters of irregular tooth pitch for slab milling or different helix angles on successive teeth.
(ii) The regenerative instability can be destroyed by the use of continuously variable spindle speed under program control.

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