VIBRATIONS

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Vibration

When a mechanical system performs oscillations about an equilibrium position, caused due to the action of a disturbing force, the system is said to be in a state of vibration.

Vibration  

Although vibration can sometimes be used to advantage – as in cleaning and mixing machines, presence is generally undesirable for three main reasons:

  structural damage – of fatigue nature due to
                                       cyclic fluctuation of loading

  physical discomfort – experienced by personnel
                                          associated with the system

  noise  –  vibration of air molecules generated
                    by a mechanical vibration

Vibration Characteristics

A vibration is characterised and assessed by three parameters:

Amplitude – it is the maximum displacement from the central / equilibrium position
                      ( measured as linear or angular quantity )

Frequency  – it is the number of cycles of oscillations completed in a unit interval of time

Phase –  is a measure of instant at which a vibration passes through the central position

       (only of importance when relation between two vibrations are considered)

Vibration Modes

This is designated by the number of nodes in a system

Node – A point in a vibrating system where the amplitude is 0

Antinode – A point in a vibrating system where the amplitude
                   is maximum.

A system can vibrate with 2, 3 or more nodes as shown below.

Forms of Mechanical Vibration

  Mechanical vibrations can occur in three forms:

Classification of Vibration

Free / Natural Vibration

If a mechanical system is displaced from its equilibrium positionand then released, the restoring force arising from either …spring elements as in vehicle suspension material stiffness as in torsional or bending systems or gravitational forces as in pendulum will cause a return towards the equilibrium position.

As there will be an overshoot and undershoot and so on, this will result in a vibration, called Free / Natural Vibration

In a free vibrationion., the system is said to vibrate at a natural frequency.

Classification of Vibration

Forced Vibration

When the mechanical system vibrates under the influence of external forces and moments, the vibratory motion is said to be forced. Forced vibrations take place at the frequency of exiting forces or moments.

For example:

Firing impulse and inertia forces from the operating cycles are the exciting forces on the elastic shaft system.

Resonance

When the frequency of the forced vibration coincide with the frequency of the natural vibration of the system,  a resonance condition is reached.

This results in a build up of amplitude which may be dangerously high to produce great fatigue stress and finally failure of the material.

Harmonic

It is a vibration with frequency multiple of the first order or fundamental frequency.

For example:

If the 1st order or the fundamental frequency is 3 cycles per sec, the second harmonic would have a frequency of 2 x 3 = 6 c/s (Hz).

Similarly, the 3rd harmonic would have a frequency of 3 x 3 = 9 c/s (Hz).

Critical Speed

If the engine is run at a speed where this frequency coincides with the natural frequency of the system, resonance condition will occur.

The resonance will produce vibrations of high amplitude. The particular engine speed at which the resonance occurs is known as Critical Speed.

For example:

It is planned to install a 4L60MC engine in a vessel.

Calculation shows hull has a natural frequency of 1.5 Hz.
This corresponds to 1.5 x 60 = 90 cycles / min.

If 4L60MC engine runs 117 rpm @MCR, so there is a risk of resonance at 90 rpm  which is within the 1st order excitation frequency 117 x 1= 117 c/s.

Barred Speed-range

The high stresses associated with resonant conditions start to built up as the engine speed approaches the critical speed, and do not come back to some safe value until the engine speed is beyond the critical speed.

The unsafe stresses either side of the critical speed are referred to as the flank stresses.

The barred speed-range of an engine is the range of speed from the beginning of unsafe flank stresses to the dying-away of these stresses at some higher speed.

Engine must not be continuously operated at speeds within the barred range.

Damping

In a vibratory system damping may be divided into …

  External damping – separate energy absorber unit
                                                to offer resistance to oscillation

  Internal damping –  provided in the material property
                                                internally. It is the capacity of the
                                                material to absorb energy.

A dynamic force acting on an elastic system may cause a resonant vibration.

External dampers are used to lower the peak amplitude at near resonant condition.

Excitation sources

According to the vibration characteristics of
2-stroke slow speed diesel engines, the excitation sources are divided into four categories:

  External moments due to inertia and gas load

  Guide force moments

  Axial Vibrations

  Torsional vibration

Axial Vibration

When the crank throw is loaded by the gas force through the connecting rod mechanism, the arms of the crank throw deflect in the axial direction of  crankshaft, exciting axial vibrations.

In order to counteract the influence on the hull from the axial vibration, all engines are equipped with an axial vibration damper in the forward end of the crankshaft.

Axial Vibration Damper

The damper usually consists of piston moving in a cylinder. The movement of the piston causes oil to be forced through small openings so that resistance to movement is set up. The resistance damps out the vibration.

Torsional  Vibration

The elastic shaft system of a multi-cylinder diesel engine is acted upon by a periodically varying torque.

This causes a harmonic displacement of masses in the plane of rotation.

This is termed as torsional vibration.

Torsional vibrations are thus made up of large number of harmonics of varying amplitude and frequency.

When crankshaft revolves at a speed such that one of these harmonics coincide with the natural frequency of the system, resonance occurs.  The shaft is said to be at critical speed.

Torsional  Vibration

Frequency of torsional vibration of a single mass is:

                       Where,  q is the stiffness in N-m / radian

                                     I  is the moment of inertia of attached mass in kg / m2

The essence of control is to adjust these two parameters, q and I to achieve a frequency which does not coincide with any of the forcing frequencies.

If controlling of q & I does not give the desired result, additional masses must be brought into the system.

Sometimes additional mass is in the form of damper / detuner.

The commonest detuning and damping devices used in marine practice are viscous-fluid dampers and spring-loaded detuners.

Torsional Vibration Damper

Silicone Damper

It comprises of a heavy floating ring mass A and a light outer casing B rigidly connected to the end of the vibrating shaft.

Space between the floating mass and the casing being filled with silicon fluid.

When the shaft rotates the inner mass A is carried round with the outer casing by the viscous drag of the fluid and will attain the shaft rpm.

When shaft vibrates, inertia of inner mass A does not allow to follow vibration but outer casing follows the vibration.

It causes shearing of silicon fluid to absorb energy of vibration and gives a large measure of damping.