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# Vibration Essay

3343 words - 14 pages

Introduction
All system which possessing mass and elasticity are capable of undergoing free vibration. The main interest of such system is the natural frequency of the vibration.

Natural frequencies are a function of system stiffness and mass. Generally, all real systems have infinite number of natural frequencies. Resonance, large vibration, will occur in a system when the forcing frequency of the system is equal to one of the natural frequencies.

Generally, vibration is a form of wasted energy and normally is undesirable is most cases. It generates noise, instability and will consequently lead to system break down which is a disastrous effect.

This project ...view middle of the document...

The vertical LDVT measures bending displacement, horizontal LDVT measures the displacement caused by torsion. The outputs of the LDVT are shown in the oscilloscope. The tachometer measures the speed of the engine.

2. Objective
The objective of this project is to:
i) To study the vertical and torsional vibration of the model under the excitation of dynamic unbalance force and couple.
ii) To study the approaches of dynamic balancing for reciprocating masses.
.
3. Scope
The scope of the project includes the study and analysis of vibrations of the four-cylinder engine. It examines the results and experiment carried out on each day of the experiment and study the problems suggested. It also discusses the open-end discussion found at the last page of the lab sheet and hence provides solutions to it.

1. Theory
In this experiment, an electric motor assembly is mounted at the end of a single circular cantilever with the mass center G of the assembly on the axis of the cantilever. The assembly consists of four individual single crank-sliders with adjustable initial crank angle. Two units of Linear Variable Displacement Transducer (LVDT) are placed at the free end of the cantilever and aligned perpendicular to each other. The vertical LVDT measures the bending displacement while the horizontal one measures the displacement caused by torsion.
[pic]
Analyzing the individual single crank-slider mechanism,
[pic]

Derive the position vector of point B.
Position vector of point B = [pic] [pic] [pic][pic]
Derive the velocity and acceleration of point B if r is very small compared with l
[pic] [pic]
[pic]
[pic]
So, we have
[pic]
[pic]

The force caused by[pic] of each cylinder on the shaft is:
[pic] (0 is higher order term)

So, if 4 cylinders are considered, the total shaking force will be:
[pic]=[pic]
Assuming all mass of each cylinder is the same, and [pic] is the crank phase angle
Substituting the trigonometry identity:
[pic]

[pic]
[pic]
[pic]
The total shaking torque of the system is derived by taking moment about the mass centre G:

[pic]
[pic]
Where zi is the distance of each individual crank from the mass center G of the assembly as shown in the diagram above, which is -3d, -d, d and 3d.

2. Literature Review
This literature review aimed to provide reviews on some of the works in free vibration and four-cylinder engine.

The William T.Thamson (1993) states that there should be some conventions of the multi cylinders for the measurements of these phase angles which should be take note.

Firstly, the first front cylinder should be reference as number 1 and phase angles will always be zero, so that it is a reference cylinder for all of the other cylinders. Secondly, the phase angles of all other cylinders will be measured with respect to that of the cylinder number 1. Thirdly, Phase angles are measured with internal to the crankshaft. This...

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