Investigation and Analysis of Track System Model

1. Case Study Fundamentals

• The fundamental of mechanics

The concept of mechanics is based on these three fundamental quantities: mass, force and time along with the three Newton’s law of motion. The latter is normally the independent variable such that interaction of the other two occurs within a predefined boundary designated as space. For the purpose of simple analysis, particles and objects are normally assumed to be moving on a rigid plane hence two dimensional analyses is pursued. Otherwise, in complex analysis, the three dimensional analysis considers the motion of the object in all the three basic directions. Mathematically, the directions are x, y and z. Besides, the system of force equilibrium is often considered and this is encapsulated by the three fundamental laws of motion.

• Branches of mechanics

The major branches of mechanics are dynamics and statics. The former mainly deals with motion of objects and particles at rest or those moving with uniform velocity throughout while the latter deals with motion of objects that move with changing velocity over a given period. Furthermore, in dynamics, there are two main sub branches: kinetics and kinematics.

• Types of motions in mechanics

The basic types of motions include: Linear and non-linear where the former deals with motion in a straight fashion from point 1 to point 2 while the latter deals with motion in a curvilinear manner such that the particle traces a curved path on a plane or space

• The five SUVAT equations

S= Ut +1/2at² ………….(1)

V²= U²+2as……………..(2)

V=U+ at………………….(3)

S= Ut-1/2at²…………….(4)

S= t(u+v)/2 …………….(5)

• Meaning of SUVAT

These are equations of linear motion in which acceleration is assumed constant all over and in free fall case, often acceleration value is same as value of gravity (9.81m/s²). They often involve displacement S, velocity (both final V and initial U), acceleration A and time t hence the acronym SUVAT

• Components of a curvilinear motion

There are two components: tangential and normal components. The former describes motion of particle such that it is always orthogonal to the movement of particle. The tangential component is parallel to the direction of particle such that should it come off the curve, the particle will trace this direction.

Given:

The train engine at point E has a velocity of 20 m/s and an acceleration of 14 m/s² acting in the direction as shown in figure 1

• The acceleration vector equation

This is given by: a= a_tu_t+ a_nu_n

• The values of the tangential and normal components of the acceleration

a_t=v’u_t= 0.27601u²t²

a_n=(v²/ρ)u_n= 14²/29.58= 6.626Un m/s

• The value of from the tangential component of the acceleration

v’=u_t/a_t= 1/3.623 u_t= 0.27601u_t m/s²

• The value of radius of curvature ρ (r) from the normal component of the acceleration

ρ=[1+(dy/dx)²]^1.5/ /d²y/dx²/ or we can use:

ρ=v²/a_n = 20²/14sin75= 29.58 m

• The magnitude of the acceleration vector

 

The magnitude of acceleration vector is given by:

a= (a_t²+ a_n²)^0.5

Now a_n= a sin 75= 14sin75= 13.522

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And at= acos75= 14cos75= 3.623

Hence a= /13.522²+3.623²/^0.5 = (13.1404+182.844)^0.5 =195.98^0.5 = 13.99m/s²

1. Overview of Trusses

• Description of truss

Truss is a rigid framework composed of rigid members that are either in tension or compression and unitarily supports structures such as roofing in buildings (Scribd, 2018).  

• Truss Configuration

The two common configuration include: the pitched truss which is triangular in basic shape while flat truss is composed of parallel members as shown in figures 2(a) and 2(b) below;

 

Figure 2(a): Pitched truss

Figure 2(b): Flat truss

• Condition for equilibrium

The basic criteria for static equilibrium in truss are:

• Sum of all forces in the x-direction must be zero; similarly, sum of forces in the othertwo directions, that is, y and z, must also be zero
• Sum of moments in all directions must be zero, that is, Sum of Mx=0, My=0 and Mz= 0
• Assumptions in truss analysis

It is assumed that the members are fixed to each other and that there is buckling in members under stress, in other words, they are rigid.

• Ways to determine if a truss is theoretical determinant or in-determinant

In determinant case, the equations of statics are just sufficient to determine the required parameters while in in-determinant, there are extra theorems that must be used to adequately define the system. For instance, Castiglione’s theorem often comes in handy.

Each test sample is 10 mm in diameter with a gage length of 50mm.

 

Figure 2: Engineering stress – strain graph

• Types of mechanical forces that can act on a body

• Definition of :
• Stress can be defined as the force acting per unit surface area in an engineering material that causes deformation or fracture. That is stress= Force/Area (Engineeringtoolbox.com, 2018)
• strain and the mathematical relationship between them

Strain is the result of stress in materials such that it designates the ratio of change in length to the original length of material (Scribd, 2018).

The two are related as: Strain = Stress/Young’s modulus that is ? = ?/E

• Material with the lowest yield stress is A. Its value is 320MPa
• Material with the lowest ultimate tensile strength is B. Its value is 500MPa
• Material with a larger modulus of elasticity is B.  Its value= gradient (in the elastic region)= (400-200)/(0.00025-0.0001)= 200/0.00015= 133.33GPa

1. Fluid Pressure Measuring equipment

Critical analysis:

• The type of equipment to use in measuring the pressure

A pressure transducer (capacitive) can be used to measure the pressure as it easily integrates well with the system that requires complex sensing to optimize the flow process (Brighthub Engineering, 2018).

• Flow rate of the fluid (beer) during transportation of the fluid (beer) from the production unit through the pipe to the filler and coupling machine       

Liquid flow meter can be used, it measures flow rates in real-time and has a digital readout unlike the conventional analogue types.

1. Fluid Basics

• Definition of Fluid

A fluid mainly designates liquid and gas states such that they easily yield to pressure and move freely without separation of mass of particles.

• Properties of Fluid

-Can easily flow under slight pressure changes

-In Newtonian Fluid, the pressure changes are often assumed uniform 

-Can easily be compressed

-Easily occupies the available space evenly through flow (in liquid) and diffusion (gas)

-Fluid kinetic energy varies linearly as temperature

• Real life application of some of these properties

-The car braking system is actuated via fluid pressure transmission

-Compressed air is normally used to drive systems in aircraft

-The hydraulic jack is used to lift heavy object such as vehicles via fluid pressure mechanism.

• The equation of state as applies to fluid.

Thi is given by PV= mRT (in gaseous state).

References

Brighthub Engineering. (2018). Pressure Measurement Devices – Inclined Manometer, Bourdon Gauge, Diaphragm Gauge, Bellows, Pressure Transducers, Electronic Pressure Sensors. [online] Available at: https://www.brighthubengineering.com/hydraulics-civil-engineering/43777-pressure-measurement-pressure-measurement-devices/ [Accessed 4 Apr. 2018].

Engineeringtoolbox.com. (2018). Stress, Strain and Young’s Modulus. [online] Available at: https://www.engineeringtoolbox.com/stress-strain-d_950.html [Accessed 4 Apr. 2018].

Scribd. (2018). Fundamentals of Engineering Mechanics | Force | Euclidean Vector. [online] Available at: https://www.scribd.com/document/241787088/Fundamentals-of-Engineering-Mechanics [Accessed 4 Apr. 2018].

Scribd. (2018). Trusses, Types, Configuration andConnections | Truss | Civil Engineering. [online] Available at: https://www.scribd.com/document/115008353/Trusses-Types-Configuration-and-Connections [Accessed 4 Apr. 2018].