Analysis of Two-Stroke Engines: Mechanical Engineering Project

This project analyzes the performance characteristics of two-stroke engines, specifically focusing on MAN B&W and a second engine with different specifications. Task 1 involves calculating and plotting piston force, guide thrust, and connecting rod thrust versus crank angle, demonstrating the forces acting within the engine. Task 2 focuses on calculating and graphing the instantaneous velocity, acceleration, and displacement of the second two-stroke engine. The analysis includes detailed descriptions of the graphs and how changes in engine parameters, such as the con rod to crank radius ratio, affect the engine's performance. The document provides insights into the relationship between crank angle and engine kinematics, offering a comprehensive understanding of engine operation.

Introduction
The MANB&W 6S80 MC engine is a six cylinder two stroke engine
having a bore of 800 mm, stroke of 3200 mm and connecting rod length
of 3000 mm. It is a mechanically driven fuel injection type engine with
exhaust valve and starting air valves. It is electronically controlled by a
Camshaft and has a super long stroke (MAN B&W Diesel A/S, 2000). It has
a turbocharger located on the exhaust side. This engine is used to perform
the first task. The second task is performed using a two stroke engine with
a bore of 600 mm, having a rated rpm of 105 and a connected rod length
of 3 m and stroke of 2.4 m.
Task 1
The force acting on a pneumatic cylinder could be expressed as
Force = Pressure x Area. Therefore, if pressure and diameter of the
cylinder are given Piston force could be calculated. Now Guide thrust is
calculated by multiplying the tangent of angle between the connecting
rod and the vertical axes with the Piston Force. Connecting Rod Thrust is
calculated by dividing the piston force with the cosine of the angle
between the connecting rod and the vertical axes. Figure 1 shows a plot of
the piston force, guide thrust and connecting rod thrust versus the crank
angle.

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Comparison of Piston Force, Guide Thrust and Connecting
Rode Thrust Vs Crank Angle
Piston Force (kN) Guide Thrust (kN) Connecting Rod Thrust (kN)
Crank Angle
Piston Force, Guide Thrust and Connecting Rod Thrust
Figure 1. Plot of Piston Force, Guide Thrust and Connecting Rod Thrust Vs
Crank Angle
The piston force and connecting rod thrust start from 6097.20 kN when the crank
angle is at 0° and increase till the crank angle reaches 13° at which point the piston force is
7600.14 kN and the connecting rod thrust is 7655.24 kN. Then they decrease respectively to
4453.53 kN and 4620.84 kN till the crank angle reaches 30°. From this point they experience
an exponential decrease until the crank angle reaches 90° at which point piston force is 759
kN and connecting rod thrust is 897 kN. Whereas the guide thrust starts at 0 kN when the
crank angle is 0° and increases to 1266.71 kN as the guide angle reaches 26°. After which it
decreases to 1232.23 kN as the crank angle reaches 30°, then it is subjected to an exponential
decrease until it reaches 478.55 kN at a guide angle of 90°. There is no side component of
thrust when the gas load acts vertically downwards at the top dead center. But as the pistons
moves downwards and the angle between the connecting rod and the vertical axes increases
the thrust due to the side component also increases.
Task 2
In this task the instantaneous velocity, acceleration and displacement of two stroke
engine is calculated. Figure 2 is a plot of displacement versus crank angle.

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Displacement Vs Crank Angle
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Displacement
Figure 2. Plot of Displacement Vs Crank Angle
From the graph it can be seen that the displacement increases with increase in crank
angle. Maximum displacement is achieved when the crank angle is 180° and the maximum
displacement is 2.4 m which is the crank diameter and is equal to the stroke. With further
increase in crank angle displacement decreases to 0 at 360°. The mid-stroke occurs in
between 75° and 80° and if the ratio between con rod and crank radius ratio is increased, the
mid stroke moves closer to 90° crank angle due to increase in length of the con rod.
Figure 3 is a plot of the instantaneous velocity versus the crank angle and it is
obtained by differentiating the instantaneous displacement with respect to time.

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Velocity Vs Crank Angle
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Velocity
Figure 3. Plot of Instantaneous Velocity Vs Crank Angle
From the graph it can be seen that maximum velocity of 14.095 m/s is reached at 70°
after Top Dead Center and before TDC. The point of maximum velocity moves closer to 90°
after Top Dead Center, if the con rod crank radius ratio is increased, due to which the graph
becomes more like a sine wave. The negative cycle in the graph indicates that the piston is
moving back up the cylinder. In this direction to the maximum velocity is 14.095 m/s but the
direction of movement of the piston is reversed.
Figure 4 is a plot of instantaneous acceleration versus the crank angle and it is
obtained by differentiating the instantaneous velocity with respect to time.

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Acceleration Vs Crank Angle
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Figure 4. Plot of Instantaneous Acceleration Vs Crank Angle
Maximum acceleration of 203.12 m/s2 occurs at 0° which is the Top Dead Center. The
acceleration of the piston then gradually decreases till it reaches 0 m/s2 between 70° and 75°.
After which the piston decelerates, then the shape of the curve changes to sinusoidal due to
the ratio between con rod and crank radius. Bottom Dead Center is reached at 180°, the piston
stops here and reverses its direction. Then the piston's rate of deceleration drops until the
acceleration becomes 0 m/s2 in between 285° and 290°. The piston then accelerates further
until the maximum acceleration of 203.12 m/s2 is reached at 360°.
References
MAN B&W Diesel A/S. (2000). Engine Selection Guide Two-stroke MC/MC-C Engines. 5th
Edition.