MCHM201 - Slider Crank Mechanism - Engineering Assignment Help

Assignment Task

Title of Practical: Slider Crank Mechanism
Abstract
This phenomenon is used to convert linear motion of an object to rotational motion and convert rotational motion to linear motion. In engineering this is used to investigate machines kinematics and resulting dynamic forces. Some factors are negligible when performing analytical calculations. The recorded data is compared to the calculated values because the mechanism works in balance and unbalanced form.

1. Introduction
The slider-crank mechanism is one of the most useful mechanisms in modern technology since it appears in most of the internal combustion engines including automobiles, trucks and small engines. The slider-crank chain consists of four bodies linked with three cylindrical joints and one sliding or prismatic joint. It is used to change circular into reciprocating motion or reciprocating into circular motion. This experiment will teach us the construction and working principle of the slide crank mechanism along with its basic applications in everyday life, along with the relationship between displacement, velocity and acceleration.
 

2. Objectives
To obtain a graph of piston velocity against crank angle using the method of instantaneous centres, assuming that the crank rotates at a constant angular velocity.
To obtain crank angles which correspond to the maximum piston velocity.
To show that for a slider crank mechanism, piston movement tends to simple harmonic motion with increasing values of connecting rod/crank ratio.

3. Apparatus
The apparatus consists of a crank with a pointer and 360o scale. The con-rod links the crank to the piston. The con-rod can be adjusted for length and is fitted with a cursor. The cursor is used to read a cross-scale which gives the instantaneous centre and thus the piston velocity. Piston displacement is read from a linear scale.

4. Theory
The slider crank mechanism is one of two mechanisms that form the basis for many complicated motions. To find the velocities using the method of instantaneous centres, consider a ridged body moving relative to a horizontal axis.
At two different points on a body (A and B), the velocities of these points will be perpendicular anywhere on the line through A and B. If these two lines meet at a point “I”, it is the point about which the body is rotating at the instant considered. “I” is called the instantaneous centre.
If the two lines are co-linear (one on top of the other) the instantaneous centre may be anywhere on them. The two velocities will be parallel but not necessarily equal. If the two lines are parallel and not co-linear, “I” is at infinity and the two velocities are parallel and equal. The body is therefore moving translationally and every point on it has the same velocity.
An instantaneous centre is not the same thing as a fixed pivot unless the body is constrained so that its motion is always a rotation about the same point. Then the point of rotation and the instantaneous centre are coincident. Thus, the instantaneous centre is at different points at different instants. So, whilst the accelerations can be expressed relative to the instantaneous centre, the centre itself can have an acceleration.

5. Method
Set the crank to zero on the circular scale. Select a con-rod length to test. Slacken both knurled nuts and adjust the position of the piston pivot. Ensure the spacer washer is between the piston and the con-rod. The motion may be locked at any position by tightening both knurled nuts. In normal use the knurled nuts will just be slack. Then for every 10o of crank rotation note the piston displacement and the cross-scale reading. The crank throw is 35mm. The con-rod lengths are 115mm, 140mm and 175mm. Tabulate the results.
When the crank angle is set to zero note the initial reading of the cross-scale. This will have to be subtracted from all the subsequent readings to obtain the true results.
Plot a graph of piston velocity against crank angle and on the same axes the piston displacement against the crank angle. Using the formula below, calculate the angle at which the velocity is a maximum and compare it to the graph.
a=Rr?2 (cos?+ cos2?n)6. Experimental Results
Con-rod = 115mm Crank Radius = 35mm Ratio = 3.2857
Crank Angle ( o ) Crank Displacement (mm) Crank Velocity (mm/s)
0 61 42
10 62 50
20 63 57
30 67 62
40 71 67
50 76 71
60 83 74
70 89 75
80 95 74
90 101 73
100 107 71
110 113 67
120 117 64
130 122 60
140 125 57
150 127 53
160 129 49
170 130 45
180 131 42
Con-rod = 140mm Crank Radius = 35mm Ratio = 4
Crank Angle ( o ) Crank Displacement (mm) Crank Velocity (mm/s)
0 36 42
10 36 50
20 38 57
30 41 63
40 45 68
50 51 71
60 56 74
70 63 75
80 69 75
90 75 74
100 81 72
110 87 69
120 92 65
130 96 62
140 100 58
150 103 54
160 105 50
170 106 46
180 106 42
Con-rod = 175mm Crank Radius = 35mm Ratio = 5
Crank Angle ( o ) Crank Displacement (mm) Crank Velocity (mm/s)
0 2 42
10 2 49
20 3 57
30 6 63
40 10 67
50 15 71
60 21 74
70 27 75
80 33 76
90 39 74
100 45 73
110 52 69
120 56 67
130 61 62
140 64 59
150 67 55
160 69 51
170 71 46
180 71 42
 

7. Graphs and Calculations
Crank Angle (o) Crank Velocity (mm/s) Crank Angle (o) Crank Velocity (mm/s) Crank Angle (o) Crank Velocity (mm/s)
0 0 0 0 0 0
10 8 10 8 10 7
20 15 20 15 20 15
30 20 30 21 30 21
40 25 40 26 40 25
50 29 50 29 50 29
60 32 60 32 60 32
70 33 70 33 70 33
80 32 80 33 80 34
90 31 90 32 90 32
100 29 100 30 100 31
110 25 110 27 110 27
120 22 120 23 120 25
130 18 130 20 130 20
140 15 140 16 140 17
150 11 150 12 150 13
160 7 160 8 160 9
170 3 170 4 170 4
180 0 180 0 180 0
a=Rr?2 (cos?+ cos2?n)a=Rr?2 (cos?+ 2cos2?-1n)0=(3.2857)(35)332 (cos?+ 2cos2?-111535)Cos=0.262 OR Cos=-1.905 = 74.81o N/S
a=Rr?2 (cos?+ cos2?n)a=Rr?2 (cos?+2cos2?-1n )0=(4)(35)332 (cos?+2cos2?-114035 )Cos=0.225 OR Cos= -2.225
= 75o N/S
a=Rr?2 (cos?+ cos2?n) a=Rr?2 (cos?+ 2cos2?-1n)0=(5)(35)342 (cos?+ 2cos2?-117535)Cos=0.5 OR Cos=-2.686 = 79.28o N/S

8. Interpretation
The slider crank mechanism produces a movement which is a slightly distorted simple harmonic motion. This is due to the effective reduction in the centre distances measured axially when the con-rod is at an angle. There would be a corresponding distortion of the velocity and acceleration graphs.
The ratio of con-rod length to crank radius increases as the con-rod length is increased. From the graphs drawn, shorter rods have a higher displacement than long rods. Thus, increasing the con-rod length results in shorter piston displacements, (causing the piston to move towards the bottom dead centre of the piston cylinder). The maximum piston velocity increases slightly with an increase in con-rod length. A short rod will increase the piston speed on the opening side, but lower speeds on the closing sides. This is shown on the graphs where the gradient of the graph is shallow at first and becomes steep afterwards. Therefore, a long rod will increase piston speeds during the exhaust events. Con-rods also require shorter pistons.
The acceleration would be a maximum at 0o. The maximum value of acceleration ours at top dead centre (TDC). Between TDC and maximum piston velocity (110o, 80o, 100o - from graphs), acceleration is positive but decreasing towards zero (the piston velocity is increasing but less rapidly). At maximum piston velocity, the piston stops speeding up and begins to slow down. At that point, the acceleration changes direction (from positive to negative) and when the velocity reaches the maximum value, at that instant the acceleration becomes zero.
 

9. Discussion
This experiment was performed to calculate the velocity of the piston of a slider crank mechanism. Upon completion of the practical, a velocity versus crank angle graph was drawn with the results that were obtained, and these graphs show the maximum velocity of the piston. A formula was used to determine the maximum velocity of the piston as well. These values from two different sources were compared.
Based on the graph, it can be seen that the maximum velocity for the 115mm con-rod was at 110o. The maximum velocity is shown to be 30.5mm/s. The maximum velocity of the 140mm con-rod was at 80o and it is shown to be 31mm/s. The maximum velocity of the 175mm con-rod was at 100o, and the maximum velocity is 32mm/s.
The calculated crank angle for the maximum velocities was 74.81o, 77o and 79.28o for the crank-rod of 115mm, 140mm and 175mm, respectively. There is a percentage difference of 68?tween the calculated and experimental results for the first case. The second case has a percentage difference of 96.25% and the third case a 79.28% difference.
The interpretation states that this motion can be described as a slightly distorted simple harmonic motion. The con-rod length plays an important role in the velocity, displacement and ratio of con-rod length to crank radius. At the maximum velocity of the piston, the acceleration of the piston will be zero. This is because the piston speeds up to a certain point to its maximum value and then begins to slow down again.
 

10. Conclusion
The slider crank mechanism is very important in all types of engines especially internal combustion engines and reciprocating engines. Proper design of the mechanism must be carried out, otherwise failure is a possibility. The size of the crank is taken according to the desired rpm/ velocity and size of the con-rod is taken according to the crank.
In this laboratory experiment, we learned to utilize various pivots to construct a slider crank mechanism. In addition, we studied the characteristics of a slider crank mechanism, such as the proportional relationship between the crank and con-rod. By observation of collected data in the displacement of the slider crank with respect to the crank angle, we were able to deduce points of maximum acceleration and velocity as well as their resembling sinusoidal waveform with respect to their corresponding graphical representations.
 

11. Recommendations
Caution must be taken when reading the velocity scale on the equipment. The markings on the Piston arm must intersect the scale markings to ensure accurate readings. If this is not done, the results that are obtained will be inaccurate.
It must be noted that with the crank angle set to zero, the initial reading on the cross-scale must be noted. This is the reading that would need to be subtracted from all subsequent readings to obtain the true results. If this is not done the experiment will not be a success.

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