Slider Crank Chain Experiment

UNIVERSITI TENAGA NASIONAL COLLEGE OF ENGINEERING

MEMB331 MACHINE DESIGN & CAD LAB SEMESTER 2 2016/2017

LAB 1: SLIDER CRANK CHAIN EXPERIMENT SECTION 4 GROUP 4

MOHD NAZIM BIN JAMALI

ME094660

SASIDEVAN A/L MUNUSAMY

ME096493

DENNIS BIN ABDUL ADAM LIONELL NITHIYA A/L NITHIYA SAGAYA SEELAN

ME095476

Performed Date

Due Date

ME095508

Submitted Date

15/11/2016

22/11/2016

22/11/2016

SUMMARY & OBJECTIVES The Slider Crank Chain are an example of the two essential instruments which frame the fundamental for numerous more convoluted movements. In this experiment, the main aim is to come by a graph for velocity of piston against angle of crank by utilizing the technique of instantaneous centers (the crank are assumed to rotate at an angular velocity that is constant). Next, the focus is to acquire the angle of crank that relates to the maximum velocity of piston and also to demonstrate that for a slider crank chain, the motion of piston approaches simple harmonic motion with ascending connecting rod values or ratio of the crank. The experiment is initiated with a connecting rod of 115mm length. Cross scale readings and piston displacement are recorded for every 10 ° increment of crank rotation. Then, connecting rods of lengths 130mm and 175mm are tested with similar steps. During the analysis, it was noted that graph obtained for piston displacement versus crank angle was a bell shaped graph. Then, it was observed that the maximum piston displacement occurs at a crank angle of 90° where the piston velocity is perpendicular to this value. Therefore, the maximum velocity also occurs at a crank angle of 90°. Meanwhile, the maximum acceleration occurs between the crank angle of 10° and 40° as well as at 360°. So, the rod length of 115 mm and 175mm gave a maximum acceleration of 0.9 mm/s 2, while rod length of 130mm gave a maximum acceleration of 1mm/s2. A sinusoidal graph was obtained; hence it is safe to assume that the piston have a motion of a simple harmonic motion. Overall, the acceleration of the piston is proportional to the velocity of the piston which in resulted in a Simple Harmonic Motion.

Result & Observation Length of connecting rod: 115 mm Radius of crank: 35 mm Ratio of crank: 3.29

Crank Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Piston Displacement, mm 60 61 62 65 69 75 80 87 92 99 105 111 116 120 124 128 129 130 130 130 130 127 125 122 118 114 108 101 95 90 81 78 72 68 64 61 60

Length of connecting rod: 130 mm Radius of crank: 45 mm Ratio of crank: 3.71

Piston Velocity, mm/s 44 50 58 64 69 74 76 78 78 77 75 71 68 64 60 56 52 48 44 41 38 33 30 27 24 20 16 13 12 12 13 14 19 22 30 36 45

Piston Acceleration, mm/s² 0 0.6 0.8 0.6 0.5 0.5 0.2 0.2 0 -0.1 -0.2 -0.4 -0.3 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.3 -0.3 -0.5 -0.3 -0.3 -0.3 -0.4 -0.4 -0.3 -0.1 0 0.1 0.1 0.5 0.3 0.8 0.6 0.9

Crank Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Piston Displacement, mm 44 45 47 50 54 59 64 71 76 83 90 96 101 105 109 111 113 114 115 115 114 113 110 107 103 98 92 85 80 74 67 62 57 52 49 47 46

Length of connecting rod: 175 mm Radius of crank: 35 mm Ratio of crank: 5.0

Piston Velocity, mm/s 44 50 58 64 70 73 77 79 79 78 75 72 69 65 61 58 53 49 45 40 37 34 29 26 23 19 15 12 12 12 13 15 18 23 30 35 45

Piston Acceleration, mm/s² 0 0.6 0.8 0.6 0.6 0.3 0.3 0.2 0 -0.1 -0.3 -0.3 -0.3 -0.4 -0.4 -0.3 -0.5 -0.4 -0.4 -0.5 -0.3 -0.3 -0.5 -0.3 -0.3 -0.4 -0.4 -0.3 0 0 0.1 0.2 0.3 0.5 0.7 0.3 1

Crank Angle 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360

Piston Displacement, mm 0 1 2 4 8 13 18 24 31 37 43 49 54 59 63 66 68 69 70 70 70 68 66 61 57 53 46 40 35 27 23 17 12 8 4 2 0

Piston Velocity, mm/s 45 50 58 64 69 73 76 78 78 78 76 74 71 67 63 58 54 50 45 40 36 32 28 24 21 18 14 13 12 11 12 15 18 23 29 35 44

Calculation of Result Ratio = Connecting Rod Length / Crank Radius = 115 mm / 35 mm = 3.29

Piston Acceleration, mm/s² 0 0.5 0.3 0.8 0.5 0.4 0.3 0.2 0 0 -0.2 -0.2 -0.3 -0.4 -0.4 -0.5 -0.4 -0.4 -0.5 -0.5 -0.4 -0.4 -0.4 -0.4 -0.3 -0.3 -0.2 -0.1 -0.1 0.1 -0.1 0.3 0.3 0.5 0.6 0.6 0.9

Piston Acceleration = (Piston Velocity, i - Piston Velocity, i+1) / 10s = (50mm/s – 45mm/s) / 10s = 0.5 mm/s²

Graph

Discussion 1. Based on the data collected, the graph obtained for displacement of the piston versus angle of crank was a graph with a bell shaped. Based on this graph that we have plotted, we can be observed that the displacement of piston is at the maximum value when the angle of crank is at 90˚. The reason is because the velocity of the piston is perpendicular to the displacement of the piston at the angle of the crank of 90˚. Next, based on the graph obtained for the velocity of the piston versus angle of the crank, the resulting line on the graph has the shape of sinusoidal. Furthermore, it can be observed that the velocity of the piston is at maximum when the angle of the crank is at 90˚ and the velocity of the piston is at minimum when the crank angle is at 270˚. Lastly, based on the graph obtained for acceleration of the piston against the angle of the crank, the shape of the graph is generally similar to the sinusoidal graph but has an inconsistent or fluctuating data for the acceleration of the crank.

2. Simple Harmonic Motion is where a particular point travels in a path where the acceleration is corresponding to its displacement from a

stationary point in its path. This type of motion, displays a single resonant frequency and sinusoidal in time.

3. The maximum velocity of the piston takes place at 90˚ because the velocity of the piston is perpendicular to the piston displacement at this particular point.

4. The increase in the ratio of the crank will certainly effect the displacement of the piston by the rod. As the length of the connecting rod increases the displacement of the piston is shorter. However, the piston velocity and acceleration is not affected by the increase in ratio. Furthermore, as the ratio increases, simple harmonic motion can be achieved.

5. Theoretically, the maximum piston acceleration should occur when the crank angle is at 180˚. However in this experiment, the maximum piston acceleration occurs in between 10˚ and 40˚, it also occurs again at 360˚.

6. For the 115 mm and 175 mm rod length, the maximum acceleration is at 0.9 mms-2. Whereas for the 130 mm rod length, the maximum piston acceleration is at 1 mms-2

7. Maximum acceleration of piston and the velocity of the piston does not occur at the same angle in this experiment. However the piston acceleration is proportional to the piston velocity and this case can be authenticated by the simple harmonic motion.

Conclusion In this experiment, we determined that the maximum piston displacement occurs at a crank angle of 90° where the piston velocity is perpendicular to this value. Therefore, the maximum velocity also occurs at a crank angle of 90°. Overal the result that we have obtained are a sinusoidal graph with some fluctuating data from the error. Hence, the motion of these piston is a Simple Harmonic Motion. To achieve a more accurate Simple Harmonic

Motion, the ratio of the rod length and piston displacement should be increase. From all these result and calculation, we found out that the maximum acceleration occurs between the crank angle of 10° and 40° as well as at 360°. So, the rod length of 115 mm and 175mm gives a maximum acceleration of 0.9 mms-2, while rod length of 130mm give a maximum acceleration of 1mms-2. In conclusion, the acceleration of piston is proportional to the velocity of piston creating a Simple Harmonic Motion.

References [1] Simple Harmonic Motion. 2009. http://hyperphysics.phyastr.gsu.edu/hbase/shm.html [2] Introduction to Harmonic Motion. 2010.

https://www.khanacademy.org/science/physics/mechanical-waves-andsound/simple-harmonic-motion-with-calculus/v/introduction-to-harmonicmotion

Appendix

The Slider Crank Chain apparatus that are used in this experiment.