Summary / Abstract

This experiment is related to the study of the slider crank chain, which is the basis of many more complicated motions. The experiment is divided into three purposes that must be accomplished.  The objectives of this experiment are to obtain a graph of piston velocity against crank angle using the method of instantaneous centers, assuming that the crank rotates at a constant angular velocity.  Secondly, the experiment is carried to obtain the crank angles which correspond to the maximum piston velocity and to show that for a slider crank chain, the piston motion tends to approach simple harmonic motion with increasing values of connecting rod/crank ratio.  Several readings were taken with the increments of ten degrees in order to study the piston displacement and velocity from the plotted graph and hence determine its characteristics.  It must be noted that the experiment is attempted for five different connecting rod lengths, which is 115mm, 130mm, 140mm, 155mm and 175mm for each purpose of the stated objectives.

In this experiment, two graphs were plotted that is the graph of piston velocity versus crank angle and the graph of piston displacement versus the crank angle.  From the attached graphs, it can be seen that for the graph of piston velocity against the crank angle, the nature of the graph is sinusoidal with specific harmonic motion for each different connecting rod length, where it makes a complete one revolution in 360 degrees.  For the graph of piston displacement against crank angle, the appearance of the graph for various connecting rod length is the same but different in its values of the piston displacement.  Basically, the maximum value of the piston displacement for each different connecting rod length occurred at 180 degrees.  Noted that the larger the connecting rod length, the smaller the value of piston displacement it achieved and vice versa.  From the result that has been recorded, the maximum piston velocity is 37 mm/s for connecting rod of length 115mm, 130mm and 140mm. While the maximum piston displacement is 70mm that lies within 170 to 190 degrees of crank angle for different value of connecting rod length.

Finally, it can be concluded this experiment has exposed the students to the study of motion (which in this case, it is related to the velocity and displacement) with the aid of the slider crank chain.  It is evident that for different value of connecting rod length and ratios, it will contribute to different values of velocity and displacement that have been recorded.  This experiment has give understanding in the study of motion although objective is not perfectly achieved due to the existence of error during the experiment.

Purpose / Objective

            The objectives of this experiment are stated as below:

1.      To obtain a graph of piston velocity against crank angle using the method of instantaneous centers, assuming that the crank rotates at a constant angular velocity.

2.      To obtain the crank angles which correspond to the maximum piston velocity.

3.      To show that for a slider crank chain the piston motion tends to approach simple harmonic motion with increasing values of connecting rod /crank ratio.

Data, Observation and Result

            Below is the mechanism of the slider crank chain diagram:

                           I_AB

                                                                                                   V_a                            X

                                                                                    A         

                                                                                                        w                       O

                                B                      V_b

                        AB = Connecting rod length (115, 130, 140, 155 or 175 mm)

                        AO = Crank radius = 35 mm

                        w = Crank angle, increase by 10 degree (from 0 to 360 degree).

                        I_AB = Instantaneous center

                        V_b = Piston velocity = OX (from experiment)

The following page shows the tabulated data for both piston displacement and velocity together with the attachment of graphs.  Below is the ratio formula that affected the result of the experiment.

                                    Ratio = Connecting rod length / crank radius

From the tabulated data and the graph, it can observed that the value of piston velocity increases until certain maximum level, where experimentally, the maximum velocity is 37 mm/s at 80 degrees of crank angle. The value is then decreases until –37 mm/s at about 280 degrees that is the minimum value before it goes back to it starting value at zero or 360 degrees of crank angle. Basically, the results for different connecting rod lengths    were almost the same. For piston displacement, the value increases steadily until it reaches the maximum value at 180 degrees and goes back to the starting value. The nature of the graph also is nearly the same but differs in it values. 

Discussion

The result of the experiment does almost meet the objectives.  It shows that the equipment is in well condition in order to carry the experiment task although there was fluctuation in the experimental results that may caused by personal error during taking the readings and during setting the pointer at the specific angle, where the pointer is not accurately set to the intended angle.  The existence of error has disturbed the result of the experiment.  Some of the errors are systematic error and personal error. The systematic error may due to the apparatus that not being well calibrated. The personal error occurred while taking the reading from the equipment. 

1. In the graph of piston velocity versus crank angle, the shape of the graph for different connecting rod length is almost the same, which is sinusoidal or sine graph.  Theoretically, there is different in the amplitude and frequency of the graph.  The graph will tends to approach a simple harmonic motion when the connecting rod or crank ratio is high.  The recorded maximum velocity is about 37 mm/s at about 80 degrees and –37 mm/s at 280 degree. From the graph of piston displacement versus crank angle, the maximum displacement occurred at 170 to 190 degrees. The nature of the graph for different ratios is almost the same and only differs by the values it’s recorded. 

2. Theoretically, the maximum piston velocity should occur at 90and 270 degrees.  However, in this experiment, it was occurred at 80 and 280 degree.   This is due to the error caused by inaccurate equipment setting or systematic error. Besides that, the parallax error or personal error made by student should be considered too.

3. The nature and form of the graph is affected by the ratio of the connecting rod length and the crank radius. The value of the ratio is depending on the value of the connecting rod length.  Therefore, increase in the connecting rod length will also increase the value of the ratio. Theoretically, the increasing of the connecting rod length will cause the piston motion tends to approach simple harmonic motion. Therefore the graph for 175 mm will approach simple harmonic motion compare with another shorter rod length.  However, this experiment is not fully achieved due to the existence of the error.  Additionally, for the graph of piston displacement versus crank angle, the larger ratio will have smaller value of piston displacement for every increment of crank angle and vice versa.

4. As stated before, the piston will be in simple harmonic motion when the connecting rod is long.  Therefore, in this experiment, the 175mm of connecting rod length will tends to approach the simple harmonic motion of the movement of the piston.

5. In this experiment, the time taken is assumed to be unity.  Below is the sample calculation of maximum acceleration for 115mm connecting rod:

            Maximum piston velocity occurred at the longest time taken over the recorded value:

            From the graph, the largest difference in the piston velocity is from –9 to 0 mm/s

                        Acceleration = dv / dt        (dt is assumed to be unity)

                                            = (0- (-9)) / 1

                                         = 9 mm/s²

So, the table below shows the maximum acceleration for five different connecting rod lengths.

6. From the result on question 5, the crank angle for maximum acceleration can be attained from the graph. Below is the table of the crank angle where its occurred for each connecting rod length:

7. The maximum acceleration is occurred at different crank angle. Actually the maximum acceleration is occurred at minimum velocity and vice versa. It can clearly be seen from the attached graph the position of the maximum velocity and acceleration.

Conclusions

            As a conclusion, it is evident that the graph of piston velocity against crank angle has been obtained by using the method of instantaneous centers with assuming that the crank rotates at a constant angular velocity.  Furthermore, the investigation of the crank angle which correspond to the maximum piston velocity is also carried out even though the ideal maximum point was fail to be at 90 and 270 degrees.  The study of piston motion that tends to approach simple harmonic motion is not fully achieved although there was an increase of the connecting rod/crank ratio due to the existing of error.  In addition, the maximum acceleration can be determined from the graph. The maximum acceleration is occurred at minimum piston velocity and vice versa.  Moreover, the experiment of the slider crank chain is really essential. It is a fundamental experiment for the advanced technology such as reciprocating engine.