Introduction
In any field of engineering, precision is very important. This is mainly because any inaccuracy of any kind can have disastrous results. This is the main idea that has led to the increased push for all engineering students to do engineering drawings and dynamics even if the student does not major in any mechanical or structural fields which are mainly known to heavily rely on drawings and design.
In the specific field of study, stress and strain in any component is directly affected by its physical dimensions. This is well explained and exhibited in the experiment in which the rods are subjected to different conditions bearing different intensities and dimensions (Paulo, 2011).
In a bid to well elaborate on this topic, several aspects are considered and the actual experiment tends to proof their validity and truth in some thermodynamics laws. The first aspect considered is expansion and allowable lengths. From simple thermodynamics, expansion is directly proportional to the amount of heat supplied or the length of the material being heated. This simple argument forms the basis of the whole experiment which tends to proof its validity.
This analysis can be used in several engineering fields including material processing where it can be used to determine quality of a material since pure materials have an almost single value of expansion rate. This results in a curve which has an arbitrary outlook in which the curve passes through all points and is perfectly smooth. The techniques used in the process are statistical thus averaged values are considered (Paulo, 2011).
In our experiment, the main aims include:
- Evaluation of a material to find its component length, overall component tolerance, step length and step tolerance and slot length and slot tolerance.
- Determine overall length, slot length and reject components percentage.
- Determine overall length, step length (by difference) and reject components percentage under this criterion.
- Compute the mean standard deviation for objectives 2 and 3 and find predicted number of rejects in a population (use statistical tables ‘area under a normal distribution’). This gives the overall length and step length and overall length and slot length. Present this data in a graphical form.
- Compare the computational values and experimental values in 2 and 3 by use of the statistical tables.
Experiment
Using the procedures provided in the booklet, carry out the experiment to determine the values of the blanks in the results section. The following diagrams may be necessary.
Using the above diagrams and some data analysis tools obtained and learnt in class, the results obtained from the experiment were are shown below.
Results
Discussion
Considering a slot, a part of the material is removed but the ends of the material left intact. This often results in a groove. In our case, the groove or slot was cut as a hole into a rod. This slot had some characteristics considered to ensure that the strength of the materials in the rod was not significantly affected.
Looking at the step, a part of the rod was cut (actually the rod was cut about half) and completely removed for a given length of the rod. Considering this, the final rod had a part which appeared semi cylinder with the other being a full cylinder.
Discussing the results, it is clear that some of the materials used produced some reject values in the experiment. The reject values in the step section were five out of the twelve rods used. Deeper into the rejects, it is clear that all steps were lower than the accepted step length values. This can be attributed the low ability of the rods treated as rejects to resist strain and stress rendering them inappropriate for the specified task. Considering a distribution curve of the above data about the overall length and range, there is an even distribution of the data about the two halves of the mean. The mean overall length can be taken to be 61.4 with a deviation of 0.35 on either sides. This makes the two limits of the data considered to be between 61.05 and 61.75 whereby all the overall lengths fit perfectly. Looking at the mean average length of the step, it is 32.5 with an allowed deviation of 0.5mm. This makes the range of step length to be between 32 and 33mm. The rejected rods are outside this bracket whereby all are shorter than 32mm in length.
Looking at the rejects, it appears that the ration of the distance to the step to the overall distance is outside the stated range of deviation in the step analysis diagram rendering them unsuitable for the specified task. This is further facilitated by the said tolerance levels (+/- 0.4) and the rejects have values giving higher levels of deviation meaning that the distribution was also outside the limits set. This produces a reject percentage of 41.67% and a mean deviation of approximately 0.28.
Changing our focus to the slot experiment, a similar set of fourteen rods is used. These rods have slits of different lengths which also fall under a certain range to have the specified levels of tolerance. The mean length of the slits is 11.0 with a maximum deviation of 0.2. This makes the rods to be classified as either rejects or acceptable for the specific tasks whereby six of the rods are rejected. In the rejects, only one of the rods have a slit lower than the minimum value of 10.8 while all the other five have a value higher than 11.2. This gives approximately 42.86% rejects in the experiment and standard deviation of about 0.23. (Robert, 2002)
Considering plotting of curves on this data, it is clear that there is uneven distribution of data. In the step experiment, the distribution about the mean is more on the lower side causing negative skewness while in the slot experiment the distribution gives a positively skewed distribution.
Considering the actual measurements of the rod, it has a length of 61.71mm which can be taken as the mean length. Considering deviations in either side, it is clear that distribution is denser on the lower side as compared to the higher end side. This results in an uneven distribution.
Turning to the results of the combination to form C1 to C12 elements and their deviations, it is clear that the deviations allow only minimal number of tolerance. This results in the table shown below.
This exemplifies the data already discussed above.
Taking a look at the distribution about the mean values from the two experiments, none has a smooth curve. This can be attributed to a number of experimental errors and human errors. It can also be attributed to the rejects associated with the experiments since they are also considered when determining the actual mean values. The table below shows some of these observations plotted on graphs.
Errors
Comparing the computational and experimental values obtained, a number of errors can be said to have contributed to the inaccuracy. Some of these errors may have resulted from inaccurate calibration of the equipment use, human error and the wide ranges given to the slot and the step. Another source of the errors might also have been the environment in which the experiments were carried out. So as to minimize the errors, the equipment required accurate calibration and repetitive determination of any measurements so as to reduce human error.
Conclusion
- Quality of a material is affected by its density.
- Hollow materials have lower levels of resistance to stress and strain than solid materials even if the solid materials have been split (Steps appear to have more resistance to strain/stress compared to slot).
- Inappropriate measurement of a material can lead to lowering of its quality since it might be weak or of poor quality so as not to fit in any of the intended purposes. (Donald, 2005.)
References
Paulo J. 2011. International journal on Manufacturing, Materials and Mechanical engineering. University of Aveiro Press, Portugal.
Mott, Robert L. 2002. Applied Strength of Materials, 4th edition. Prentice-Hall
Donald R. 2005. The Science & Engineering of Materials, Thomson-Engineering, 5th edition
