Lessons learned from open-ended, un-supervised laboratory work in first year engineering dynamics

Introduction

The management of the exercise, the equipment design and the main lessons learned from the first trial are documented in this paper for the benefit of those who may wish to implement a similar exercise.

The exercise was found to be moderately successful in achieving its expectations. The main difficulty was in scheduling the exercise so as to provide adequate feedback to the students. Some improvements are identified which hold the promise of making the exercise of significant value.

Management of the Exercise

Moment of Inertia of a Rotor and Suspended Mass

A certain machinery component appears as a rotor with a crank from which a mass is suspended. Since this component is to be made using various rotor diameters, crank radii and various suspended masses, it is required to be able to predict the effective moment of inertia of the component for any given combination of these parameters and for any given crank position.

The objective of this laboratory then is to characterize the equivalent moment of inertia of this type of component. A formula in terms of the following parameters is expected:

Rotor radius: Crank radius: Suspended mass: Crank position:

R r ms q

At your disposal is a physical model of the component which may be used to validate any theoretical proposals (see the shop drawing on the reverse side). This model is housed within the dynamics laboratory. An optical sensor and data acquisition software are also provided to enable the angular velocity of the rotor to be measured. To run this software, it is necessary to type 'Dynlab0' at the C: prompt on the computer.

You will work with your laboratory group to perform this task. Each group member shall work individually and place his/her contribution to the overall task in a group file that will be maintained by the school clerk. Each contribution should be written in the same style as a normal laboratory work report. The group file will be available for other group members to view for the purpose of being able to build upon the previous work that has been performed.

As a suggestion, some of the sub-tasks that could be usefully undertaken by different group members have been identified as:

• Prediction of the moment of inertia using geometry but excluding the effects of the suspend mass.
• Design of an experiment to verify the calculated moment of inertia using the Work/Energy Equation.
• Design of an experiment to verify the calculated moment of inertia using Newton's Second Law.
• Experimental characterization of the effects of different suspended masses.
• Experimental characterization of the effects of different crank radii.
• Review of previous work performed to this point.
• Quantification of friction in the experimental work.
• Error analysis of the experimental results.
• Predictions taking into account the suspended mass.
• Review of previous work and presentation of final recommendation.

Submit your contributions in person to the school clerk who will date stamp the submission and file it in the group file for reference by others in your group.

Assessment

At the end of semester, all contributions will be graded on the basis of their presentation, originality and significance in contributing to the overall task. This mark is worth 10% of the total unit assessment.

It is emphasized that the review of other students' work will be essential to your own report. It is common for students' (and not only students) work to be flawed and the correction of previous mis-conceptions is necessary and will be considered significant. Consequently it is entirely acceptable for previous work of unacceptable standard to be re-worked by another group member.

Timetabling

This laboratory work has not been time-tabled. It may be performed and submitted at any time prior to the end of semester. It is recommended however that to avoid the risk of others simultaneously doing the same work, that you submit your contribution at an early date. The dynamics laboratory is available for student use during normal office hours.

Experimental Rig Design

Figure 1: The experimental rig

Around the periphery of the rotor, a thin flange extends which has been drilled with regularly spaced holes. A photo-voltaic sensor then generates an electrical pulse whenever one of these holes passes the position of the fixed photo-voltaic sensor. This pulse is connected in parallel to both a speaker and a data acquisition card inside a personal computer.

The speaker provides an audio impression of the angular velocity of the rotor. High and low pitch of the audible signal corresponds to high and low angular velocity. This is very helpful since it is otherwise very difficult to observe small changes in angular velocity by eye-sight.

The data-acquisition system is a commercial sound-blaster card which has been utilized to collect voltage data from the photo-voltaic sensor. A simple Pascal program provides various utilities such as recording data, processing it into angular velocity, saving it to disk and viewing it in graphical form on the personal computer screen. The computer used is a near obsolete model. The low cost of the components used provides some protection against theft.

Free spinning of the system reveals interesting behaviour which attracts the curiosity of those who observe it. Typical angular velocity data for the system is shown in Figure 2. While the rotor appears to be undergoing a simple decaying sinuisoidal oscillation, closer inspection shows various peculiarities. For instance, the up stroke lasts longer than the down stroke. The motion is reasonably complex with separate effects caused by the reciprocating motion of the suspended mass and the out of balance of the crank and rotor. Although the motion is reasonably complex, it may be easily analysed as shown in the next section.

Figure 2: Angular velocity of the rig when free spinning

Desired Solution

It is ultimately desired to obtain an equivalent moment of inertia Iequ which may be defined as follows in terms of some arbitrary moment M applied to the complete machine component:

Figure 3: Concept of an Equivalent Moment of Inertia

To see if such a formulation is possible, the rig may be treated as a rigid body comprising the rotor and crank and a particle of mass ms which is the suspended mass. The rotor and crank has a moment of inertia of Io. The suspended mass is connected to the crank of length l and mass mc at a radius of r. The corresponding free-body diagram is shown in Figure 4.

Figure 4: Free-body diagram of the system

Solution of the equations of motion results in the following expression:

Thus it is seen that a simple Iequ of the form shown in Equation 1 is not possible. Rather the motion of the system is governed by an equation of the form:

With now expressed as a function of , repeated integrations and differentiation will yield the versus time function shown in Figure 2. It is now possible to understand the peculiar behaviour exhibited by the system such as that shown in Figure 2.

General Observations

• problem solving
• report writing
• design of experiments
• specific skills in engineering dynamics

Report writing skills were found to be generally poor. As such, many reports were un-readable with the consequence that successive students were unable to read and criticize previous work. Provided that an attempt is made to read previous reports, this is not necessarily bad. In having to read poor reports, students soon realize the practical value of being able to write clearly and begin to appreciate the importance of such report writing skills as structure and presentation. It is necessary that students understand that heavy emphasis in assessment will be placed on the review of previous work section of their report.

In the realm of experiment design, it was noted that many students undertook an experimental investigation of the problem before any theoretical understanding of the behaviour of the rig had been developed. Without the guidance of the theory, these reports were typically meaningless and inconclusive. This would be an ideal situation in which to illustrate the importance of theory working in tandem with experimental work. It is regrettable that time limited the amount of feedback that could be given to the students.

In regard to the theory, it was noted that many students struggled with the concept of an equivalent moment of inertia. Given that they were only just being introduced to mass moments of inertia, the concept of an equivalent moment of inertia proved beyond their comprehension. Again it is considered that proper feedback which emphasized the difference would be useful to the students. Generally the theory was at a first year level, however at the time of the exercise, the students were still in the process of absorbing this theory and had difficulty in applying it to a new problem. Implementation of the exercise in second year may circumvent this problem.

It was observed that many students left their contribution to the last week. This effectively destroyed any opportunity for the group's work to grow in a sequential fashion, rather many students ended up working simultaneously on the same type of investigation. It is considered that future exercises must timetable individual completion dates for students so that it will be possible to gradually build up a body of knowledge that subsequent students can review.

Main Lessons Learned

The teaching benefits of the rig were found to be primarily of a generic nature rather than particularly related to dynamics. Consequently implementation of this particular exercise may be considered in any teaching unit generally related to dynamics. Similar exercises based on the same concept could be useful in a first year generic skills type teaching unit.

Time considerations dictate that this particular exercise is best implemented in the second year of the course. This allows scheduling early in the teaching semester with the opportunity for feedback later. Furthermore, with more time available, students may be assigned individual completion dates to allow a better sequence of work to develop.

Assessment and supervision requirements of the laboratory work compare very favourably with traditional types of laboratory work. This is particularly evident if it is considered that in some cases, unsupervised laboratory sessions have greater learning potential than laboratory sessions of the traditional type.