Cooperative Teaching Exploring A Multidisciplinary Engineering Problem

The simple case study presented constitutes an illustrative example of how surprisingly rich an open-ended experimental problem may prove to be. This has involved an instrumented soft drink can and a PC as the starting point for a fruitful multidisciplinary investigation that ended up bringing together manpower and know-how from various engineering areas in a very rewarding cooperative teaching and learning exercise. Introduction The increasing specialisation of modern engineering curricula may contribute to an excessive fragmentation of teaching subjects, which hinders the formation of a global picture in the student’s mind. In the course of their basic experimental training, engineering students are, very routinely, supposed to achieve confirmatory results of simple physical laws or effects. The current availability of icon-based user-friendly graphical software for monitoring, control, data acquisition and interpretation, has provided students with an excellent training facility, which is intuitive, open, interactive and flexible . In our opinion the exploration of this kind of tool in experimental engineering education can foster student creativity, turning passive observers into active participants and promoting a deeper understanding of the underlying physical and mathematical concepts, in line with Kolb’s theory of experiential learning . We strongly believe that the use of carefully selected interdisciplinary problems has an extremely important role to play in helping to integrate knowledge from distinct engineering fields, with the added benefit of providing excellent opportunities for a cooperative learning/teaching/research practice, which can be highly motivating, creative and stimulating for both students and teachers. The starting point – a familiar object “Instrumentation for Measurement” is a 3 year, 2 semester, discipline of the 5-year degree course in Mechanical Engineering, run at FEUP under the responsibility of the second author (TR), in which around 60% of the time is devoted to “hands on” laboratory activity involving over 140 students. In order to comply with the demands for a non-conventional final project topic coming from a highly dynamic group of students led by the third author (PP), an open experimental problem was devised (by TR) using a very familiar object – a beverage can. P ge 730.1 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright  2002, American Society for Engineering Education The students’ assignment involved: (i) Getting one can and carefully measuring its dimensions. (ii) Instrumenting a similar can with strain gauges aligned in the axial and hoop directions and with a temperature sensor. (iii) Estimating the strains magnitude by applying well-known formulas from engineering mechanics for an infinitely long thin-walled circular cylinder of isotropic elastic material with closed ends , considering an applied internal pressure around 50 psi (0.345 MPa) . (iv) Using a data acquisition system to digitally record the can lid opening. (v) Processing the gathered data in order to evaluate the duration of the corresponding transient stage. (vi) Determining the strain increments and calculating the corresponding internal can pressure. (vii) Checking the consistency of the estimated, measured and/or calculated values for strains and internal pressure. The students would be granted bonus points if the range of strain values to be measured was adequately estimated beforehand, together with the corresponding data acquisition sampling rate, since these were important requisites for getting the experiment first time right. This humble test probe has already received the attention of several authors 4-7 and, as we shall see, it has indeed a lot to offer. A preliminary step – determination of material parameters With the generous help of our metallurgy experts the material parameters of the beverage can were identified, namely using emission spectroscopy analysis. The lid material is an aluminium alloy, while a steel alloy has been used for the can body. A test specimen from the can body was prepared for a tensile loading test (Figure 1) whose results are included in Table 1. Figure 1 – Can body specimen Table 1 – Material parameters Can component Material identification Young modulus, E (GPa) Yield stress, Y (MPa) Top lid Aluminium 5052 (AA) 70 240 Body Steel C2D1 (EN10016-3) 205 455 P ge 730.2 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright  2002, American Society for Engineering Education The first step – the experimental results The can has been instrumented with one bonded strain gauge rosette (MM gauge type EA-06125RA-120) for strain variation measurement and with a K type thermocouple (connected to a digital multimeter with cold junction compensation) for temperature monitoring (see Figure 2). Two elements of the strain gauge rosette, oriented in the principal strain directions, are inserted in two distinct bridge circuits (Modular RDP 600 System module type 628), using the three leading wire technique. Each conditioning circuit is prepared for 1⁄4 bridge configuration using strain gauges of 120 Ω nominal resistance. Two digital voltmeters (Keithley 2000) are used for initial quantification tests and adjustments of each bridge circuits. The data acquisition system comprises a PC with a software package from LabTech and a DAS PCL-818HG card with programmable gain. The A/D conversion resolution depends on the gain selected, which was defined taking into account the estimated magnitude of the strain decrement. The sampling rate for data acquisition was adjusted for the expected duration of the transient caused by the can opening (Figure 3). Instrumented can Conditioning circuit Modular RDP 6000 Data acquisition terminals Application developed using LabTech Figure 2 – The instrumented can and the measurement system Figure 3 – Popping the can open The results obtained were later processed and are listed below. P ge 730.3 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright  2002, American Society for Engineering Education Table 2 – Experimental results Can temperature 17.1oC Duration of the transient associated to the can opening 70 ms Longitudinal strain, εz -114 με Hoop strain, εθ -500 με The second step – checking the experimental results Isotropic elasticity and the long thin-walled circular cylinder simplifying model were the basic assumptions for checking the consistency of the results. Using the values for εθ and εz from Table 2, a Poisson ratio ν of 0.307 was found from ν = (εθ-2εz)/(2εθ-εz) (1) The internal pressure p was determined from the hoop strain εθ (a strategy less sensitive to errors in Poisson ratio than using the longitudinal strain εz ) as p = 2 t E εθ /[r(2-ν)] (2) where t and r are respectively the can wall thickness (0.11 mm) and radius (33 mm) at mid height, which led to a value for p of 0.404 MPa (58.54 psi). The corresponding hoop and longitudinal stresses θ and z are given by θ = p r / t (3) z = p r /(2 t) (4) and are found to be 121.09 MPa (17561.5 psi) and 60.54 MPa (8780.8 psi), respectively. Finally the generalized Hooke’s law led to -113.56 με and -497.57 με respectively for the longitudinal and hoop strains, which are in superb agreement with the measured values of Table 2. On the other hand, the computed internal pressure of 0.404 MPa (or 58.54 psi) is slightly above the expected reference value of 50 psi (0.345 MPa). The third step – the numerical modelling – linear finite element analysis In order to investigate more thoroughly the structural response of the can and as a complement to the experimental work, the decision was taken to explore the problem further by performing a numerical study, with the help of the first and fourth authors (JCM and RT). Using the available geometrical and material data a two dimensional axisymmetric 8-noded isoparametric finite element mesh was set up , with a total of 340 elements and 1684 nodes. The mesh is depicted in Figure 4, which includes enlarged views of the top and base zones of the can mesh. A purely linear elastic small strain analysis was first carried out, applying the previously encountered internal pressure value of 0.404 MPa (58.54 psi). The corresponding hoop and longitudinal stress distribution at mid-height is shown in Figure 4 and can be seen to agree perfectly well with the values reported above. This seems to validate, on one hand, P ge 730.4 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright  2002, American Society for Engineering Education the adoption of the long thin-walled circular cylinder formulas for stress estimation and, on the other hand, it indicates that the effect on the stress field of the lid and base cross section geometry is confined to the can extremities, at least for such low pressure level. Figure 4 – Finite element mesh and stress distribution obtained with a linear analysis The fourth step – numerical modelling continued – geometrically non-linear analysis Encouraged by these preliminary results we then decided to investigate the can behaviour in the large deformation range, including base dome reversal. A geometrically non-linear analysis was performed , using the arc-length method to steer the applied internal pressure past limit points. Material non-linearity was not considered at this stage, so as to better assess the contribution of each type of non-linearity to the can response. Figure 5 illustrates the P ge 730.5 Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition Copyright  2002, American Society for Engineering Education evolution of the can geometry, while Figure 6 shows the pressure – vertical displacement curve for point A of the base dome (see Figure 4).