Comparison of three-dimensional finite element and photoelastic results for a scroller shaft.

Rusu-Casandra, Aurelia ; Iliescu, Nicolae ; Baciu, Florin 等

1. INTRODUCTION

The scroller shafts (Fig.1) which are parts of several technological equipments have the function to transport the material to be processed from the supply to the injecting or cutting compartment, by developing a certain compression force that provides the required pressure for a constant flow rate evacuation (Mott, 2005). In order to carry out this function, the scroller shafts are made with variable geometry (the step is decreasing and the height of the flanks is increasing towards the compression compartment) therefore the stress state in the flanks is different from one coil to another and difficult to calculate with classical analytical methods (Rusu-Casandra, 2008).

On evaluating various alternative methods of analysis, both analytical and experimental, the three-dimensional finite element and the three-dimensional photoelastic methods have been chosen for the stress analysis of a scroller shaft. In order to perform a structural optimization of the scroller shaft, it was necessary to validate the mathematical model of calculation using the photoelasticity technique. (Iliescu, Atanasiu, 2006; Paipetis, 1990).

2. NUMERICAL CALCULUS

A finite element study was performed using SOLIDWORKS software (*** 2009). The finite element mesh (Fig.2) was generated for the model using 3D elements with four nodes (Huebner et al., 2001).

Two identical models with a Poisson's ratio value applicable to photoelastic materials subjected to variable pressure have been supplementary loaded one with a compression force P=30 N and the other with a torque T=2 Nm applied on the crank of the scroller shaft.

[FIGURE 1 OMITTED]

Both the applied loads and boundary conditions used for the finite element model were chosen to be similar to those of the photoelastic model. The contour plots of the principal stresses difference [[sigma].sub.1]-- [[sigma].sub.2] in the two models subjected to compression and torsion respectively, obtained using the finite element method, are presented in Fig. 3 and Fig. 4.

3. PHOTOELASTIC INVESTIGATION

The "frozen stress" method of the three-dimensional photoelasticity was used next. The two models have been made of an epoxy resin, Araldite D at 1:1 scale, by cold casting, in moulds of silicone rubber. The material to be processed simulated by textile pieces imbued in silicone oil was introduced into each feeder and transported in the processing compartment using a crank. Both assemblies have been fed until the shafts were self-locked.

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The test procedure consisted of a cycle in which the two assemblies were heated slowly to 1000 and held 30 min to reach equilibrium. Then one of the models was compressed with a force P=30 N and the other loaded with a torque T=2 Nm through a weight placed on the crank. With loads maintained, the models were cooled at 20C per hour to room temperature. The photoelastic patterns were "frozen" into models by the above procedure. After cooling, slices with thickness of 5 mm used for analysing the models were taken, so that the middle plane of slices included the geometric axis of the scroller shaft.

A disc made of the same material as the models, diametrical compressed, followed the same thermal cycle. The disc was used to calibrate the material, resulting the stress photoelastic constant of the model [f.sub.[sigma]] = 38 x [10.sup.-3] MPa / fringe.

When polarized light from a circular polariscope was passed through the slices of the two models, fringe-patterns were obtained. Figure 5 and Fig. 6 show the isochromatic patterns photographed for the two investigated models subjected to compression and torsion respectively. In Fig. 7 and Fig. 8 are plotted the curves of the principal stresses difference [[sigma].sub.1] - [[sigma].sub.2] on the boundary of the two models, using the above isochromatic patterns.

4. CONCLUSIONS

The analysis of stresses in a scroller shaft was performed numerically and experimentally for two cases of loading: compression and torsion, In both cases the structure was subjected also to variable pressure. The results obtained led to the following conclusions:

compartment is high in both models, theoretical and experimental (Fig. 3 and Fig. 7). The values decrease on the flanks of coils two and three towards the crank end of the shaft. On the real structure the distribution of stresses is similar to that on the models and the magnitude of the stresses can be readily calculated if the real compression force is known.

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b) Regarding the second case of loading, i.e. torsion, Fig. 4 and Fig. 8 reveal that the stresses in the two models, theoretical and experimental, have lower values, exception making the two ends of the shaft.

c) The agreement between the calculated and the measured results is good, very small differences may be seen.

As a general conclusion, it can be remarked that the scroller shaft has the main function to transport the material to the processing compartment, the maximum stresses occurring in the first coil flank and in the cross-sections of the two ends of the shaft. This study should find important use in scroller shaft design optimization.

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5. REFERENCES

Huebner, K.; Dewhirst, D.; Smith, D.& Byrom, T. (2001). The Finite Element Method for Engineers, Wiley-Interscience, ISBN 978-0471370789, Canada

Iliescu, N.; Atanasiu, C. (2006). Metode tensometrice in inginerie (Stress Analysis Techniques in Engineering), Editura AGIR, ISBN 973-720-078-0, Bucuresti

Mott, R. (2005). Machine Elements in Mechanical Design, Pearson Prentice Hall, ISBN 0130618853, United Kingdom

Paipetis, S. (1990). Photoelasticity in Engineering Practice, Routledge, ISBN 978-0853343639, United Kingdom

Rusu-Casandra, A. (2008). Elasticity in Engineering, Editura AGIR, ISBN 978-973-720-188-1, Bucuresti

*** (2009) Solidworks User Manual, Dassault Systemes SolidWorks Corp, Concord, MA, USA