Fig.9 - Experimental vs numerical force for rear longitudinal loading (ROPS)
The following paragraphs (5.1.1 - 5.1.4) will show a comparison between the numerical and the experimental approval results. Note that the experimental ROPS phase was only undertaken after the numerical results met the Code 04 requirements. As a matter of fact, the numerical forces generated by the pusher’s action were recorded and then compared to the experimental results for the longitudinal and side loading. The prescribed energy was obtained by simply integrating the force vs displacement curves. With regards to the crushing tests, the compression force was applied at the corresponding location but without recording the displacement. The likelihood of failure was evaluated by examining the accumulated equivalent plastic strains generated during the test.
Fig.10- Longitudinal loading. Grey: elastic region areas. Colored: main plastic strain areas
5.1.1 Longitudinal loading
As described in the Fig.3, the main goals of this test were to absorb 6.16 KJ of energy on applyication of a longitudinal load and, most importantly, to guarantee the integrity of the clearance zone.
The overall behavior of the ROPS structure accorded with the experimental results, as depicted in Fig.8. In addition to this, the force vs displacement curves were in agreement, as shown in Fig.9.
The stiffness of the cabin was well predicted in the first part of the test (see Fig.9) where the main tubular structure was in an elastic regime. Nonetheless, once the stresses on the tubular components began exceeding the yield strength, the slope began to decrease significantly in comparison to the experimental test. This difference may be mainly attributed to the material model, as well as to the cold forming history of the components which was not taken into account. Note that, since the characterization was done prior to the testing,no reverse engineering was done to tune the material model. Hence, a further improvement in the results could be expected as a result of performing numerical tuning on the steel materials, but this was not the objective of the current study.
None of the plastic deformations found in the ROPS were considered to be critical (Fig.10). Concerning the clearance zone, none of the structural components penetrated into its volume. The critical state, which corresponds to the maximum longitudinal displacement at 6.16 KJ, did not penetrate the clearance zone.
Fig.11 - Numerical vs experimental rear crushing test
5.1.2 Rear crushing
The aim of this test was to apply a compressive load of 88 KN on the rear side of the ROPS structure.
The ROPS structure was well-designed because it could withstand the 88 KN load without compromising the clearance zone. In addition, the new plastic strains induced in the structure were limited and, therefore, not critical.
5.1.3 Side loading
In accordance with the standards, after the rear test, the side loading was sequentially applied to achieve 7.7 KJ of energy absorption.
Note that once a test was successfully passed, the pushers were re-positioned and the next test was started. To include the history of the ROPS structure (plastic strains, stresses, and its updated geometry) and to speed up the engineering process, the full restart feature was sequentially used as well. There was, therefore, no need to re-run the previous load steps to continue with the ROPS study.
The ROPS structure showed good agreement in terms of deformations as well as loading response (force vs displacement). In this case, the numerical behavior of the ROPS structure made it appear stiffer compared to the experimental test (Fig.13). In point of fact, the numerical curve was mainly above the experimental one, meaning that the energy time calculated by integrating the curve was higher as well. Despite this, the results were satisfactory.
Based on engineering judgment, the new plastic strains were not critical, and the integrity of the clearance zone was preserved.
Fig.12 - Numerical vs experimental side loading test
5.1.4 Front crushing
The final test of the ROPS sequence is front crushing. Here too, the force applied to the front side of the cabin was 88 KN. No particular weak-points were found in the structure and the clearance zone was, therefore, guaranteed.
After this test, the ROPS structure numerically met the Code 4 requirements and was therefore ready for the approval test. In accordance with the numerical findings, the experimental ROPS results did not show any particular failure areas.
In this phase, three sequential sphere-impacts on the FOPS structure were numerically investigated. On the one hand, the engineers checked that the maximum deflection of the overhead protection did not interfere with the clearance zone. One the other hand, the maximum plastic strains were analyzed to assess their likelihood of failure since material failure was not implemented in the model.
Fig.13 - Experimental vs numerical force for side loading (ROPS)
5.2.1 First impact
For this impact, high plastic strain values were found at the pinned connection of the top hatch. At first glance, such plastic strains may not seem critical, but possible differences in mechanical properties (scatter) for manufacturing reasons, could cause local failure. Simulations showed that the clearance zone was guaranteed provided that no failure occurs at the opening / closure mechanism. For this reason, although not shown in the current study, the mechanism was reinforced prior to approval testing.
5.2.2 Second impact
The second impact also guaranteed the integrity of the clearance zone. Limited plastic strains were found at the brackets of the sheet metal reinforcement. This reinforcement was necessary to contain the maximum deflection caused by the steel ball. No critical areas were found.
5.2.3 Third impact
Fig.14 - Numerical vs experimental front crushing test
Some critical areas in terms of plastic strain were found at the bolted connections of the top lid meaning that local failure could occur. Moreover, despite the fact that the clearance zone’s integrity was guaranteed, the distance between the overhead assembly and the clearance zone at the maximum deflection point was not sufficient to approach the experimental test with confidence. Hence, further improvements (not shown in the current study) were introduced to conservatively handle possible misalignments with the real test. After analyzing the first and third impacts and implementing the modifications, the experimental FOPS approval test was undertaken and passed.