The ROPS protective structure is mainly made of a reinforced tubular welded steel frame which is joined to the tractor chassis by means of the platform. The platform forms the lower part of the protective structure and is fixed to the tractor by four supports. Silent blocks are mounted on the front and rear supports in order to provide cushioning and, therefore, comfort to the driver.
The FOPS protective structure is an assembly mainly of plastic materials that is designed to provide overhead protection for the driver.

3.1 Code 4 - ROPS
According to OECD Code 4, the ROPS tests must be conducted in the following sequence:

1. Longitudinal loading
2. Rear crushing
3. Side loading
4. Front crushing

For further details about the pushers (geometry, location), clearance zone etc. the reader is referred to the Code 4 reference.

In longitudinal and side loading, the protective structure has to absorb energy, while in rear and front crushing, it has to sustain the prescribed loads. In any of these cases, to pass the test, the clearance zone (the central green box in Fig.2) may not be penetrated by any part of the protective structure. The magnitude of the energy required, as well as that of the crushing force depends upon the reference mass of the tractor, in this case, 4,400 kg. The rate of load application shall be such that it can be considered as static. This was numerically executed in the simulation by performing a quasi-static analysis.

That is, using the explicit dynamics solver, the pusher’s speed was selected so that the kinetic energy of the system remained below the total internal energy by a couple of orders of magnitude, thus minimizing the inertial effects. Note that the energy required is the product of the pusher’s displacement by the force necessary to deform the cabin. Each load step implies a loading and unloading phase. The key aspect of ROPS testing is that all loading steps are linked, that is, the deformation of the cabin at the first loading step will influence the following ones and so forth. Thus, the location of the pusher for the next load step can only be determined after the unloading phase.

 

In other words, the positions of all the pushers cannot be determined in advance, because they depend on the deformation history of the cabin. For instance, the engineer cannot predict the necessary displacement to fulfill the energy requirement in the first load step, therefore, this displacement must be tracked down and, once obtained, the simulation must be re-run with the unloading phase by simply moving the pusher backwards.
Here, the LS-DYNA’s ability to output restart files is of great value since it saves lots of CPU time. In particular, the full-restart feature allows the inclusion of new parts such as the pushers. The only keyword that the engineer needs to use to initialize the old parts in the restart phase, is *STRESS_INITIALIZATION. In the Fig.3 the loading sequence is summarized along with the energy and force requirements.

3.2 Code 10 – FOPS
The OECD Code 10 states that the drop test object shall be a spherical objected dropped from a height sufficient to develop 1365 J. The drop object shall be either be made of solid steel or consist of a ductile iron sphere with a typical mass of 45 kg and a diameter between 200 and 250 mm (the current study employed a diameter of 220 mm). For this investigation, a sequence of three different impacts were chosen, as shown in Fig.4.

Two different FE models were created.
A first model was created for the ROPS testing, and a second one that included the overhead assembly was created for the FOPS testing.

4.1 ROPS structure (cabin)
The cabin’s CAD geometry was accurately meshed with 2D shell elements since most of the components were tubular steel frames and thin metal sheets. An average mesh size of 10 mm corresponded to a good trade-off between accuracy and computational time. In point of fact, the average mesh size was reduced from 15 mm down to 5 mm to study its influence on the results obtained. It was found that the 10 mm mesh size provided a meaningful convergence.
The total number of elements in the simulation corresponded to 80207 shell elements. A fully-integrated formulation (ELFORM=16) was employed for the study.
The sheet metal pieces were connected (welded) using the *CONSTRAINED_NODAL_RIGID_BODY option in LS-DYNA. Therefore, the welds were modeled as non-breakable connections between the parts. In fact, this approach was very useful at the early design stage to identity potential critical areas. Subsequently, more detailed methods using continuum elements were used to evaluate any weld failure. Nodal rigid body spiders were also used to model the bolted connections.
*MAT_24 (elastoplastic) with experimental tensile-true stress-strain curves was used to characterize the steel pieces in the cabin. In particular, three types of steel were mainly employed: S-235, S-275 and S-355 (UNI EN 10025).
*CONTACT_AUTOMATIC_SINGLE_SURFACE was used to model all the cabin components. This contact considers potential self-contacts as well as contact between components (including shell thickness). From the user point of view, the definition of such contact only requires a set of *PARTs in the model. This allows it to be immediately defined without the need to individually search for potential interacting parts. The tractor was fixed to the ground by means of four supports.

4.2 Silent blocks
The cabin is suspended over the tractor by means of four rubber silent blocks, which are components used for absorbing and dampening vibrations to increase the driver’s comfort. Two are located at the front and two at the rear. The behaviour of the silent blocks was modeled using beam elements (ELFORM=6). The radial and longitudinal stiffness were set up according to the experimental results. This was achieved using *MAT_GENERAL_NONLINEAR_6DOF_DISCRETE_BEAM. This material model allows for the definition of an arbitrary translational force curve along the local axis of the beams. Hence, it is very useful to define different axial as well as radial behaviour, including bottoming out, where the rubber material cannot further absorb energy and becomes stiff. This effect can easily be included for consideration by means of a steep increase in the force vs displacement behaviour.

4.3 Pushers
In a ROPS test, the pushers are the components that transmit forces to the cabin to achieve a certain amount of energy (force vs displacement) or, more simply, a specific crushing force value. The load to the ROPS structure needs to be uniformly applied by means of a stiff beam (normal to the direction of the load). Such beams are bound to prevent lateral displacement. During the experiment, force and displacements are recorded as the load is applied, typically by means of a hydraulic system.. In the numerical simulation, the force was the result of a prescribed motion to the pushers. Specifically, the pushers were modeled as rigid components and a specific *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE was assigned between each of these components and the rest of the cabin. The universal joint type occurring between the hydraulic piston and the stiff beam was directly modeled using the rigid body motion (CON1 and CON 2) constraint included in the *MAT_RIGID (*MAT_20 card).

4.4 FOPS structure (roof)
The FOPS structure is an overhead assembly conceived to transfer the impact loadings from potential falling objects to the cabin structure. The model consisted of 338K shell elements varying from 2.5 to 6 mm, depending upon the component. Fully-integrated formulation (ELFORM=16) was used. In this case, the mesh size was reduced to 5 mm to better capture the plastic strain gradients on the components. The bolted connections between the components were modeled with rigid body spiders (*CONSTRAINED_NODAL_RIGID_BODY). Most of the materials in the overhead assembly are plastics, with the exception of the central reinforcement plate which is made of S-235 steel. The plastic material was characterized using *MAT_24 (elastoplastic) and the tensile stress-strain behavior was added as an input curve. No failure was implemented in the model, so plastic strains along with engineering judgement were used to identify critical areas.

5.1 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.

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.

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.

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.

5.2 FOPS
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.

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

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.

 

6.1 ROPS
All ROPS steps were successfully passed.

6.2 FOPS
All FOPS steps were successfully passed. However, some critical areas were identified and the final overhead protection system was reinforced. The final version of the overhead assembly improved on the results illustrated in the current study.