An approach to characterization of the agricultural self-propelled machines stability
Graphical abstract
Introduction
Tractor aggregates and mobile agricultural machines are often driven beyond the safety restrictions, when the centrifugal force and the terrain slope may cause their instability. The overturning suppression methods for these machines can be roughly classified in a few groups:
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passive protection devices, with fixed configuration and position;
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active protection devices, generally hydraulically driven and electronically supported;
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analytical and numerical methods, for the foregoing assessment of the stability range of each specific configuration of a mobile agricultural machine or it’s aggregate.
The paper is focused on the third group of methods. The initial activities of this kind were focused on formulation of the simple 2D analysis of the tractors’ stability, moving over the longitudinal or lateral slope. Fabbri and Molari (2004) studied the influence of the mass center height on the lateral stability of the narrow track tractor. This study, taking into account more than 100 tractors, has shown that there are still difficulties in removing measurement errors within the limit of ±3 mm, required by the standard (OECD Code 6, 2009). Guzzomi (2012) analyzed the impact of mass distribution on the front and rear wheels of the tractor and the impact of the tractor's position on its stability. He has applied the specific geometric model, intended to evaluate the quasi-static angles of the tractor’s safe operation at sloped terrain. 2D approaches were upgraded to the 3D level simulation of the influence of configuration, design and working conditions on the static and dynamic stability of mobile agricultural machines and aggregates (Petrović et al., 2007, Cerović et al., 2015). Pranav and Pandey (2008) presented a mathematical model and software for ballast management simulation on agricultural tractors. Ahmadi, 2011, Ahmadi, 2013 examined the effects of different geometries and the impact of the mass on the tractor’s lateral stability and formulated the adequate dynamic model. They found that the maximum static lateral angle of 45° still allows safe operation of the tractor. The other authors also reported similar values of the critical angle (Khoury Junior et al., 2009, Gravalos et al., 2011; Franceschetti et al., 2014). Denis et al. (2016) presented a 3-D model and made an assessment of the dynamic stability of the grape harvester. They suggested electronic guidance of the hydro-cylinders that control the position and stability of the tractor. Smart farming technologies and simulation models of mobile agricultural machines stability were reported and tested by many others (Li et al., 2016, Liakos et al., 2018, Lampridi et al., 2019, Sun et al., 2019 etc.). Considering that real stability tests are expensive, the experiments were sometimes carried out with scaled models imitating real machines scaled designs, Koc and Liu (2013).
The stability still remains an important problem of mobile agricultural machines application, and therefore it is in the focus of interest of many researchers, requiring extensive long term research. However, if the overturn of the tractor happens, the protective structure (ROPS) seems to be the best protection for driver (Ayers et al., 2018), especially the Hydro-ROPS. However, ROPS provides passive protection. The most effective way to eliminate any kind of consequences is to prevent overturning. For this purpose, Kise and Zhang (2006) suggested the use of the “sensor-in-the-loop (SIL)” technology. They estimated tractor’s dynamic behavior using the fast stereo photo camera. The acquired images were processed using a mathematical model that calculates the kinematic parameters of the tractor motion and defines the critical values at distance of 8 m before the point of possible overturning in order to prevent it.
The practice has defined a range of safe work primarily for tractors but also for other self-propelled agricultural machines through a series of security and design criteria, related to:
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allowed maximum longitudinal and lateral slopes of the terrain;
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prescribed measuring equipment of mobile machines for operation on sloped terrains;
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recommended speeds over sloped terrains;
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necessary equipment for the operator protection in case of overturning (ROPS or cab);
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recommendations for lowering the machines and aggregates centers of gravity, etc.
Combining principles of theoretical mechanics with 3D analytical geometry, the computer program SSPM has been developed, presented and verified in this study. This software is intended to facilitate the analysis, comparison and optimization of different configurations of self-propelled agricultural machines in operation on horizontal and sloped flat terrains at constant velocities and radii of trajectory with respect to their static and dynamic stability. It calculates critical pitch and roll angles of the self-propelled machine and the maximum allowed slope of the flat terrain under the given conditions. The software title SSPM symbolizes its purpose: estimation of the stability range of self-propelled agricultural machines travelling over the sloped terrains. With respect to most of existing mathematical models in this area of agricultural engineering, the SSPM algorithm utilizes the simple theoretical formulas of spatial analytical geometry related to rotation of reference coordinate system and five representative points of the self-propelled machine aggregate of interest (four contact points with terrain and the gravity center of the system) around the coordinate axes. Literally, different terrain slopes are simulated analytically by two successive rotations of these referent points, defined by appropriate pitch and roll angles. Consequently, only simple algebra expressions are used, without a need for complex mathematics or demands for special skills of the user involved, providing the simplicity and high speed execution of the computer program. Therefore, formulated analytical model represents a suitable tool for a preliminary analysis, testing and optimization of the combines consisting of a tractor (self-propelled drive machine) and adequate implements, applied in the field crop production. In addition, it could provide useful information for more efficient planning and conducting the future experimental work on the self-propelled machines stability (see the experimental study of Bietresato and Mazzetto, 2018, among others).
Although a number of idealised assumptions is used, the SSPM is still a suitable tool, which provides preliminary results for final experimental checking of the self-propelled agricultural machines stability. The operational flexibility of the software is provided by introducing the factor of safety, which is entered by user on the base of his experimental work, practical and theoretical experience, combines configuration, operational conditions, etc.
Section snippets
Software introduction
The program SSPM is intended for preliminary checking the static and dynamic stability of tractors with carried implements and other self-propelled agricultural machines in uniform motion on flat horizontal and sloped terrain. The executive version of the program is portable, written and compiled in the FORTRAN programming language, under the MS WINDOWS operating system. The hardware requirements correspond to the operating system, demanding only the additional 5 MB of free space on a hard
Results and discussion
Measurement results of the critical pitch and roll angles induced by adequate rotations of the scaled tractor model are presented in Fig. 12. The abscissa and ordinate axes represent critical roll and pitch angles of the test platform, respectively.
The maximum value of allowed static pitch angles for the tested model tractor on the test platform was 55° downward, at roll angle of 0° which leading to a rollover around the front axle. It did not change appreciably within the range of the roll
Conclusion
Practice implies that tractor stability can be improved by optimizing the combination of four relevant groups of factors: the increased distance between the self-propelled machine wheels, the enchanted quality of the terrain (surface layer especially), the decreased height of the gravity center and the adequate position and weight of the tractor attachments and ballast.
This paper presents a simple analytical model for characterization of static and dynamic stability ranges of the self-propelled
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The work is granted by the Ministry of Education, Science and Technological Development of the Republic of Serbia – project number TR 31051: “Improvement of biological processes in the function of rational use of energy, increase of productivity and quality of agricultural products”, within the framework of the contract for the realization and financing of scientific research work in 2020 between the Faculty of Agriculture in Belgrade and the Ministry, contract registration number:
References (25)
Dynamics of tractor lateral overturn on slopes under the influence of position disturbances (model development)
J. Terramech.
(2011)- et al.
ROPS designs to protect operators during agricultural tractor rollovers
J. Terramech.
(2018) - et al.
Online adaptive observer for rollover avoidance of reconfigurable agricultural vehicles
Comput. Electron. Agric.
(2016) - et al.
Static measurement of the centre of gravity height on narrow-track agricultural tractors
Biosyst. Eng.
(2004) - et al.
Comparison between a rollover tractor dynamic model and actual lateral tests
Biosystems Engineering
(2014) - et al.
An experimental study on the impact of the rear track width on the stability of agricultural tractors using a test bench
J. Terramech.
(2011) - et al.
Sensor-in-the-loop tractor stability control: look-ahead attitude prediction and field tests
Comput. Electron. Agric.
(2006) - et al.
Parameter sensitivity for tractor lateral stability against Phase I overturn on random road surfaces
Biosyst. Eng.
(2016) - et al.
Physics engine application to overturning dynamics analysis on banks and uniform slopes for an agricultural tractor with a rollover protective structure
Biosyst. Eng.
(2019) Development of a tractor dynamic stability index calculator utilizing some tractor specifications
Turk. J. Agric. For.
(2013)
Increasing the safety of agricultural machinery operating on sloping grounds by performing static and dynamic tests of stability on a new-concept facility
Int. J. Saf. Secur. Eng.
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2023, Computers and Electronics in AgricultureCitation Excerpt :Rollover mechanism and tractor stabilization control method investigation: After years of research and development since the middle of the 20th century, basic theoretical research on tractor stability control has been enriched. At present, research on driving lateral stability mainly focuses on dynamic modeling (Petrović et al., 2021, Watanabe and Sakai, 2021a, Watanabe and Sakai, 2020, Watanabe and Sakai, 2019a, Li et al., 2016, Li et al., 2015, Previati et al., 2014, Ahmadi, 2013, Guzzomi and Rondelli, 2013, Guzzomi, 2012, Ahmadi, 2011), stability analysis and evaluation (Liu and Koc, 2013, Koc and Liu, 2013), and stability control algorithm optimization (Petrović et al., 2021, Zhang et al., 2020, Qi et al., 2019a, 2019b). However, according to the literature mentioned above, although many static/quasi-static mechanical models of tractors can be used to describe the attitude change law and instability mechanism of the tractor and each subsystem, the simplified method of the pure rigid body system cannot identify the dynamic motion law of the tractor.
Actively steering a wheeled tractor against potential rollover using a sliding-mode control algorithm: Scaled physical test
2022, Biosystems EngineeringCitation Excerpt :Relevant studies have mainly focused on the mathematical modelling, evaluation, the prediction of lateral stability, and experimental research. Recent efforts that contribute to this field have focused on the improvement of the mathematical models, mainly reflected in approaches such as the optimisation of the stability algorithm (Petrović et al., 2021), dynamic model configuration (Ahmadi, 2011, 2013; Guzzomi, 2012; Li et al., 2015), interpretation of rollover behaviour and a tractor driving simulation (Li et al., 2016; Watanabe and Sakai, 2019, 2020, 2021), real-time rollover monitoring (Liu & Koc, 2013), and the influence of tyre mechanics (Previati et al., 2014). Although these models can explain the attitude change law and the instability mechanism of whole machines and subsystems, simplified methods cannot reveal the lateral dynamic motion rule for the tractor.