Stability Models of Heavy Vehicle

Transcription

1 Contemporary Engineering Sciences, Vol. 11, 2018, no. 92, HIKARI Ltd, Stability Models of Heavy Vehicle Gonzalo Moreno, Simón Figueroa and Bladimir Ramon Department of Mechanical Engineering, University of Pamplona Pamplona, Colombia Copyright 2018 Gonzalo Moreno, Simón Figueroa and Bladimir Ramon. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In many countries around the world, heavy vehicles are very important, since they are the means to move industrial production, but due to their size, these vehicles have low stability and they are propensity to rollover, which seriously affected the road safety. In this context, the static rollover threshold (SRT) is the factor used to define the stability of these vehicles, but there are several factors defined by the literature. In the present study a literature review of heavy vehicle stability factors is made, and an experimental problem of the SRT factor calculation is shown. Keywords: Stability models, Heavy vehicle, Road safety, Rollover 1. Introduction The stability problems of heavy vehicles (HV s) frequently cause the rollover of these vehicles, this road accident type occur during cornering or evasive maneuvers and may be defined as a maneuver in which the vehicle rotates 90 degrees or more around its longitudinal axis such that the body, and not only the wheels, makes contact with the ground. There are three ways to identify the rollover of vehicles, the real static models (Tilt Table Rollover Test) [1, 5], the real dynamics models [3, 17, 20], and the mathematical or simulation models. However, due to the high costs associated with the first two kinds of tests, mathematical models are the most used in research. Taking into consideration this aspect, a variety of measurements have been defined to parameterize the stability of HV s, being the Static Rollover Threshold (SRT) the most used; this factor represents the maximum lateral acceleration in a quasi-static situation immediately before one tire loses contact with the ground [6, 7, 18]. In the classic analysis (Fig. 1) [6], when the vehicle makes a turn and taking moments about the A point, the lateral tire forces counterbalance the lateral

2 4570 Gonzalo Moreno et al. inertial force, resulting in a roll moment, and at the rollover threshold condition, the normal load F z 2 reaches zero, then, the SRT factor can be calculated by Eq. (1): Figure 1: Rigid vehicle model. Source: Adapted of Gillespie [6]. SRT a g t y 2 h (1) This factor depends on the location of the CG, and this location is influenced by several characteristics of the vehicle; taking into account this, the paper is organized as follows. Section 2 introduces the main two-dimensional models of SRT factor. Section 3 introduces the main three-dimensional models of SRT factor; the results are analyzed and discussed within a case study in Section 4. Lastly, in Section 5, we give conclusions. 2. Two-Dimensional Models The main models consulted in the literature considered the influence of the suspension and tires on the lateral and vertical CG location, and the influence of the bank angle on the load distribution of the vehicle, all this characteristic affect the vehicle behavior [4, 6, 7, 9, 16, 19], some models are analyzed below. 2.1 Winkler model This model considers the influence of the suspension and tires (Fig. 2), making the same analysis of the rigid model, Eq. (2) shows the SRT factor,

3 Stability models of heavy vehicle 4571 Figure 2: Winkler model. Source: Adapted of Winkler [19]. t t SRT 2 W (2) Equation (2) show that the lateral CG movement is greater that the vertical CG movement, which makes the stability factor is smaller compared to the rigid model. 2.2 Rill model This model includes the roll stiffness of the suspension, and the equivalent vertical rubber stiffness of the tire (Fig. 3), Eq. (3) shows the SRT factor for this model, Figure 3: Rill model. Source: Adapted of Rill [16].

4 4572 Gonzalo Moreno et al. SRT R t 1 2 * l h kt 0 l12 k 1 12 * (3) k * k m g l 12 k Ls b m g l 2 12 (4) t k (5) * T kt m g Equation (3) shows that the denominator is greater than that indicated in Eq. (1), which makes that the stability factor is smaller, and additionally, the second term of the equation must be subtracted. 2.3 Chang models This model takes into account the influence of the suspension and the bank angle (Fig. 4), Eq. (6) show the SRT factor, Figure 4: Chang model. Source: Adapted of Chang [4]. t 2 h SRT C 2 1 (6) h h0 Equation (6) shows that the bank angle increases the SRT factor, but the roll angle of the suspension decreases this factor. 2.4 Gillespie model This model takes into account the roll stiffness of the suspension [6], Eq. (7) show the SRT factor,

5 Stability models of heavy vehicle 4573 Figure 5: Gillespie model 1. Source: Adapted of Gillespie [6]. t h h0 SRT 2 G 1 (7) h Equation (7) shows that the numerator is smaller than that indicated in Eq. 1, which makes that the stability factor is smaller. 2.5 Moreno model This model takes into account some characteristics of the vehicle and the road [10, 12], using the Davies Method, the SRT factor is represented by the Eq. (8), Figure 6: Moreno model 1. Source: Adapted of Moreno [12]. h1 e SRT M 1 (8) h1 e Equation (8) shows that the suspension and the tires allow the CG movement, which decreases the SRT factor, and the bank angle allows the increases of this factor.

6 4574 Gonzalo Moreno et al. 3. Three-Dimensional Models Although there are few three-dimensional models developed, these are very important, since they allow seeing the stability as a three-dimensional phenomenon; some models are analyzed below. 3.1 Navin model This model defines a virtual roll axis from fifth-wheel to rear outside trailer tire (Fig. 7), and considering a moment about this axis, the SRT factor is represented by the Eq. (9), Figure 7: Navin model. Source: Adapted of Navin [14]. SRT N t lr e h5 lr e 1 h h0 2 L L t lr e lr e 1 h h5 2 L L (9) This model takes into account the suspension and the longitudinal CG location, but don t have into account the stiffness of the chassis, which would allow its front and rear parts to roll almost independently, which would change the roll axis of the vehicle in the rollover threshold [8, 16, 17]. 3.2 Moreno model Using the same methodology of the two-dimensional model (Section 2.5) [11], the researchers developed a three-dimensional model that considers the main characteristics of trailer and the road (Fig. 8), the SRT factor is defined by the Eq. (10).

7 Stability models of heavy vehicle 4575 Figure 8: Moreno model 2. Source: Adapted of Moreno [11]. h cos cos 1 e t1 Fz 3 P1 Fz 17 W SRT M 2 1 cos cos cos (10) h1 P1 e W h1 e P l sin t cos 1 / (11) Of the models analyzed, this is the most complete and specific, since that take into account the great majority of characteristics that influence on the SRT factor calculation. 4. Stability Models Comparison Using the model and the parameters of the Moreno [11], Fig. 9 shows the SRT factor for the main models developed in this work, additionally and considering that the lateral load transfer on the front axle (LLR f ) is approximately 70% of the LLT r coefficient on the rear axle (16); and that the recommended maximum lateral load transfer for the rear axle (LLT r ) is 60% [17, 20], the SRT factor used in USA [2], New Zealand [15], and Moreno [11] were compared.

8 4576 Gonzalo Moreno et al. Figure 9: SRT models. Source: The authors. Figure 9 shows that the SRT factor for the Moreno models [11, 12] is less than the ones currently used in the world, this fact would make that the road safety greater [13]. On the other hand, the SRT factor is dependent on lateral acceleration. Rearranging the Eq. (1) and replacing the lateral acceleration as shown in Eqs. (12) and (13). SRT 2 a V y R (12) g g V SRT g R (13) Using the Eq. (13), Table 1 shows the speed limits for a vehicle making a curve of radius R = 120 m, and taking into account the SRT factor for the three cases highlighted in Fig. 9. Table 1 Maximum speed of the trailer model - B-train. Research SRT factors. Max. speed (V)(km/h) USA [2] New Zealand [15] Moreno Model [11] Source: The authors. Table 1 shows how the SRT factor can influence the speed limits of the vehicles. The velocity of the Moreno model [11] has a decrease of around 6.3 % with respect to the velocity in USA [2] and around 2.1 % with respect to the velocity in New Zealand [15].

9 Stability models of heavy vehicle Conclusions The results of this study demonstrate that when the vehicle length is considered, the SRT factor becomes smaller, and this is a real problem. If we use the twodimensional SRT factor as an important feature to characterize the vehicle stability, we are neglecting the longitudinal effects. The case study shows that when it is used the three-dimensional model [11], the SRT factor is approximately 38 % lower than the reported value for a rigid vehicle. The SRT factor decrease is important, as it allows to set new road speed limits, which contributes with road safety and decreases vehicle stability related to accidents, which are very high nowadays. References [1] D. Arribas Mantelli, A.L. Martín López, Modelos matemáticos de la estabilidad lateral de Vehículos de Transporte Colectivo, [2] D. Baker, R. Bushman, C. Berthelot, Effectiveness of truck rollover warning systems, Transportation Research Record: Journal of the Transportation Research Board, Transportation Research Board of the National Academies, 1779 (2001), [3] S. Bogard, C. Winkler, J. Sullivan, M. Hagan, A field operational test of a roll stability advisor for heavy trucks, In 8th International Symposium on Heavy Vehicle Weights and Dimensions. Gauteng, South Africa, (2004). [4] T. Chang, Effect of Vehicles Suspension on Highway Horizontal Curve Design, Journal of Transportation Engineering, 127 (2001), no. 1, [5] J. Gertsch, O Eichelhard, Simulation of dynamic rollover threshold for heavy trucks, SAE Technical Paper, (No ), [6] T.D. Gillespie, Fundamentals of Vehicle Dynamics, 7th ed., SAE International, Warrendale, PA, [7] A. Hac, Rollover Stability Index Including Effects of Suspension Design, SAE International - SAE 2002 World Congress, Detroit, (2002). [8] R. Kamnik, F. Boettiger, K. Hunt, Roll dynamics and lateral load transfer estimation in articulated heavy freight vehicles, Proceedings of the Institution of

10 4578 Gonzalo Moreno et al. Mechanical Engineers, Part D: Journal of Automobile Engineering, 217 (2003), no. 11, [9] K. Lambert, A Study of Vehicle Properties that Influence Rollover and their Effect on Electronic Stability Controllers, PhD Thesis, Auburn University, Auburn - Alabama, USA, [10] G. Moreno, E. Flórez, C. Peña, Stability study of heavy vehicles, Revista Colombiana de Tecnologías de Avanzada, 2 (2018), no. 30, [11] G. Moreno, L. Nicolazzi, R.S. Vieira, D. Martins, Stability of Long Combination Vehicles, International Journal of Heavy Vehicle Systems, 25 (2018), no. 1, [12] G. Moreno, L. Nicolazzi, R.S. Vieira, D. Martins, Suspension and tyres: the stability of heavy vehicles, International Journal of Heavy Vehicle Systems, 24 (2017), no. 4, [13] G. Moreno, R.S. Vieira, D. Martins, Highway designs: effects of heavy vehicles stability, DYNA, 85 (2018), no. 205, [14] F.P. Navin, Estimating Truck's Critical Cornering Speed and Factor of Safety, Journal of Transportation Engineering, 118 (1992), no. 1, [15] NZTA, Heavy vehicle stability guide Available at: Accessed on: 17/04/ [16] G. Rill, Road Vehicle Dynamics: Fundamentals and Modeling, Boca Ratón, Florida: CRC Press, [17] H.K. Walker, J.R. Pearson, Recommended Regulatory Principles for Interprovincial Heavy Vehicle Weights and Dimensions, Tech. rep., CCMTA/RTAC Vehicle Weights and Dimensions Study Implementation Committee Report, [18] C. Winkler, Experimental Determination of the Rollover Threshold of Four Tractor- Semitrailer Combination Vehicles, Final Report to Sandia Labs, Contract Report No. UMTRI-87-43, 1987, 79.

11 Stability models of heavy vehicle 4579 [19] C. Winkler, P. Fancher, Z. Bareket, S. Bogard, G. Johnson, S. Karamihas, C. Mink, Heavy Vehicle Size and Weight -Test Procedure for Minimum Safety Performance Standards, UMTRI Research Review, University of Michigan Transportation Research Institute. Ann Arbor, Detroit, [20] J. Woodrooffe, P. Sweatman, A. Arbor, D. Middleton, R. James, J.R. Billing, National Cooperative Highway Research Program NCHRP. Report 671. Review of Canadian Experience with the Regulation of Large Commercial Motor Vehicles. Ed. National Academy of Sciences, Washington, D.C., Nomenclature a a y e Fzi g h h0 h1 CG kls kt kθ L lre l13 m R t t1 t2 Δt V W ψ ϕ θ distance between the front axle and the trailer CG lateral acceleration tangent of the bank angle tire normal load i gravity acceleration height of the center of gravity height of the roll center instantaneous lateral distance between the zero-reference frame and the instantaneous CG height equivalent leaf stiffness of the suspension equivalent vertical rubber stiffness of the tire stiffness of the suspension wheelbase of the trailer distance from the CG to the rear axle distance between the fifth-wheel and the front axle mass of the vehicle radius of curvature vehicle track front track width of the trailer model front axle width. lateral movement of the CG relative to the center of track vehicle speed trailer weight trailer/trailer angle bank angle roll angle of the suspension Received: October 3, 2018; Published: November 5, 2018