On-Road Center of Gravity Height Estimation - A Possible Approach for Decreasing Rollover Propensity of Heavy Trucks

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1 Seoul 2000 FISITA orld Automotive Congress June 12-15, 2000, Seoul, Korea F2000G320 On-Road Center of Gravity Height Estimation - A Possible Approach for Decreasing Rollover Propensity of Heavy Trucks Eugen M. NEGRUS 1), Mihail COCOSILA 2) *, 1) Professor, Politechnica University of Bucharest, ROMANIA 2) Reader, Politechnica University of Bucharest, ROMANIA ABSTRACT. Rollover of tractor/semi-trailer trucks is a serious concern by its human and financial consequences. No widely accepted method to prevent these harmful events has been found so far. A solution to this problem might be to detect and warn the operator on the center of gravity height of the heavy truck in on-road conditions. Estimating the center of gravity position of a vehicle while in motion may be a feasible approach, according to previous work. A more complicated problem is performing the estimation for a tractor/semi-trailer combination vehicle by measurements done on the tractor exclusively. The paper presents simple formulas which allow the above estimation for a minimal number of parameters and acquired data. Calculations done on the data describing the steady-state cornering of a real truck showed that an estimation with an error of about 20-22% of the center of gravity height by measurements done on the tractor vehicle exclusively seems possible. As the target of the approach in this paper is the driver s education by allowing him/her a better sense of the truck s rollover propensity and not the accurate measurement of the center of gravity height, the results obtained seem encouraging. KEYORDS: tractor/semi-trailer combination, rollover, center of gravity height, estimation, driver education INTRODUCTION Although not the most important cause of accidents involving tractor/semi-trailer combinations, rollover causes the largest number of injuries and fatalities among the people riding these vehicles. Furthermore, rollover accidents generate the largest damages to the environment. Because of technical and financial constraints the only feasible way to avoid some of the above accidents in the near future seems to be the operators education for a safer driving manner. One of the solutions leading to this aim is to evaluate the CG height of a heavy vehicle in on-road conditions. It is clearly shown in the literature (1)** that the higher the CG position the more susceptible is a vehicle to roll over. arned that his/her vehicle has a higher CG position after an important loading or even a change of the semi-trailer, the operator might adopt a safer driving attitude. Educating the operators this way might lead to the prevention of some accidents caused by the lose of lateral stability. On-road evaluation of the CG height is not an easy task for any vehicle. A possible approach in this direction is to use some simple geometric formulas and a system of * cocos@aro1.aurut.pub.ro **Numbers in parentheses designate references at the end of paper transducers able to measure the roll angle and the lateral acceleration of the sprung mass (1)(4). In case of a tractor/semi-trailer combination vehicle the real challenge is to perform the above estimation by measurements done on the tractor exclusively. This target is imposed by practical reasons since instrumenting the semi-trailer of a combination vehicle is to be avoided because of cost and exploitation matters. BASIC PHILOSOPHY In order to better understand the approach utilized for the on-road evaluation of the CG height, it is first assumed that the vehicle consists of a single sprung mass supported by a single axle (i.e. unsprung mass). hile negotiating a turn in steady-state conditions the vehicle unsprung mass tilts outwards with respect to the ground with a relatively small angle φu. The sprung mass tilts as well with respect to the unsprung mass with a supplementary angle φs. The approach utilized in this paper is to neglect φu and to assume φs as being measured with respect to the ground and not to the unsprung mass (Figure 1). 1

2 Figure 1 - Single axle vehicle while negotiating a turn This is an usual approach in the literature (1) and leads to an overestimation of the measured roll angle as seen in Figure 1. Since the target of the current researches is to try to prevent some rollover events by making the driver more careful with dangerous road situations, this overestimation might not necessarily be a disadvantage. ith the above assumptions, for small angles, based on the roll equilibrium of the sprung mass, one may find the CG height of the vehicle body as being (1): k h = h + r s r 1 1+ s φ s a y g (1) It is presumable that the design characteristics (h r and k r ) of the vehicle are known and the weight s can be measured on road as many freight vehicles are equipped with on-road load measuring devices. The only two pieces of information necessary to be further known are the lateral acceleration ay and the roll angle of the sprung mass φs. A possible approach for measuring these two quantities is to instrument the vehicle with three tilt sensors - two on the rear axle trailing arms and one on the body. On-road measurements done for a minivan while negotiating quasi steady-state turns showed a quite encouraging consistence of the results (1)(2). CENTER OF GRAVITY HEIGHT EVALUATION FOR A MULTI-AXLE TRUCK The method and results presented above are relevant for a one-axle vehicle. Since a real tractor/semi-trailer combination has significant differences regarding the axles stiffnesses and loads, applying the above method could be done through two approaches: either to lump the vehicle to a single axle or to choose a representative axle. In either case the truck is considered as negotiating a steady-state turn and as being rigid in roll (i.e. the roll angle is constant along the vehicle). Furthermore, all the suspensions have linear characteristics and there is no backlash at the articulation between tractor and semi-trailer. LUMPED VEHICLE: This approach consists of reducing the whole truck to a single axle which represents a weighted average of all axles in terms of roll centers position and stiffness. Thus one may obtain the CG height of the sprung mass as being: h h med k = r s r + (2) a 1 y s 1+ φ g s where h med r represents the roll center height as an average of the axles roll centers height weighted with the axle loads: 2

3 h r med h ri si = si (3) sufficient to know the roll center position and stiffness for the tractor s rear axle. Assuming that the semi-trailer is relatively uniformly loaded, evaluating the equation In the above equation hri represents the height of the roll center relative to the road surface and si the load corresponding to the sprung mass for each axle i of the truck respectively. The roll stiffness of all truck suspensions can be calculated in advance by adding all the roll stiffnesses of the axles springs kri assumed as being connected in parallel: k r = k ri (4) The al load of the truck is, obviously, a sum of those on the axles: s = si (5) Consequently, if knowing the roll centers position as well as the roll stiffness of all axles, the loads supported by the axles are the only parameters necessary to be known in advance. This would imply a weighing system on the whole truck (including the semi-trailer) what many vehicles have indeed today. Besides the above parameters, in order to obtain an estimation of the sprung mass CG height for a single axle truck, there is also necessary to measure the lateral acceleration ay and the roll angle φs. Since the vehicle is assumed as rigid in roll, the two pieces of information could be acquired anywhere on its body. Therefore instrumenting the tractor for this purpose would be sufficient. REPRESENTATIVE AXLE: If choosing a representative axle it is of interest to evaluate the CG height only for the sprung mass relative to the drive (rear) axle of the tractor. The reason for this choice is the critical behavior of the drive axle for the rollover process. As shown in (1), the lift-off of the drive axle s interior wheels relative to the cornering marks the rollover threshold for most of the vehicles in the targeted category. This approach simplifies significantly the vehicle instrumenting since it requires a weighing system on the drive axle alone. Similarly, it is k h = h + r 2 s 2 r 2 s φ s leads to the CG height of the sprung mass relative to the drive axle. In the above formula the subscript 2 refers the drive axle (generically denoted as the second) of the truck, as shown in Figure 2. Obviously both the lateral acceleration ay and the roll angle of the sprung mass φs could be measured by instrumenting the tractor alone. EVALUATIONS FOR A REAL TRACTOR/SEMI-TRAILER COMBINATION It has been considered the situation of the vehicle investigated theoretically and experimentally by Miller and Barter (3) for a cornering in quasi-static conditions. This vehicle is, in fact, materialized into two variants: a combination between a Scammell Crusader tractor and a Crane Fruehauf semi-trailer utilised at tilt table tests and a Scania tractor and the same semi-trailer but with slight modifications regarding the CG height and the roll stiffness for road tests respectively. The two vehicles will be referred by the names of their tractors in the calculations below. LUMPED VEHICLE: The evaluation of the CG height according to the Eq (2) requires to know the ratio ay / φs. This one was calculated from the correlation ratio between the lateral acceleration and the roll angle measured during the tilt table and road tests (3) since the experimental researches in (1) demonstrated a virtually linear dependency between ay and φs. Taking into account the vehicle s main mass and geometry parameters the following calculation data could be obtained: a y g (6) Table 1 - Lumped heavy truck. Calculation data for the center of gravity height evaluation Data Numerical value ay of obtaining h med r 0.55 m Eq (3) k r s 1 / φs x ay / g x 10 6 Nm/ rad (Scammell Crusader) x 10 6 Nm/ rad (Scania) x 10 5 N (Scammell Crusader) x 10 5 N (Scania) [1 / degrees] (Scammell Crusader) [1 / degrees] (Scania) Eq (4) Eq (5) Test data processing (3)(5) 3

4 Using the data in the above table and based on Eq (2) it has been obtained a CG height value hs estimated = 2.39 m for the Scammell Crusader vehicle and 3.21 m for the Scania vehicle respectively. On the other hand, by knowing the exact values of the tractor and semi-trailer CG heights respectively, one can obtain the real value for the CG of the whole truck as a weighted average of the heights of the two vehicles above: h s real h + h = st st sr sr + st sr (7) where the subscript T means tractor and the subscript R refears the semi-trailer. Consequently, one can obtain hs real = 1.87 m for the Scammell Crusader vehicle and 2.56 m for the Scania one respectively. This means the on-road evaluation of the CG height generated an overestimation with about 22% for the first combination vehicle and with 20% for the second one respectively. REPRESENTATIVE AXLE: The other approach suggested above was to evaluate the CG height for the sprung mass relative to the rear axle of the tractor. This evaluation is performed according to the Eq (6) and the calculation data in the table below: Table 2 - Representative axle. Calculation data for the center of gravity height evaluation Data Numerical value ay of obtaining h r m Automaker s data (3) k r2 s2 1 / φs x ay / g 16.9 x 10 5 Nm/ rad (Scammell Crusader) 7.4 x 10 5 Nm/ rad (Scania) 1.59 x 10 5 N (Scammell Crusader) 1.54 x 10 5 N (Scania) [1 / degrees] (Scammell Crusader) [1 / degrees] (Scania) Automaker s data (3) Automaker s data (3) Test data processing (3)(5) ith the above data one can obtain from the Eq (6) the value hs estimated = 2.12 m for the Scammell Crusader vehicle and 1.68 m for the Scania vehicle respectively. The real value for the targeted truck is calculated on the basis of a weighted average of the CG heights for the sprung masses relative to the tractor and to the semi-trailer respectively supported by the tractor s drive axle, according to the notations in Figure 2: real h s 2 = st A B T h + R A + B st sr A + B T T R R s 2 A + B C T T h A + B sr T T (8) Figure 2 - Load distribution on a tractor/semi-trailer combination vehicle 4

5 Based on the above equation one can obtain hs real = 1.86 m for the Scammell Crusader vehicle and 2.55 m for the Scania truck. Therefore the approximate values resulted from the evaluation represent an overestimation with about 12% for the first combination vehicle and an underestimation with above 34% in the second case. CONCLUSIONS Estimating the CG height of a heavy truck while in motion with the purpose of warning the driver about a dangerous loading condition might be an interesting approach in the effort to preventing some rollover accidents of these vehicles. The method of estimation presented above is based upon simple geometric equations regarding the equilibrium of the sprung mass while negotiating a curve and requires inexpensive instrumentation of the tractor alone. Evaluations of the CG position made for a heavy truck during a steady-state cornering lead to results with reasonable error margins despite the use of approximate relations for cost reducing reasons. There is not to be expected any of the above methods to allow an accurate measurement of the CG height while on-road. The results indicated an overestimation of the CG height with 20 to 22% for the lumped vehicle approach as well as an overestimation with 12% for one vehicle and an underestimation with 34% for the other in the representative axle approach respectively. However the data indicated by Miller and Barter (3) should be regarded with some circumspection. Thus one may ask how the same semitrailer could have, in combination with two different tractors but for the same load, once the center of gravity at 1.98 m and the other time at 2.74 m above the ground. Using a qualitative judgement it can be affirmed that it is likely the evaluation of the CG height for the lumped vehicle leads to values closer to the reality than the drive axle approach. This is probable to happen since the first evaluation is less influenced by the nonuniformities in load and stiffness of the different axles of the vehicle. However, the lumped vehicle approach has the disadvantage of the necessity of measuring the loads and stiffness of all axles. Fortunately this target is fairly easy to reach for common vehicles. In real applications which would use modern data acquisition systems with large data samples it is expected the above errors to be smaller. Furthermore, one should not forget that the target of the above evaluations could not be the actual calculation of the CG height of a tractor/semitrailer combination. The only reasonable goal could be the discrimination between several CG positions due to an important change in the loading condition of a truck and the appropriate informing of the driver (as in Figure 3). In this context the results obtained in the above paper might be judged as encouraging and further confirmations are expected to be produced by experimental tests. DANGER ARNING CAUTION NORMAL Figure 3 - Possible output on CG height warning 5

6 NOMENCLATURE ay CG φu φs g hr hs kr s lateral acceleration center of gravity unsprung mass roll angle sprung mass roll angle gravitational acceleration roll center height sprung mass CG height suspension roll stiffness sprung mass weight ACKNOLEDGEMENTS Mihail Cocosila would like to express his gratitude to dr. Bruce Dunwoody from the University of British Columbia in Canada who supervised his graduate studies and initiated some of the research ideas developed in the above paper. The author would also like to thank Mr. Ted Spaetgens, President of Lo-Rez Vibration Control Ltd., for supporting and encouraging his graduate studies in Canada. REFERENCES [1] COCOSILA, M., Roll Sensing of Heavy Trucks. Master of Applied Science Thesis, The University of British Columbia, Vancouver, Canada. [2] COCOSILA, M., A Rollover arning Approach for Tractor/Semi-Trailer Combinations. 16 th International Conference Science and Motor Vehicles 97, YU , Belgrade, Yugoslavia. [3] MILLER, D..G., BARTER, N.F., Roll-over of Articulated Vehicles. Conference on Vehicle Safety Legislation - the Engineering and Social Implications, Paper # C203/73, IMechE, UK. [4] NEGRUS, E.M., COCOSILA, M., On-Road Estimation of the Center of Gravity Height of A Vehicle. VIII-th International Automotive Conference CAR 97, Pitesti, Romania. [5] NEGRUS, E.M., COCOSILA, M., On-Road Center Of Gravity Height Estimation For A Tractor/ Semi-Trailer Combination. ESFA '98 International Conference, Bucharest, Romania. 6