The Traffic Accident Reconstruction Origin -Article-

Dr. Irving O. Ojalvo and Dr. Oren Masory

This paper compares the analytical response of a low speed, in-line, vehicle impact with that of a simulated bumper test involving a rigid striker. Results from a previously validated analysis procedure indicate that a rigid pendulum mass impact test on a vehicle bumper, such as the one currently mandated by the federal government, yields significantly different results from that of a typical two-vehicle impact. This paper then proposes methods by which the existing government tests could be extended to yield additional design and analysis data that could be used to help design lower vehicle compartment loadings.

The stated purpose of the US federal bumper standard is to ensure that manufacturers produce vehicles which have reduced hardware damage repair costs when they are involved in low speed collisions. However, a more serious problem in such accidents is not property damage, but occupant injury (e.g. whiplash and lower back trauma), wherein the cost in dollars and suffering far exceeds those for vehicle repairs.

Many low velocity highway collisions remain unrecorded because they result in minimal personal injury and vehicle damage. However, a significant number cause cosmetic or functional loss to the vehicles and/or their occupants. In addition, a significant percentage result in fraudulent personal injury claims (a RAND Institute study estimates that associated medical costs are excessive by over 34% -see Ref 1). Hence, the phenomenon of low velocity vehicle impact is important in both human suffering and financial terms.

In this paper we explore extensions to Ref. 2, the Federally Mandated Bumper Test (FMBT), for evaluating low velocity collisions of vehicles under realistic highway conditions. This topic is important because the data provided from the FMBTs are not sufficient for evaluating occupant loading. To assist with the evaluation, we employ a previously validated efficient analysis procedure [3-5] to simulate an FMBT. The numerical results are then compared with those for simulated two-vehicle impacts. The comparison highlights the difference between FMBTs and two-vehicle impacts. In addition, we shall indicate how one may extrapolate these results for realistic highway conditions. Other features of the paper include recommendations on how such tests could be easily extended to yield valuable design data which would not only result in vehicles with reduced repair costs, but could also be used to improve occupant safety in future vehicle designs.

In addition, for an actual two-vehicle impact, the front and rear bumpers of two different vehicles of different mass are usually involved. This fact introduces another proposed extension to FMBTs, in which the rigid impactor test weight must be adjusted to match the weight of the car being struck. A more objective and realistic determination of vehicle/occupant impact tolerance would involve vehicle testing with a uniform striking weight.

Figure 2

In earlier papers [3,4] an efficient analytical model for low velocity vehicle impact was proposed. This model was linear, had only two degrees of freedom. Each vehicle was represented by a flexibly suspended mass, and a separate energy absorber (see Figure 2). Time varying closed-form solutions for the motion of each vehicle's centroid during impact were developed and presented in terms of the gross vehicle properties (stiffness, damping, and mass) and the initial relative velocity between them.

The governing dynamic equations and initial conditions for the idealized system were given by:

where,

with the initial conditions:

Modal coordinates were next introduced:

where

with

As a result of these substitutions, the resulting matrix equations became, after premultiplication by [F]^T

where [C]=c_eq[F]

Solutions were then obtained in closed form and the model was validated by adjusting the stiffness and damping parameters, K and C, respectively, so that the output matched actual vehicle crash data presented in [3,5].

Figure 3

Figure 4

To justify the assumption of linearity, the normalized test data for 8, 16 and 24 km/h (5, 10 and 15 mph) impacts were normalized to 10 mph and plotted on the same axes for comparison purpose (see Figure 3). Following this, an analytical solution, for c₁ = c₂ = 200 N-sec/cm (115 lb-sec/in), k₁ = k₂ = 6.6 KN/cm (3,750 lb/in), m₁ = 966 kg (2,125 lb) and m₂ = 930 kg (2,046 lb), was superimposed on these results. As may be seen from Figure 4, it is clear that the linear model of [3] is reasonably valid considering its simplicity. Although, the test data clearly indicate additional higher frequency response content than the two degree of freedom model can reproduce, the errors in peak G loading are small. By this it is meant that the peak G's between any single test and the remaining normalized (for impact speed) data is greater than the difference between peak analytical results and all the remaining test data.

To investigate the implications of an FMBT in a preliminary way, one of the vehicles in the model depicted in Figure 1 was replaced by a rigid impactor (see Figure 5) with mass (966 KG) equal to that of the pendulum-struck vehicle. A time history solution for a 4 km/h (2.5 mph) impact with this vehicle is presented in Figure 6. This was accomplished using the proposed analysis simulation by increasing k₂ to infinity and setting c₂ equal to 0 in the analysis described in [3,5].

Figure 5

Figure 6

Peak acceleration numerical results for the FMBT simulation are compared to the response analysis obtained if the impactor had an energy absorber and bumper system equal to that of a struck vehicle. As may be seen in Figure 6, the result is that the rigid impact test yields over twice as severe a peak impact G loading over approximately half the time interval as that between two flexible vehicles for the same relative impact speed. In fact, to match peak G's between the pendulum test and a two vehicle collision, it is necessary to increase the two-vehicle impact speed by a factor of 2.36 for the parameters used in this simulation.

There are several important reasons for the numerical solution difference between the FMBT and two-vehicle simulation. During actual vehicle impacts, the presence of two energy absorbing bumpers have the effect of reducing the effective stiffness and damping at impact. This reduces the impact force between the vehicles such that a greater relative speed between vehicles is required to produce an equal impact force to the vehicles and their occupants. These differences could be easily augmented in the FMBT by using an impactor with an agreed upon weight and a flexibly suspended energy absorbing system that approximates the average passenger car that is currently on the road in this country. Since cars must be state registered, data on the national average car weight could be determined, and since this information is computerized, it could be easily updated each year.

In addition, when performing the FMBTs, manufacturers could be required to obtain test data to determine the effective spring constant and damping to be used for future simulations and low speed testing. Such data could be readily obtained from rigidly mounted accelerometers which would yield a car's centroidal decayed oscillatory response to 2 or 4 km/hr impacts with a rigid impactor. The response curve could then be analyzed using well established techniques to determine its effective in-line, low speed impact damping and spring constants, and since the data could be computerized, data from previous years' tests could be used to design a uniform striker's stiffness and energy absorbing properties.

1."Whiplash may be fraud or may be real: It's hard to tell the Difference," Insurance Institute for Highway Safety Status Report, Vol. 30, No.8, Sept 16, 1995, pp. 8-10.

2.Code of Federal Regulations 49, Transportation, Part 581 "Bumper Standard," Office of Fed'l Register, US Govt Print, Wash DC, October 1997 pp. 765-767.

3. Ojalvo, I. U. & Cohen, E. C., "An Efficient Model for Low Speed Impact of Vehicles," Society of Automotive Engineers 970779 & SP-1226 (pp. 193-203), 1997.

4.Thomson, R.W. and Romilly, D.P., ^"Simulation of Bumpers During Low Speed Impacts", Proceedings of the Canadian Multidisciplinary Road Safety Conference VIII, Saskatchewan, June 1993.

5. Ojalvo, I. U., Weber, B. E., Evensen, D., Szabo, T. J. & Welcher, J. B., "Low Speed Car Impacts with Different Bumper Systems: Correlation of Analyses with Tests," 1998 SAE International Congress &Exposition, Detroit, MI, February 1998.

Dr. Irving O. Ojalvo can be reached at Florida Tech Associates 5030 Champion Blvd., Suite 315 Boca Raton, FL 33496 1-800-358-9909

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