Stiffness Parameters for
Vehicle Collision Analysis
Gustav A. Nystrom, Ph.D., P.E.
The Society of Automotive Engineers publishes thousands of papers every year. The most outstanding 200 or 300 papers are then honored by publication in the yearly "SAE Transactions". An Experts.com Member has now been honored for two papers dealing with the same vehicle collision subject exactly ten years apart.
Dr. Nystroms 1991 paper was entitled "Stiffness Parameters for Vehicle Collision Analysis." That paper compared the two computer programs (CRASH and SMAC) which at the time were used almost universally to evaluate automotive crashes. The paper was the first to provide a consistent means of converting CRASH crush parameters into SMAC crush parameters. The paper received significant acclaim and was published in the SAE Transactions.
Ten years later, at the same SAE session, G. A. Nystrom published a paper entitled "Stiffness Parameters for Vehicle Collision Analysis, an Update". The 2001 paper re-visited the subject of evaluating computer programs used to analyze automotive crashes. By 2001 there were a handful of different programs being used. The 2001 paper evaluated these programs and showed that overall, the differences between the different programs used properly are smaller than the uncertainties in the crash coefficients. The paper also showed that some programs could easily yield the previously unrecognized and ridiculous result of "negative crush". If negative crush were physically possible, it would mean that after a frontal crash a car would be longer than before the crash!
The 2001 paper generated significant discussion when it was presented in Detroit. Very recently, it was honored by publication in the SAE Transactions, where it will join its 1991 predecessor. Dr. Nystrom was well prepared to write the two vehicle collision papers: his Ph.D. thesis at Stanford dealt with modeling of automobile crashes.
An Abstract of each paper is set forth below. Both papers are aimed at engineers who analyze car crashes. Copies of the two papers (numbered 910119 and 2001-01-0502 respectively) can be obtained from the Society of Automotive Engineers.
STIFFNESS PARAMETERS FOR VEHICLE COLLISION ANALYSIS (1991)
By: Gustav A. Nystrom, Garrison Kost, and Stephen M. Werner
Failure Analysis Associates
Two widely used computer programs developed for the analyses of vehicle collisions are CRASH and SMAC. This paper reviews stiffness parameters which are used in the application of these programs, and methods to select these parameters. The paper also introduces a rational method to select stiffness parameter KV for the SMAC program.
The CRASH program expresses the vehicle force-crush relationship as:
FC = A + B * CR, where FC is the force per unit width, and CR is the vehicle residual crush. The "stiffness parameters", A and B, define a linear relation with a zero-crush intercept. For collinear impacts, these parameters are used in determining crush energy, which in turn is used in determining changes in velocities of the impacting vehicles.
Over the years, considerable effort has been expended by numerous researchers to determine A and B for a variety of vehicles, and a substantial body of vehicle crash test data has been developed and analyzed to this end.
The SMAC program permits time-history dynamic analyses of vehicle collisions. It expresses the vehicle force-deformation relationship by the linear equation,
FS = KV * CT, where FS is the force per unit width, KV is the stiffness parameter, and CT is the vehicle total crush. The KV stiffness parameter is usually varied for different vehicles or different classes of vehicles, and, as shown in this paper, should also be varied as a function of vehicle crush.
The method suggested in this paper for the selection of KV is based on
This approach allows the SMAC stiffness calculations to benefit from the extensive database of A and B parameters that has been collected. In addition, the method provides a rational basis for selection of stiffness KV that is dependent on crush distance.
- the premise that the analyst accepts the vehicle force-crush relationship FC = A + B * CR, and
- the idea that KV should be chosen such that the crush energies under the force-deformation curves FC and FS are equivalent.
STIFFNESS PARAMETERS FOR VEHICLE COLLISION ANALYSIS, AN UPDATE (2001)
By: Gustav A. Nystrom
Amador Newtonian Engineering
At the 1991 SAE Congress, a paper entitled "Stiffness Parameters for Vehicle Collision Analysis" was published. The section that attracted the most interest dealt with various methods to relate the CRASH stiffness parameters (A and B) to the SMAC stiffness parameter (KV). The discussion immediately following the paper presentation revealed one more method (developed by Fonda) to relate the CRASH and SMAC parameters consistently with regards to crash energy.
These last ten years there have been three significant developments concerning a consistent CRASH-SMAC conversion. Firstly, a greater range of software providers has developed more variations of each basic computer program. Secondly, the CRASH algorithm has been extended so that it treats rebound more like the old SMAC. And thirdly, two completely different versions of SMAC have been released which provide for a bilinear force-displacement curve like the old CRASH. The lack of clarity regarding the various crash algorithms became evident during the 2000 SAE Congress, when a paper was presented which concluded that to achieve consistent results for a crash between two vehicles, the CRASH "A" values for the two vehicles needed to be the same.
This paper re-visits the question of how to relate CRASH to SMAC calculations. Because the crash algorithms have become more complicated, the re-visit employs numerical integrations, which were not required for the paper ten years ago. The calculated results clearly show under what conditions the various CRASH and SMAC algorithms will yield consistent results for frontal in-line collisions.
A new set of force-crush relations based upon elastic-plastic theory is introduced. Compared to previously published force-crush relations, the new one is found to be simpler, easier to handle numerically, and lead to somewhat more realistic crash pulses.
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