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Research Papers

Optimal Restraint for the Thoracic Compression of the SID-IIs Crash Dummy Using a Linear Spring-Mass Model

[+] Author and Article Information
Guy S. Nusholtz

Chrysler Group LLC,
CIMS 483-05-10,
800 Chrysler Drive,
Auburn Hills, MI 48326

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received December 3, 2008; final manuscript received September 6, 2012; published online March 28, 2013. Editor: J. Karl Hedrick.

J. Dyn. Sys., Meas., Control 135(3), 031007 (Mar 28, 2013) (8 pages) Paper No: DS-08-1354; doi: 10.1115/1.4023397 History: Received December 03, 2008; Revised September 06, 2012

The optimal restraint for minimizing the peak thoracic compression of the SID-IIs side crash test dummy subjected to a prescribed impact is studied using a linear spring-mass model. This model consists of the thoracic and pelvic masses and three springs which connect the masses and interface them with an impacting surface through the restraint. The problem is posed as an optimal control problem, with the restraint, which could be any physical structure (e.g., an airbag) operating in a finite allowable space, treated as a displacement control element. Via an assumption of the linearity of the dummy model and a discretization scheme, the problem is approximated and transformed into a linear programming problem for numerical solution. Numerical solutions are obtained under different prescribed impacting surface motion histories, different restraint space values, and constraints on dummy responses. Results show that the general characteristics of the optimal restraint response is a rapid ramp up in velocity in the very beginning of the event, followed by a period of lower level of loading where the thoracic compression builds up, and then an approximately constant acceleration to maintain the compression. The corresponding theoretically minimum thoracic compression values under the various conditions studied are presented.

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References

Humanetics Innovative Solutions, 2012, “SID-IIs Small Side Impact Dummy,” retrieved Aug. 28, http://www.humaneticsatd.com/crash-test-dummies/side-impact/sid-iis
Shi, Y., and Nusholtz, G. S., 1999, “Data-Based Models for Spine Acceleration Response of the Side Impact Dummy,” Proceedings of 43rd Stapp Car Crash Conference, Paper No. 99S-96.
Shi, Y., Wu, J., and Nusholtz, G. S., 2000, “A Data-Based Model of the Impact Response of the SID,” SAE, Paper No. 2000-01-0635. [CrossRef]
Kowsika, M., Shi, Y., and Nusholtz, G. S., 2005, “ES-2 Dummy: Lumped Spring-Mass Model and Parametric Evaluation of Response,” Proceedings of 19th Enhanced Safety of Vehicles (ESV) Conference, Paper No. 398.
Wu, J., Nusholtz, G. S., and Bilkhu, S., 2002, “Optimization of Vehicle Crash Pulses in Relative Displacement Domain,” Int. J. Crashworthiness, 7(4), pp. 397–414. [CrossRef]
Shi, Y., Wu, J., and Nusholtz, G. S., 2003, “Optimal Frontal Vehicle Crash Pulses—A Numerical Method For Design,” Proceedings of 18th Enhanced Safety of Vehicles (ESV) Conference, Paper No. 514.
Balandin, D. V., Bolotnik, N. N., Pilkey, W. D., and Purtsezov, S. V., 2005, “Impact Isolation Limiting Performance Analysis for Three-Component Models,” ASME J. Dyn. Sys., Meas., Control, 127(3), pp. 463–471. [CrossRef]
Balandin, D. V., Bolotnik, N. N., and Pilkey, W. D., 2001, Optimal Protection From Impact, Shock, and Vibration, Taylor and Francis, Philadelphia, PA.

Figures

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Fig. 1

The SID-IIs dummy and the optimal restraint model containing spring-mass representation of the dummy

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Fig. 2

Thoracic compression time history of optimization runs with different number of discretization in a 50 ms interval. Impactor has constant velocity of 9 m/s, and the allowable space between the impactor and the control points is 8 cm.

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Fig. 3

(a) The optimal control acceleration time history. u1: thoracic control point; u2 pelvic control point. (b) Velocity time history for the impactor (z1v), the control points (y1v for thoracic, y2v for pelvic), and the thoracic mass (x1v) and pelvic mass (x2v). The control point velocity time histories correspond to the accelerations shown in Fig. 3(a). (c) Thoracic compression (y1-x1), pelvic compression (y2-x2) and lumbar spine shear deformation (x2-x1) with the optimal solution. (d) Constrained responses normalized by their individual limits. z1-y1: space at thorax (limit: 10 cm); z2-y2: space at pelvis (limit: 10 cm); x1acc: thoracic mass acceleration (limit: 650 m/s2); f2: external pelvic load (limit: 8.8 kN). (e) thoracic control point force (f1) and pelvic control point force (f2) time history. (f) Thoracic control point force versus the relative motion between the impactor and the control point at thoracic location (f1) and pelvic location (f2).

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Fig. 4

(a) Velocity time history for impactor (z1v), the control points (y1v for thoracic, y2v for pelvic), and the thoracic mass (x1v) and pelvic mass (x2v). The control point velocity time histories correspond to the accelerations shown in Fig. 4(a). (b) Thoracic compression (y1-x1), pelvic compression (y2-x2) and lumbar spine shear deformation (x2-x1) with the optimal solution. (c) Constrained responses normalized by their individual limits. z1-y1: space at thorax (limit: 6 cm); z2-y2: space at pelvis (limit: 8 cm); x1acc: thoracic mass acceleration (limit: 650 m/s2); f2: external pelvic load (limit: 8.8 kN). All constraints are satisfied within numerical tolerances. (d) Thoracic control point force (f1) and pelvic control point force (f2) time history.

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Fig. 5

The minimum thoracic compression theoretically possible as a function of the allowable space. Initial velocity is as shown, and −14 g deceleration is assigned to the impactor.

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Fig. 6

(a) Control point acceleration time history (u1: thoracic control point; u2: pelvic control point). The 100 g limit on the accelerations is clearly reflected. (b) Control point velocity time history (y1v for thoracic, y2v for pelvic), and the thoracic mass (x1v) and pelvic mass (x2v). The control point velocity time histories correspond to the accelerations shown in Fig. 6(a). (c) Thoracic compression (y1-x1), pelvic compression (y2-x2) and lumbar spine shear deformation (x2-x1) with the optimal solution. (d) Constrained responses normalized by their individual limits. z1-y1: space at thorax (limit: 10 cm); z2-y2: space at pelvis (limit: 10 cm); x1acc: thoracic mass acceleration (limit: 650 m/s2); f2: external pelvic load (limit: 8.8 kN). (e) Thoracic control point force (f1) and pelvic control point force (f2) time history.

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