- Email: [email protected]
Analysis of human body dynamics in simulated rear-end impacts
Human Movement Science 17 (1998) 821±838
Analysis of human body dynamics in simulated rear-end impacts Shyh-Chour Huang
*
Department of Mechanical Engineering, National Kaohsiung Institute of Technology, 415 Chien Kung Road, Kaohsiung, Taiwan 807, ROC
Abstract The objective of this study is to simulate the dynamic response of the human body within a rear-end impacted vehicle. A nonlinear mathematical model of a human body and a restraint system has been formulated. The model consists of connected rigid bodies representing the torso and limbs of the human frame. Nonlinear springs and dampers are used at the connection joints to represent human anatomical characteristics and limits imposed by muscles, ligaments, and soft tissue. Equations of motion are written for this model by using Kane's equation and multibody dynamics analysis procedures developed by Huston. The equations are integrated numerically for a number of speci®c cases where experimental data are available. Results show excellent agreement between the model and the experiments. The results of several accident simulations are also presented. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Rear-end impacts; Human body model; Multibody system
*
Fax: 886 7 3110486; e-mail: [email protected]
0167-9457/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 9 4 5 7 ( 9 8 ) 0 0 0 3 0 - X
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S.-C. Huang / Human Movement Science 17 (1998) 821±838
1. Introduction Since the number of vehicles is increasing rapidly and since there are now more trac accidents than ever before, safety and cost play a signi®cant role in the manufacture of automobiles. In order to increase vehicle safety, many countries stipulate that all vehicles must meet national vehicle safety standards. Vehicle manufacturers must also consider vehicle safety issues, such as air bag, the Antilock Brake Systems, and seat and restraint systems. However, there are practical limits to the repeated use of destructive experiments to improve new devices, since such work entails high costs and large amounts of time. Therefore, there is a need for computer simulation to save the cost and time of developing products. Recently, there has been considerable discussion about the in¯uence of seatback and seat belts on occupant dynamics in rear-end impacts. In 1987, Collision Safety Engineering presented a report that indicates that seat belts play an important role in rear-end impacts. The report also showed that the belts decrease the incidence of any injury by 12% and reduce the incidence of serious injury by over 57% [1]. Warner et al. [2] also described how the controversy over seats can be classi®ed into two types: One suggests that rigid seats are better because they provide a better constraint for occupant. The other argument maintains that a yielding seat is better than rigid one because it can absorb energy to protect the occupant. In 1992, Viano [3] indicated that when the seatback angle increases rapidly the probability of injury also increase. Most studies of the factors associated with injury in rear-end impacts indicate that the following factors signi®cantly aect the incidence of neck injury: (a) head displacement, rotation and acceleration; (b) the relative velocity between head and torso; (c) the occupant ramping up the seatback; and (d) the rebounding phenomenon. In 1993, Svensson et al. [4] indicated that the angular displacement between the head and the chest is generally larger for rear-seats than frontseats. McConnell et al. [5] showed that although the traditional whiplash neck response to rear-end impacts and the widely accepted hyperextension or hyper¯ection cervical injury mechanism have been extensively written about, the reason why whiplash occurs is still unknown. Compared to other experiments, this research, which used real people as subjects, found that all the subjects have light neck injury after lower velocity rear-end impact. There have been a number of noteworthy eorts to obtain numerical simulation of vehicle accident victim dynamics. Among these are the works of McHenry [6], McHenry and Naab [7], Young [8], Robbins et al. [9],
S.-C. Huang / Human Movement Science 17 (1998) 821±838
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Huston et al. [10], Karnes et al. [11], Fleck [12], Huston et al. [13], Wismans et al. [14], Prasad [15], Wismans and Hermans [16] and Huang [17]. But all these works did not discuss about rear-end impact environment. In this paper, an attempt is made to use the computer to investigate the dynamic response of the occupant during automobile rear-end impacts. The procedure uses a ®nite segment human body model seated in an accelerating vehicle. The model consists of a ®nite-segment representation of the occupant, together with the restraint system (seat and belts). The occupant model consists of 15 rigid bodies representing the torso and limbs of the human frame. Nonlinear springs and dampers are used at the connection joints to represent human anatomical characteristics and limits imposed by muscles, ligaments, and soft tissue. Equations of motion are written for this model by using Kane's equation [18] and multibody dynamics analysis procedures developed by Huston et al. [19]. The paper is divided into ®ve parts. Sections 2 and 3 provide a brief description of the biodynamic model and the analysis procedures. Section 4 brie¯y describes the speci®c features of the computer code, with veri®cation and some illustrative applications of occupant dynamics under various rearend impacts environment presented in Section 5. Section 6 provides a discussion and concluding remarks. 2. The biodynamic model The model developed in this study can be used to analyze rear-end impact situations. The seatback, and headrest constraints were applied to the model to simulate rear-end impact dynamic environment. This model consists of three submodels. They are the human body model, the contact model and the restraint belts model. 1. Human body model: The human body model consists of 15 rigid bodies representing the torso, the head, the neck, the feet and the upper and lower arms and legs. It is a three-dimensional model with ball-and-socket joints except for the elbows and knees which were modeled as hinge joints (Table 1). The ball-and-socket joint is described by three relative orientation variables, and the hinge joint by one rotational variable. These joints are provided with damping restraints to limit joint angle rotations. The motion of each joint is simulated by spring and damper to simulate the behavior of the soft tissue (muscle and tendon). A representation of this model is given in Fig. 1.
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Table 1 Type of joint used for the model Joint
Type of joint
B2 ±B3 B3 ±B4 B4 ±B5 B5 ±B6 B4 ±B7 B7 ±B8 B4 ±B9 B9 ±B10 B2 ±B11 B11 ±B12 B12 ±B13 B2 ±B14 B14 ±B15 B15 ±B16
Ball-and-socket Ball-and-socket Ball-and-socket Hinge Ball-and-socket Hinge Ball-and-socket Ball-and-socket Ball-and-socket Hinge Hinge Ball-and-socket Hinge Hinge
2. Contact model: Human body's interaction with constraint planes, modeled on a series planes that represent headrest and seatback (Fig. 2), is sensed by body segments. The reaction forces on the bodysegments are generated as a function of the penetration of the segments into the contact planes. In the model the generated load of this contact can be expressed by a constraint force and an equivalent moment acting on the mass center of the colliding body. The contact model has two basic contact routines. They are damping force and spring force. (a) Damping force: The relative velocity vector v between the contacting segment and the contact point can be resolved into tangential component Dvt and normal component Dvn as shown in Fig. 3. The damping force Fd is de®ned as Fd c Dvn ; 1 where c is the damping coecient. When the body crosses an intrusion plane that is in loading condition (increasing penetration), damping force is employed in the direction opposite to the velocity of the body relative to the plane. In the case of unloading condition (decreasing penetration) no damping force is acted to the contacting body. (b) Spring force: Spring routine using the force de¯ection characteristics computes the spring force Fs as a function of the penetration displacement
S.-C. Huang / Human Movement Science 17 (1998) 821±838
825
Fig. 1. Human body model.
and the stiness characteristics and apply the corresponding spring force and equivalent moment to the contacting segment. Spring force Fs is divided into two parts, normal constraint force (normal to intrusion surface) and friction force (parallel to intrusion surface in the direction opposite to the relative velocity component Dvt ) as shown in Fig. 4. The equivalent torque Te is generated by the cross product of the distance r (from mass center of the contacting segment to contact point) and the spring force. They can be expressed in equations in the following: Fs Fn un lFn ut ;
2
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S.-C. Huang / Human Movement Science 17 (1998) 821±838
Fig. 2. The con®guration of the seatback and headrest model.
Fig. 3. The relative velocity resolved into two components (p:contact point).
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Fig. 4. The spring force resolved into two components (p:contact point, g:mass center).
Te r Fs ; 3 where un represents the normal unit vector of the intrusion plane, ut is the unit vector of velocity component which is parallel to the intrusion plane, and l is the coecient of coulomb friction. Fn is the constraint force normal to the intrusion plane which incorporates by a nonlinear spring force and hysteretic eect. Fn can be modeled as: (i) Loading (Xp > 0 and v á un > 0) ( for Xp < S; K0 Xp Fn 4 2 K0 Xp K1 S ÿ Xp for Xp > S; (ii) Unloading (Xp > 0 and v á un < 0) ( H K0 Xp for Xp < S; Fn 3 H K0 Xp K2 S ÿ Xp for Xp > S;
5
H 1 ÿ E; 6 where Xp is the penetration displacement of the intrusion surface from collision point, H the ratio of unloading Fn to loading Fn in linear region, E the energy dissipation index, S the separation point for the linear and nonlinear stiness, K0 , K1 and K2 are the stiness parameters. In this paper the contact stiness K0 and K1 , listed in Table 2, are based on the data provided in Ref. [20]. K2 can be expressed by the following equation.
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Table 2 Contact parameters between body segments and planes Plane
K0 (N/m)
K1 (N/m2 )
S(m)
E
l
Seat pan Seatback
48 570 48 570
32 246 220 32 246 220
0.02 0.06
0.56 0.56
0.65 0.65
Fig. 5. The con®guration of the restraint belt.
K2 1 ÿ H K0 Smax K1 Smax ÿ S2 = Smax ÿ S3 ; 7 where Smax is the maximum penetration. 3. Restraint belts model: The restrainted belts (Fig. 5) are modeled as spring that can be attached between speci®ed points in the vehicle frame and the bodies of the human model. Each belt length from the point in the body
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to the point in the vehicle frame is calculated separately. In the current version belts can be used to simulate lap and shoulder belts. 3. Description of the analysis procedures The human body model of Fig. 1 is a multibody system. To simulate an accident victim, the model is regarded as being seated relative to a vehicle frame, which in turn is regarded as moving relative to an inertial frame. As such it may be studied using Kane's equations [18] and Huston method [19] for the analysis of such systems. With Kane's equations non-working constraint forces between adjoining bodies are automatically eliminated in the analysis. Tedious calculation of derivatives of scalar energy functions is avoided. Moreover the equations are in a form which is ideally suited for automated numerical development and solution. The following sections present an outline of a procedure for using Kane's equations and Huston method with the model. 1. Kinematics: For the model of Fig. 1, there are 54 variables that describe the position and orientation of the model: 6 for the translation and rotation of vehicle frame in the inertial frame, 6 for the movement of B2 in the vehicle frame, and 42 for the orientations of the remaining 14 bodies relative to their adjacent lower numbered bodies. Since the hinge joints are used to simulate the elbows, knees, and ankles, the degrees of freedom are reduced by 12, leaving 42 degrees of freedom. Let the variables xb b 1; . . . ; 42 be generalized coordinates that describe these degrees of freedom. The angular velocities of the kth body and the velocities of their mass centers, in an inertial reference frame R, may be expressed in the form: vk vkbm x_ b nom and xk xkbm x_ b nom ; 8 where the vkbm and the xkbm are components of the partial velocity and partial angular velocity array as de®ned by Kane [18]. The nom (m 1±3) are mutually perpendicular unit vectors ®xed in R. By dierentiating both Eq. (8) the mass center accelerations of the bodies and their angular accelerations may be expressed as ak vkbmxb v_ kbm x_ b nom and ak xkbmxb x_ kbm x_ b nom : 9 2. Kinetics: Let the model be subjected to applied forces from gravity and from contact with the seatback, seat belts, and headrest, all of which may be represented on a typical body Bk by a force Fk passing through the mass
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center Gk of the body together with a couple having torque Tk . Then the generalized applied force Fb for the coordinate xb may be expressed as Fb vkbm Fkm xkbm Tkm
10
where Fkm and Tkm are the nom components of Fk and Tk . Similarly, let the inertia forces on the model be represented on Bk by a force Fk passing through Gk , together with a couple having torque Tk . Then the generalized inertia force for the generalized coordinate xb may be expressed as: Fb vkbm Fkm xkbm Tkm ; Fkm
where see that
and Tkm are the nom components Fk and Tk may be expressed as:
11 of
Fk ÿmk ak ;
Fk
and
Tk .
From Kane [18], we 12
13 Tk ÿI k ak ÿ xk I k xk ; where mk is the mass of Bk and Ik is the central inertia dyadic of Bk . Finally, Kane's equations state that the sum of the generalized applied and inertia forces is 0 for each coordinate xb . That is, Fb Fb 0
b 1; 2; . . . ; 42:
14
By substituting from Eqs. (8)±(13), the governing equations of motion, Eq. (14) of the system may be expressed as abqxq fb ;
15
where the abq and fb (b,q 1,. . .,42) [19] are: abq mk vkbm vkqm Ikmn xkbm xkqn ;
16
fb Fb ÿ mk vkbm v_ kpm x_ p Ikmn xkbm x_ kpn x_ p ersm xkbm xkqr xkpn Iksn x_ q x_ p ; 17 where the Iksn are the nom components of Ik and where ersm is the permutation symbol. 4. Computer code Eq. (15) forms a set of 42 simultaneous ®rst-order ordinary dierential equations determining the 42 generalized coordinates of the system. Since
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the coecients abq and fb of these equations are algebraic functions of the physical parameters and the generalized coordinates, the equations are in a form that is ideally suited for numerical integration. Once these equations of motion are developed the governing equations can be solved numerically using a fourth-order Runge±Kutta integration routine. The numerical simulation model by the analysis code contains the following information. (a) Physical data for the bodies of the human body model. Such data consist of the masses and inertia matrices of the bodies, the local components of the vectors locating their mass centers and their connection joints. (b) Physical data for the seat belt attachment. Such data consist of the local coordinates of the attachment points of the belts in the vehicle and on the human model, and the elastic/plastic properties of the webbing. (c) Geometric data de®ning the structure of the vehicle interior (the cockpit intrusion planes). (d) Kinematic data de®ning the vehicle motion (acceleration pro®le). The output consists of a time history of the position, velocity, and acceleration pro®les of the connecting joints and the mass centers of the bodies of the human body model. This data is expressed relative to both the inertial frame R and the vehicle frame B1 . The integration also determines the forces in the seat belt webbing. 5. Veri®cation and examples In the ®rst stage of this study, a three-dimensional multibody system simulator for rear-end crash environment was developed. There is little experimental data available to date which can be used to check or verify the proceeding mathematical model and others like it. However, an attempt at veri®cation was made for some data gathered by Viano [3]. The rear-end impact tests were conducted on the General Motors Research Laboratories Hyge Sled using a range of impact severities from 4.2±9.6 m/s change in velocity simulating rear-end impact. An automotive bucket seat modi®ed for an initial angle of 9°, 22° or 35° from the vertical. In all cases a loosely attached lap-belt was used to prevent the dummy from entirely leaving the seat structure should rideup of the seatback occur. The chest and neck extension angles were measured. These angles then were calculated using the model
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Fig. 6. Comparison of simulative and experimental rotation-time histories for the chest (seatback angle ± 9°, 10g).
Fig. 7. Comparison of simulative and experimental rotation-time histories for the chest (seatback angle ± 22°, 10g).
with approximately input, seatback structure and restraint belt con®guration. A comparison of the results is shown in Figs. 6±11. From the comparisons we can see that both the peak values and the general shapes of the simulation curves agree with the experimental data. In the examples we examine the response of occupant dynamics during a rear-end crash environment. The constraint planes used in these examples were the headrest, seatback. Two dierent examples were considered: (1) the eects of velocity upon head and chest accelerations were computed; the input data were modeled by using an initial velocity equal to 4.2, 6.4 and 9.6 m/s with initial seatback set at angle 22° from vertical.
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Fig. 8. Comparison of simulative and experimental rotation-time histories for the chest (seatback angle ± 35°, 10g).
Fig. 9. Comparison of simulative and experimental rotation-time histories for the neck (seatback angle ± 9°, 10g).
Fig. 10. Comparison of simulative and experimental rotation-time histories for the neck (seatback angle ± 22°, 10g).
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Fig. 11. Comparison of simulative and experimental rotation-time histories for the neck (seatback angle ± 35°, 10g).
(2) the eects of seatback angle upon the head rotation relative to chest were computed (case1: with headrest; case2: without headrest); the input data were modeled by using an initial seatback angle of 9°, 22° and 35° from vertical with initial velocity equaled 4.2 m/s. In the ®rst example, the results are shown in Figs. 12 and 13. We can see that with ®xed seatback angle, the accelerations of head and chest increase with the increase in velocity. This increased acceleration signi®cantly ag-
Fig. 12. Head acceleration for increasing velocity with ®x seatback angle (22°).
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Fig. 13. Chest acceleration for increasing velocity with ®x seatback angle (22°).
Fig. 14. Head rotation relative to chest for increasing seatback angle with ®x velocity (4.2 m/s, with headrest).
gravates a dynamic force of head and chest. In the second example, for case 1 (with headrest), the results are shown in Fig. 14. From the ®gure, we can see that with ®xed velocity, the relative rotations of head to chest increase with the decreasing of the angle of the seatback. In this case the maximum relative rotations of head to chest in 35°, 22° and 9° are separately 16°, 30.2° and 39.8°. For case 2 (without headrest), in Fig. 15, the maximum relative
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Fig. 15. Head rotation relative to chest for increasing seatback angle with ®x velocity (4.2 m/s, without headrest).
rotations of head to chest in 35°, 22° and 9° are separately 51.9°, 51.6° and 40.6°. 6. Conclusion The results of this analysis are consistent with those developed experimentally, numerically, and empirically. They also show that the velocity and the seatback angle are two important factors that aect human injuries during vehicle rear-end impact. Next, the results clearly illustrate a whiplash eect of seat angle and headrest (Figs. 14 and 15). When such impacts occur, lap belts eciently prevent the occupant sliding upward along the seatback. Although the whiplash injury is not well understood now, it is the major reason for occupants injury. The results also show that it is possible to build a reliable multibody system simulation model of rear-end impact crash vehicle occupants and the advantages of using multibody dynamics procedures in studying the kinematics and dynamics of vehicle rear-end impact crash victims. Nevertheless, the unrealistic conditions of anthropomorphic structure must be considered before these simulations can be projected into real life situations. It appears that future work will include re®nements of the model. Application of the model in the design of vehicle interior and safety devices is clear but is yet to be developed.
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Acknowledgements The author would like to express gratitude to the National Science Council of the Republic of China for ®nancial aid under grants NSC 86-2213-E-151005. References [1] M.B. James, C.E. Strother, C.Y. Warner, R.L. Decker, T.R. Perl, Occupant protection in rearend collisions: I. Safety priorities and seat belt eectiveness, SAE Paper 912913, 1991, pp. 2019± 2027. [2] C.Y. Warner, C.E. Strother, M.B. James, R.L. Decker, Occupant protection in rear-end collisions: II. The role of seat back deformation in injury reduction, SAE Paper 912914, 1991, pp. 2028±2039. [3] D.C. Viano, In¯uence of seatback angle on occupant dynamics in simulated rear-end impacts, SAE Paper 922521, 1992, pp. 157±164. [4] M.Y. Svensson, P. Lovsund, Y. Haland, S. Larson, Rear-end collisions ± A study of the in¯uence of backrest properties on head-neck motion using a new dummy neck, SAE paper 930343, 1993. [5] W.E. McConnell, R.P. Howard, H.M. Guzman, Analysis of human test subject kinematic responses to low velocity rear end impacts, SAE Paper 930889, 1993, pp. 21±30. [6] R.R. McHenry, Analysis of the dynamics of automobile passenger restraint systems, in: Proceedings of The Seventh Stapp Car Crash Conference, 1963, pp. 207±249. [7] R.R. McHenry, K.N. Naab, Computer simulation of the crash victim ± A validation study, in: Proceedings of The Tenth Stapp Car Crash Conference, 1966, pp. 126±163. [8] R.D. Young, A three-dimensional mathematical model of an automobile passenger, Research Report 140-2, Texas Transportation Institute, Texas A & M University, College Station, Texas, 1970 (National Technical Information Service Report PB 197 159). [9] D.H. Robbins, R.O. Bennett, B.M. Bowman, User oriented mathematical crash victim simulator, in: Proceedings of The 16th Stapp Car Crash Conference, 1972, pp. 128±148. [10] R.L. Huston, R.E. Hessel, C.E. Passerello, A three-dimensional vehicle-man model for collision and high acceleration studies, SAE 740275, 1974. [11] R.N. Karnes, J.L. Tocher, D.W. Twigg, PROMETHEUS ± A crash victim simulation, in: K. Saczalski, G.T. Singley III, W. Pilkey, R.L. Huston (Eds.), Aircraft Crashworthiness, University Press of Virginia, Charlottesville, VA, 1975, pp. 327±345. [12] J.T. Fleck, CALSPAN 3-D crash victim simulation program, in: K. Saczalski, G.T. Singley III, W. Pilkey, R.L. Huston (Eds.), Aircraft Crashworthiness, University Press of Virginia, Charlottesville, VA, 1975, pp. 229±310. [13] R.L. Huston, R.E. Hessel, J.M. Winget, Dynamics of a crash victim ± A ®nite segment model, Paper presented at the AIAA, ASME, SAE Structure, Structural Dynamics and Materials Conference, Denver, USA, 1975. [14] J. Wismans, T. Hoen, Wittebrood, Status of the MADYMO crash victim simulation program, Paper presented at The Tenth International Conference on Experimental Safety Vehicles, Oxford, England, UK, 1985. [15] P. Prasad, MADYMO 2D simulation of sled tests, SAE Paper 880640, 1988. [16] J. Wismans, J.H.A. Hermans, MADYMO 3D simulation of Hybrid III dummy sled tests, SAE 880645, 1988. [17] S.C. Huang, Biomechanical modeling and simulations of automobile crash victims, Computers and Structures 57 (3) (1995) 541±549.
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[18] T.R. Kane, Dynamics of nonholonomic systems, Journal of Applied Mechanics 28 (1961) 574±578. [19] R.L. Huston, C.E. Passerello, M.W. Harlow, Dynamics of multirigid-body systems, ASME Journal of Applied Mechanics 45 (4) (1978) 889±894. [20] P. Prasad, Sled testing of Hybrid III, SAE 880637, 1988.
Analysis of human body dynamics in simulated rear-end impacts Shyh-Chour Huang
*
Department of Mechanical Engineering, National Kaohsiung Institute of Technology, 415 Chien Kung Road, Kaohsiung, Taiwan 807, ROC
Abstract The objective of this study is to simulate the dynamic response of the human body within a rear-end impacted vehicle. A nonlinear mathematical model of a human body and a restraint system has been formulated. The model consists of connected rigid bodies representing the torso and limbs of the human frame. Nonlinear springs and dampers are used at the connection joints to represent human anatomical characteristics and limits imposed by muscles, ligaments, and soft tissue. Equations of motion are written for this model by using Kane's equation and multibody dynamics analysis procedures developed by Huston. The equations are integrated numerically for a number of speci®c cases where experimental data are available. Results show excellent agreement between the model and the experiments. The results of several accident simulations are also presented. Ó 1998 Elsevier Science B.V. All rights reserved. Keywords: Rear-end impacts; Human body model; Multibody system
*
Fax: 886 7 3110486; e-mail: [email protected]
0167-9457/98/$19.00 Ó 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 9 4 5 7 ( 9 8 ) 0 0 0 3 0 - X
822
S.-C. Huang / Human Movement Science 17 (1998) 821±838
1. Introduction Since the number of vehicles is increasing rapidly and since there are now more trac accidents than ever before, safety and cost play a signi®cant role in the manufacture of automobiles. In order to increase vehicle safety, many countries stipulate that all vehicles must meet national vehicle safety standards. Vehicle manufacturers must also consider vehicle safety issues, such as air bag, the Antilock Brake Systems, and seat and restraint systems. However, there are practical limits to the repeated use of destructive experiments to improve new devices, since such work entails high costs and large amounts of time. Therefore, there is a need for computer simulation to save the cost and time of developing products. Recently, there has been considerable discussion about the in¯uence of seatback and seat belts on occupant dynamics in rear-end impacts. In 1987, Collision Safety Engineering presented a report that indicates that seat belts play an important role in rear-end impacts. The report also showed that the belts decrease the incidence of any injury by 12% and reduce the incidence of serious injury by over 57% [1]. Warner et al. [2] also described how the controversy over seats can be classi®ed into two types: One suggests that rigid seats are better because they provide a better constraint for occupant. The other argument maintains that a yielding seat is better than rigid one because it can absorb energy to protect the occupant. In 1992, Viano [3] indicated that when the seatback angle increases rapidly the probability of injury also increase. Most studies of the factors associated with injury in rear-end impacts indicate that the following factors signi®cantly aect the incidence of neck injury: (a) head displacement, rotation and acceleration; (b) the relative velocity between head and torso; (c) the occupant ramping up the seatback; and (d) the rebounding phenomenon. In 1993, Svensson et al. [4] indicated that the angular displacement between the head and the chest is generally larger for rear-seats than frontseats. McConnell et al. [5] showed that although the traditional whiplash neck response to rear-end impacts and the widely accepted hyperextension or hyper¯ection cervical injury mechanism have been extensively written about, the reason why whiplash occurs is still unknown. Compared to other experiments, this research, which used real people as subjects, found that all the subjects have light neck injury after lower velocity rear-end impact. There have been a number of noteworthy eorts to obtain numerical simulation of vehicle accident victim dynamics. Among these are the works of McHenry [6], McHenry and Naab [7], Young [8], Robbins et al. [9],
S.-C. Huang / Human Movement Science 17 (1998) 821±838
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Huston et al. [10], Karnes et al. [11], Fleck [12], Huston et al. [13], Wismans et al. [14], Prasad [15], Wismans and Hermans [16] and Huang [17]. But all these works did not discuss about rear-end impact environment. In this paper, an attempt is made to use the computer to investigate the dynamic response of the occupant during automobile rear-end impacts. The procedure uses a ®nite segment human body model seated in an accelerating vehicle. The model consists of a ®nite-segment representation of the occupant, together with the restraint system (seat and belts). The occupant model consists of 15 rigid bodies representing the torso and limbs of the human frame. Nonlinear springs and dampers are used at the connection joints to represent human anatomical characteristics and limits imposed by muscles, ligaments, and soft tissue. Equations of motion are written for this model by using Kane's equation [18] and multibody dynamics analysis procedures developed by Huston et al. [19]. The paper is divided into ®ve parts. Sections 2 and 3 provide a brief description of the biodynamic model and the analysis procedures. Section 4 brie¯y describes the speci®c features of the computer code, with veri®cation and some illustrative applications of occupant dynamics under various rearend impacts environment presented in Section 5. Section 6 provides a discussion and concluding remarks. 2. The biodynamic model The model developed in this study can be used to analyze rear-end impact situations. The seatback, and headrest constraints were applied to the model to simulate rear-end impact dynamic environment. This model consists of three submodels. They are the human body model, the contact model and the restraint belts model. 1. Human body model: The human body model consists of 15 rigid bodies representing the torso, the head, the neck, the feet and the upper and lower arms and legs. It is a three-dimensional model with ball-and-socket joints except for the elbows and knees which were modeled as hinge joints (Table 1). The ball-and-socket joint is described by three relative orientation variables, and the hinge joint by one rotational variable. These joints are provided with damping restraints to limit joint angle rotations. The motion of each joint is simulated by spring and damper to simulate the behavior of the soft tissue (muscle and tendon). A representation of this model is given in Fig. 1.
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Table 1 Type of joint used for the model Joint
Type of joint
B2 ±B3 B3 ±B4 B4 ±B5 B5 ±B6 B4 ±B7 B7 ±B8 B4 ±B9 B9 ±B10 B2 ±B11 B11 ±B12 B12 ±B13 B2 ±B14 B14 ±B15 B15 ±B16
Ball-and-socket Ball-and-socket Ball-and-socket Hinge Ball-and-socket Hinge Ball-and-socket Ball-and-socket Ball-and-socket Hinge Hinge Ball-and-socket Hinge Hinge
2. Contact model: Human body's interaction with constraint planes, modeled on a series planes that represent headrest and seatback (Fig. 2), is sensed by body segments. The reaction forces on the bodysegments are generated as a function of the penetration of the segments into the contact planes. In the model the generated load of this contact can be expressed by a constraint force and an equivalent moment acting on the mass center of the colliding body. The contact model has two basic contact routines. They are damping force and spring force. (a) Damping force: The relative velocity vector v between the contacting segment and the contact point can be resolved into tangential component Dvt and normal component Dvn as shown in Fig. 3. The damping force Fd is de®ned as Fd c Dvn ; 1 where c is the damping coecient. When the body crosses an intrusion plane that is in loading condition (increasing penetration), damping force is employed in the direction opposite to the velocity of the body relative to the plane. In the case of unloading condition (decreasing penetration) no damping force is acted to the contacting body. (b) Spring force: Spring routine using the force de¯ection characteristics computes the spring force Fs as a function of the penetration displacement
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Fig. 1. Human body model.
and the stiness characteristics and apply the corresponding spring force and equivalent moment to the contacting segment. Spring force Fs is divided into two parts, normal constraint force (normal to intrusion surface) and friction force (parallel to intrusion surface in the direction opposite to the relative velocity component Dvt ) as shown in Fig. 4. The equivalent torque Te is generated by the cross product of the distance r (from mass center of the contacting segment to contact point) and the spring force. They can be expressed in equations in the following: Fs Fn un lFn ut ;
2
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Fig. 2. The con®guration of the seatback and headrest model.
Fig. 3. The relative velocity resolved into two components (p:contact point).
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Fig. 4. The spring force resolved into two components (p:contact point, g:mass center).
Te r Fs ; 3 where un represents the normal unit vector of the intrusion plane, ut is the unit vector of velocity component which is parallel to the intrusion plane, and l is the coecient of coulomb friction. Fn is the constraint force normal to the intrusion plane which incorporates by a nonlinear spring force and hysteretic eect. Fn can be modeled as: (i) Loading (Xp > 0 and v á un > 0) ( for Xp < S; K0 Xp Fn 4 2 K0 Xp K1 S ÿ Xp for Xp > S; (ii) Unloading (Xp > 0 and v á un < 0) ( H K0 Xp for Xp < S; Fn 3 H K0 Xp K2 S ÿ Xp for Xp > S;
5
H 1 ÿ E; 6 where Xp is the penetration displacement of the intrusion surface from collision point, H the ratio of unloading Fn to loading Fn in linear region, E the energy dissipation index, S the separation point for the linear and nonlinear stiness, K0 , K1 and K2 are the stiness parameters. In this paper the contact stiness K0 and K1 , listed in Table 2, are based on the data provided in Ref. [20]. K2 can be expressed by the following equation.
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Table 2 Contact parameters between body segments and planes Plane
K0 (N/m)
K1 (N/m2 )
S(m)
E
l
Seat pan Seatback
48 570 48 570
32 246 220 32 246 220
0.02 0.06
0.56 0.56
0.65 0.65
Fig. 5. The con®guration of the restraint belt.
K2 1 ÿ H K0 Smax K1 Smax ÿ S2 = Smax ÿ S3 ; 7 where Smax is the maximum penetration. 3. Restraint belts model: The restrainted belts (Fig. 5) are modeled as spring that can be attached between speci®ed points in the vehicle frame and the bodies of the human model. Each belt length from the point in the body
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to the point in the vehicle frame is calculated separately. In the current version belts can be used to simulate lap and shoulder belts. 3. Description of the analysis procedures The human body model of Fig. 1 is a multibody system. To simulate an accident victim, the model is regarded as being seated relative to a vehicle frame, which in turn is regarded as moving relative to an inertial frame. As such it may be studied using Kane's equations [18] and Huston method [19] for the analysis of such systems. With Kane's equations non-working constraint forces between adjoining bodies are automatically eliminated in the analysis. Tedious calculation of derivatives of scalar energy functions is avoided. Moreover the equations are in a form which is ideally suited for automated numerical development and solution. The following sections present an outline of a procedure for using Kane's equations and Huston method with the model. 1. Kinematics: For the model of Fig. 1, there are 54 variables that describe the position and orientation of the model: 6 for the translation and rotation of vehicle frame in the inertial frame, 6 for the movement of B2 in the vehicle frame, and 42 for the orientations of the remaining 14 bodies relative to their adjacent lower numbered bodies. Since the hinge joints are used to simulate the elbows, knees, and ankles, the degrees of freedom are reduced by 12, leaving 42 degrees of freedom. Let the variables xb b 1; . . . ; 42 be generalized coordinates that describe these degrees of freedom. The angular velocities of the kth body and the velocities of their mass centers, in an inertial reference frame R, may be expressed in the form: vk vkbm x_ b nom and xk xkbm x_ b nom ; 8 where the vkbm and the xkbm are components of the partial velocity and partial angular velocity array as de®ned by Kane [18]. The nom (m 1±3) are mutually perpendicular unit vectors ®xed in R. By dierentiating both Eq. (8) the mass center accelerations of the bodies and their angular accelerations may be expressed as ak vkbmxb v_ kbm x_ b nom and ak xkbmxb x_ kbm x_ b nom : 9 2. Kinetics: Let the model be subjected to applied forces from gravity and from contact with the seatback, seat belts, and headrest, all of which may be represented on a typical body Bk by a force Fk passing through the mass
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center Gk of the body together with a couple having torque Tk . Then the generalized applied force Fb for the coordinate xb may be expressed as Fb vkbm Fkm xkbm Tkm
10
where Fkm and Tkm are the nom components of Fk and Tk . Similarly, let the inertia forces on the model be represented on Bk by a force Fk passing through Gk , together with a couple having torque Tk . Then the generalized inertia force for the generalized coordinate xb may be expressed as: Fb vkbm Fkm xkbm Tkm ; Fkm
where see that
and Tkm are the nom components Fk and Tk may be expressed as:
11 of
Fk ÿmk ak ;
Fk
and
Tk .
From Kane [18], we 12
13 Tk ÿI k ak ÿ xk I k xk ; where mk is the mass of Bk and Ik is the central inertia dyadic of Bk . Finally, Kane's equations state that the sum of the generalized applied and inertia forces is 0 for each coordinate xb . That is, Fb Fb 0
b 1; 2; . . . ; 42:
14
By substituting from Eqs. (8)±(13), the governing equations of motion, Eq. (14) of the system may be expressed as abqxq fb ;
15
where the abq and fb (b,q 1,. . .,42) [19] are: abq mk vkbm vkqm Ikmn xkbm xkqn ;
16
fb Fb ÿ mk vkbm v_ kpm x_ p Ikmn xkbm x_ kpn x_ p ersm xkbm xkqr xkpn Iksn x_ q x_ p ; 17 where the Iksn are the nom components of Ik and where ersm is the permutation symbol. 4. Computer code Eq. (15) forms a set of 42 simultaneous ®rst-order ordinary dierential equations determining the 42 generalized coordinates of the system. Since
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the coecients abq and fb of these equations are algebraic functions of the physical parameters and the generalized coordinates, the equations are in a form that is ideally suited for numerical integration. Once these equations of motion are developed the governing equations can be solved numerically using a fourth-order Runge±Kutta integration routine. The numerical simulation model by the analysis code contains the following information. (a) Physical data for the bodies of the human body model. Such data consist of the masses and inertia matrices of the bodies, the local components of the vectors locating their mass centers and their connection joints. (b) Physical data for the seat belt attachment. Such data consist of the local coordinates of the attachment points of the belts in the vehicle and on the human model, and the elastic/plastic properties of the webbing. (c) Geometric data de®ning the structure of the vehicle interior (the cockpit intrusion planes). (d) Kinematic data de®ning the vehicle motion (acceleration pro®le). The output consists of a time history of the position, velocity, and acceleration pro®les of the connecting joints and the mass centers of the bodies of the human body model. This data is expressed relative to both the inertial frame R and the vehicle frame B1 . The integration also determines the forces in the seat belt webbing. 5. Veri®cation and examples In the ®rst stage of this study, a three-dimensional multibody system simulator for rear-end crash environment was developed. There is little experimental data available to date which can be used to check or verify the proceeding mathematical model and others like it. However, an attempt at veri®cation was made for some data gathered by Viano [3]. The rear-end impact tests were conducted on the General Motors Research Laboratories Hyge Sled using a range of impact severities from 4.2±9.6 m/s change in velocity simulating rear-end impact. An automotive bucket seat modi®ed for an initial angle of 9°, 22° or 35° from the vertical. In all cases a loosely attached lap-belt was used to prevent the dummy from entirely leaving the seat structure should rideup of the seatback occur. The chest and neck extension angles were measured. These angles then were calculated using the model
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Fig. 6. Comparison of simulative and experimental rotation-time histories for the chest (seatback angle ± 9°, 10g).
Fig. 7. Comparison of simulative and experimental rotation-time histories for the chest (seatback angle ± 22°, 10g).
with approximately input, seatback structure and restraint belt con®guration. A comparison of the results is shown in Figs. 6±11. From the comparisons we can see that both the peak values and the general shapes of the simulation curves agree with the experimental data. In the examples we examine the response of occupant dynamics during a rear-end crash environment. The constraint planes used in these examples were the headrest, seatback. Two dierent examples were considered: (1) the eects of velocity upon head and chest accelerations were computed; the input data were modeled by using an initial velocity equal to 4.2, 6.4 and 9.6 m/s with initial seatback set at angle 22° from vertical.
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Fig. 8. Comparison of simulative and experimental rotation-time histories for the chest (seatback angle ± 35°, 10g).
Fig. 9. Comparison of simulative and experimental rotation-time histories for the neck (seatback angle ± 9°, 10g).
Fig. 10. Comparison of simulative and experimental rotation-time histories for the neck (seatback angle ± 22°, 10g).
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Fig. 11. Comparison of simulative and experimental rotation-time histories for the neck (seatback angle ± 35°, 10g).
(2) the eects of seatback angle upon the head rotation relative to chest were computed (case1: with headrest; case2: without headrest); the input data were modeled by using an initial seatback angle of 9°, 22° and 35° from vertical with initial velocity equaled 4.2 m/s. In the ®rst example, the results are shown in Figs. 12 and 13. We can see that with ®xed seatback angle, the accelerations of head and chest increase with the increase in velocity. This increased acceleration signi®cantly ag-
Fig. 12. Head acceleration for increasing velocity with ®x seatback angle (22°).
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Fig. 13. Chest acceleration for increasing velocity with ®x seatback angle (22°).
Fig. 14. Head rotation relative to chest for increasing seatback angle with ®x velocity (4.2 m/s, with headrest).
gravates a dynamic force of head and chest. In the second example, for case 1 (with headrest), the results are shown in Fig. 14. From the ®gure, we can see that with ®xed velocity, the relative rotations of head to chest increase with the decreasing of the angle of the seatback. In this case the maximum relative rotations of head to chest in 35°, 22° and 9° are separately 16°, 30.2° and 39.8°. For case 2 (without headrest), in Fig. 15, the maximum relative
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Fig. 15. Head rotation relative to chest for increasing seatback angle with ®x velocity (4.2 m/s, without headrest).
rotations of head to chest in 35°, 22° and 9° are separately 51.9°, 51.6° and 40.6°. 6. Conclusion The results of this analysis are consistent with those developed experimentally, numerically, and empirically. They also show that the velocity and the seatback angle are two important factors that aect human injuries during vehicle rear-end impact. Next, the results clearly illustrate a whiplash eect of seat angle and headrest (Figs. 14 and 15). When such impacts occur, lap belts eciently prevent the occupant sliding upward along the seatback. Although the whiplash injury is not well understood now, it is the major reason for occupants injury. The results also show that it is possible to build a reliable multibody system simulation model of rear-end impact crash vehicle occupants and the advantages of using multibody dynamics procedures in studying the kinematics and dynamics of vehicle rear-end impact crash victims. Nevertheless, the unrealistic conditions of anthropomorphic structure must be considered before these simulations can be projected into real life situations. It appears that future work will include re®nements of the model. Application of the model in the design of vehicle interior and safety devices is clear but is yet to be developed.
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Acknowledgements The author would like to express gratitude to the National Science Council of the Republic of China for ®nancial aid under grants NSC 86-2213-E-151005. References [1] M.B. James, C.E. Strother, C.Y. Warner, R.L. Decker, T.R. Perl, Occupant protection in rearend collisions: I. Safety priorities and seat belt eectiveness, SAE Paper 912913, 1991, pp. 2019± 2027. [2] C.Y. Warner, C.E. Strother, M.B. James, R.L. Decker, Occupant protection in rear-end collisions: II. The role of seat back deformation in injury reduction, SAE Paper 912914, 1991, pp. 2028±2039. [3] D.C. Viano, In¯uence of seatback angle on occupant dynamics in simulated rear-end impacts, SAE Paper 922521, 1992, pp. 157±164. [4] M.Y. Svensson, P. Lovsund, Y. Haland, S. Larson, Rear-end collisions ± A study of the in¯uence of backrest properties on head-neck motion using a new dummy neck, SAE paper 930343, 1993. [5] W.E. McConnell, R.P. Howard, H.M. Guzman, Analysis of human test subject kinematic responses to low velocity rear end impacts, SAE Paper 930889, 1993, pp. 21±30. [6] R.R. McHenry, Analysis of the dynamics of automobile passenger restraint systems, in: Proceedings of The Seventh Stapp Car Crash Conference, 1963, pp. 207±249. [7] R.R. McHenry, K.N. Naab, Computer simulation of the crash victim ± A validation study, in: Proceedings of The Tenth Stapp Car Crash Conference, 1966, pp. 126±163. [8] R.D. Young, A three-dimensional mathematical model of an automobile passenger, Research Report 140-2, Texas Transportation Institute, Texas A & M University, College Station, Texas, 1970 (National Technical Information Service Report PB 197 159). [9] D.H. Robbins, R.O. Bennett, B.M. Bowman, User oriented mathematical crash victim simulator, in: Proceedings of The 16th Stapp Car Crash Conference, 1972, pp. 128±148. [10] R.L. Huston, R.E. Hessel, C.E. Passerello, A three-dimensional vehicle-man model for collision and high acceleration studies, SAE 740275, 1974. [11] R.N. Karnes, J.L. Tocher, D.W. Twigg, PROMETHEUS ± A crash victim simulation, in: K. Saczalski, G.T. Singley III, W. Pilkey, R.L. Huston (Eds.), Aircraft Crashworthiness, University Press of Virginia, Charlottesville, VA, 1975, pp. 327±345. [12] J.T. Fleck, CALSPAN 3-D crash victim simulation program, in: K. Saczalski, G.T. Singley III, W. Pilkey, R.L. Huston (Eds.), Aircraft Crashworthiness, University Press of Virginia, Charlottesville, VA, 1975, pp. 229±310. [13] R.L. Huston, R.E. Hessel, J.M. Winget, Dynamics of a crash victim ± A ®nite segment model, Paper presented at the AIAA, ASME, SAE Structure, Structural Dynamics and Materials Conference, Denver, USA, 1975. [14] J. Wismans, T. Hoen, Wittebrood, Status of the MADYMO crash victim simulation program, Paper presented at The Tenth International Conference on Experimental Safety Vehicles, Oxford, England, UK, 1985. [15] P. Prasad, MADYMO 2D simulation of sled tests, SAE Paper 880640, 1988. [16] J. Wismans, J.H.A. Hermans, MADYMO 3D simulation of Hybrid III dummy sled tests, SAE 880645, 1988. [17] S.C. Huang, Biomechanical modeling and simulations of automobile crash victims, Computers and Structures 57 (3) (1995) 541±549.
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[18] T.R. Kane, Dynamics of nonholonomic systems, Journal of Applied Mechanics 28 (1961) 574±578. [19] R.L. Huston, C.E. Passerello, M.W. Harlow, Dynamics of multirigid-body systems, ASME Journal of Applied Mechanics 45 (4) (1978) 889±894. [20] P. Prasad, Sled testing of Hybrid III, SAE 880637, 1988.