Accepted Manuscript

Collision mitigation and vehicle transportation safety using integrated vehicle dynamics control systems

Mustafa Elkady, Ahmed Elmarakbi, John MacIntyre, Mohammed Alhariri

PII: S2095-7564(15)30648-6

DOI: 10.1016/j.jtte.2016.08.002

Reference: JTTE 107

To appear in: Journal of Traffic and Transportation Engineering (English Edition)

Received Date: 1 October 2015 Revised Date: 7 August 2016 Accepted Date: 18 August 2016

Please cite this article as: Elkady, M., Elmarakbi, A., MacIntyre, J., Alhariri, M., Collision mitigation and vehicle transportation safety using integrated vehicle dynamics control systems, Journal of Traffic and Transportation Engineering (English Edition) (2017), doi: 10.1016/j.jtte.2016.08.002.

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1 Original research paper

3 Collision mitigation and vehicle transportation safety

4 using integrated vehicle dynamics control systems

6 Mustafa Elkady a,b, Ahmed Elmarakbi c*, John MacIntyre c, Mohammed Alhariri c

8 a School of Engineering, Lebanese International University, Beirut, Lebanon

9 b Faculty of Engineering, Ain Shams University, Cairo, Egypt

10 c Faculty of Engineering and Advanced Manufacturing, University of Sunderland, Sunderland, SR6 0DD, UK

12 Highlights

13 • Integrated vehicle dynamics control systems for collisions improvement.

14 • Development of a new dynamics/crash mathematical model for vehicle collisions.

15 • Development of a new occupant- based lumped mass-spring-damper mathematical model.

16 • Vehicle response and occupant behaviour are captured and analyzed accurately.

19 Abstract

20 The aim of this paper is to investigate the effect of vehicle dynamics control systems

21 (VDCS) on both the collision of the vehicle body and the kinematic behaviour of the

22 vehicle's occupant in case of offset frontal vehicle-to-vehicle collision. A unique

23 6-degree-of-freedom (6-DOF) vehicle dynamics/crash mathematical model and a

24 simplified lumped mass occupant model are developed. The first model is used to define

25 the vehicle body crash parameters and it integrates a vehicle dynamics model with a

26 vehicle front-end structure model. The second model aims to predict the effect of VDCS on

27 the kinematics of the occupant. It is shown from the numerical simulations that the vehicle

28 dynamics/crash response and occupant behaviour can be captured and analysed quickly

29 and accurately. Furthermore, it is shown that the VDCS can affect the crash characteristics

30 positively and the occupant behaviour is improved.

34 Keywords:

35 Vehicle transportation safety; Collision mitigation; Vehicle dynamics and control; Mathematical

36 modelling; Occupant kinematics.

Corresponding author. Tel.: +44 191 515 3877.

E-mail address: ahmed.elmarakbi@sunderland.ac.uk (A. Elmarakbi).

38 1 Introduction

39 Vehicle dynamics control systems (VDCS) exist on the most modern vehicles and play important roles

40 in vehicle ride, stability, and safety. For example, anti-lock brake system (ABS) is used to allow the

41 vehicle to follow the desired steering angle while intense braking is applied (Bang et al., 2001; Yu et al.,

42 2002). In addition, the ABS helps reducing the stopping distance of a vehicle compared to the

43 conventional braking system (Celentano et al., 2003; Pasillas-Lepine, 2006). The active suspension

44 control system (ASC) is used to improve the quality of the vehicle ride and reduce the vertical

45 acceleration (Alleyne and Hedrick, 1995; Yue et al., 1988). From the view of vehicle transportation

46 safety, nowadays, occupant safety becomes one of the most important research areas and the

47 automotive industry increased their efforts to enhance the safety of vehicles. Seat belts, airbags, and

48 advanced driver assistant systems (ADAS) are used to prevent a vehicle crash or mitigate vehicle

49 collision when a crash occurs.

50 The most well-known pre-collision method is the advance driver assistant systems (ADAS). The aim

51 of ADAS is to mitigate and avoid vehicle frontal collisions. The main idea of ADAS is to collect data from

52 the road (i.e., traffic lights, other cars distances and velocities, obstacles, etc.) and transfer this

53 information to the driver, warn the driver in danger situations and aid the driver actively in imminent

54 collision (Gietelink et al., 2006; Seiler et al., 1998). There are different actions may be taken when these

55 systems detect that the collision is unavoidable. For example, to help the driver actively, the baking

56 force can be applied in imminent collision (Jansson et al., 2002), in addition, the brake assistant system

57 (BAS) (Tamura et al., 2001) and the collision mitigation brake system (CMBS) (Sugimoto and Sauer,

58 2005) were used to activate the braking instantly based on the behaviour characteristics of the driver,

59 and relative position of the most dangerous other object for the moment.

60 Vehicle crash structures are designed to be able to absorb the crash energy and control vehicle

61 deformations, therefore simple mathematical models are used to represent the vehicle front structure

62 (Emori, 1968). In this model, the vehicle mass is represented as a lumped mass and the vehicle

63 structure is represented as a spring in a simple model to simulate a frontal and rear-end vehicle collision

64 processes. Also, other analyses and simulations of vehicle-to-barrier impact using a simple mass spring

65 model were established by Kamal (1970) and widely extended by Elmarakbi and Zu (2005, 2007) to

66 include smart-front structures. To achieve enhanced occupant safety, the crash energy management

67 system was explored by Khattab (2010). This study, using a simple lumped-parameter model,

68 discussed the applicability of providing variable energy-absorbing properties as a function of the impact

69 speed.

70 In terms of the enhancing crash energy absorption and minimizing deformation of the vehicle's

71 structure, a frontal structure consisting of two special longitudinal members was designed (Witteman

72 and Kriens, 1998; Witteman, 1999). This longitudinal member system was divided into two separate

73 systems: the first, called the crushing part, guarantees the desired stable and efficient energy

74 absorption; the other, called the supporting part, guarantees the desired stiffness in the transverse

75 direction. For high crash energy absorption and weight efficiency, new multi-cell profiles were

76 developed (Kim, 2002). Various design aspects of the new multi-cell members were investigated and

77 the optimization was carried out as an exemplary design guide.

78 The vehicle body pitches and drops at fontal impact are the main reason for the unbelted driver neck

79 and head injury (Chang et al., 2006). Vehicle pitch and drop are normally experienced at frontal crash

80 tests. They used a finite element (FE) method to investigate the frame deformation at full frontal impact

81 and discussed the cause and countermeasures design for the issue of vehicle body pitch and drop. It

82 found that the bending down of frame rails caused by the geometry offsets of the frame rails in vertical

83 direction during a crash is the key feature of the pitching of the vehicle body.

84 The effect of vehicle braking on the crash and the possibility of using vehicle dynamics control

85 systems to reduce the risk of incompatibility and improve the crash performance in frontal

86 vehicle-to-barrier collision were investigated (Hogan and Manning, 2007). They proved that there was a

87 slight improvement of the vehicle deformation once the brakes were applied during the crash. A

88 multi-body vehicle dynamic model using ADAMS software, alongside with a simple crash model was

89 generated in order to study the effects of the implemented control strategy.

90 Their study showed that the control systems were not able to significantly affect the vehicle dynamics

91 in the offset barrier impact. In addition, it was found that in offset vehicle-to-vehicle rear-end collision,

92 the ABS or direct yaw control (DYC) systems can stabilize the vehicle. However, these control systems

93 affected each other and cannot work together at the same time.

94 The behaviour of a vehicle at high-speed crashes is enhanced by using active vehicle dynamics

95 control systems (Elkady and Elmarakbi, 2012). A 6-degree-of-freedom (6-DOF) mathematical model

96 was developed to carry out this study. In this model, vehicle dynamics was studied together with a

97 vehicle crash structural dynamics and a validation of the vehicle crash structure of the proposed model

98 was achieved. Four different cases of VDCS were applied to the model to predict the most effective one.

99 An extension to this study, an occupant model has been developed and the effect of VDCS on the

100 occupant kinematics has been analyzed (Elkady and Elmarakbi, 2012).

101 The main aim of this research is to investigate the effect of the VDCS on vehicle collision mitigation,

102 enhance vehicle crash characteristics, and improve occupant biodynamics responses in case of 50%

103 vehicle-to-vehicle offset crash scenario. For that purpose, different seven cases of VDCS are applied to

104 the vehicle model, there are three new cases which are not mentioned in the previous publications.

105 2 Methodology

106 A vehicle frontal collision can be divided into two main stages, the first one is a primary impact, and the

107 second one is a secondary impact. The primary impact indicates the collision between the front-end

108 structure of the vehicle and an obstacle (another vehicle in this paper). The secondary impact is the

109 interaction between the occupant and the restraint system and/or the vehicle interior due to vehicle

110 collisions.

111 2.1 Vehicle dynamics/crash model

112 Using mathematical models in crash simulation is useful at the first design concept because rapid

113 analysis is required at this stage. In addition, the well-known advantage of mathematical modelling

114 provides a quick simulation analysis compared with FE models. In this paper, a 6-DOF vehicle

115 dynamics/crash mathematical model, shown in Fig. 1(a), has been developed to optimize the VDCS,

116 which will be embedded in the control unit, in impending impact at offset vehicle-to-vehicle crash

117 scenarios for vehicle collision mitigation. The ABS and the ASC systems are co-simulated with a full car

118 vehicle dynamic model and integrated with a front-end structure. It is worthwhile mentioning that vehicle

119 components, which significantly affect the dynamics of a frontal impact, are modelled by lumped

120 masses and nonlinear springs.

125 motion in longitudinal direction (x axis), translational motion on vertical direction (z axis), pitching motion

126 (around y axis), rolling motion (around x axis), and yawing motion in case of offset collision (around z

127 axis at the point of impact). Four spring/damper units are used to represent the conventional vehicle

128 suspension systems. Each unit has a spring stiffness ks and a damping coefficient c. The subscripts f, r,

129 R and L denote the front, rear, right and left wheels, respectively. The ASC system is co-simulated with

130 the conventional suspension system to add or subtract an active force element u. The ABS is

131 co-simulated with the mathematical model using a simple wheel model. The unsprung masses are not

132 considered in this model and it is assumed that the vehicle moves in a flat-asphalted road, which means

133 that the vertical movement of the tyres and road vertical forces can be neglected.

134 To represent the front-end structure of the vehicle, four non-linear springs with stiffness ks are

135 proposed: two springs represent the upper members (rails) and two springs represent lower members of

136 the vehicle frontal structure. The subscript u denotes the upper rails while the subscript l denotes the

137 lower rails. The bumper of the vehicle is represented by a lumped mass mb and it has a longitudinal

138 motion in the x direction and rotational motion for the non-impacted side of each bumper.

139 The general dimensions of the model are shown in Fig. 1(a), where lf, lr, l and h represent the

140 longitudinal distance between the vehicle's CG and front wheels, the longitudinal distance between the

121 (a)

123 Fig. 1 Mathematical model. (a) 6-DOF vehicle dynamics/crash mathematical model. (b) Free body diagram of the mathematical model.

124 In this full-car model, the vehicle body is represented by lumped mass m and it has a translational

141 CG and rear wheels, the wheel base and the high of the CG from the ground, respectively. a is the

142 distance between the centre of the bumper and the right/left frontal springs; b is the distance between

143 the CG and right/left wheels.

144 The free body diagram of the mathematical model is shown in Fig. 1 (b), which represents the different

145 internal and external forces applied on the vehicle body. Fs, FS, Fb, Fz and Ff are front-end non-linear

146 spring forces, vehicle suspension forces, braking forces, normal forces and friction forces between the

147 tyres and the road due to vehicle yawing, respectively.

148 2.1.1 Equations of motion of vehicle-to-vehicle crash scenario

149 The model in the case of offset frontal vehicle-to-barrier is thirteen DOF namely longitudinal and vertical

150 movements, pitching, rolling and yawing motions for each vehicle body, the longitudinal movement of

151 the two bumpers as one part, and the rotational motion for the non-impacted side of each bumper. The

152 two bumpers of each vehicle are considered as lumped masses, and dealt as one mass to transfer the

153 load from one vehicle to another. Fig. 2 shows the vehicle model before and after collision in case of

154 offset frontal vehicle-to-vehicle crash scenario. The equations of motion of the mathematical model

155 shown in Fig. 2 are developed to study and predict the dynamic response of the primary impact of offset

156 vehicle-to-vehicle crash scenario. Fig. 3 is used to describe the deformation of the front springs due to

157 vehicle pitching around its CG and vehicle yawing around the point of impact for the two vehicles,

158 respectively. Fig. 1 is also used to derive the equations of motion of the two vehicle models. The detailed

159 equations of motion were created in a previous study by the authors (Elmarakbi et al., 2013).

160 161 162

183 Fig. 3 Front-end deformations before and after pitching. (a) For vehicle pitching. (b) For vehicle yawing.

184 2.1.2 Forces applied to the vehicle

185 There are different types of forces which are applied on the vehicle body. These forces are generated by

186 crushing the front-end structure, conventional suspension system due to the movement of the vehicle

187 body and the active control systems such as the ABS and ASC. The free body diagram shown in Fig.

188 1 (b) illustrates these different forces and their directions.

189 To simulate the upper and lower members of the vehicle front-end structure, multi-stage piecewise

200 201 202

linear force-deformation spring characteristics are considered. The non-linear springs used in the multi-body model ADAMS (Hogan and Manning, 2007) are taken to generate the n stage piecewise spring's characteristics as shown in Fig. 4(a), while the general relationship between the force and the deflection, Fig. 4(b), is used to calculate the force of the vehicle's front-end. The suspension forces of the vehicle body are also calculated.

— ADAMS model (lower member)

..........Mathematical model (lower member)

- ADAMS model (upper member) 140r-------Mathematical model (upper member)

/ / / S / Stage (n-1) Stage n

Kn/ Stage 2

/Stage 1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 Deformation (m)

Deformation

Fig. 4 Force deformation characteristics. (a) For upper and lower rails. (b) General piecewise.

The detailed equations of these forces and the validation of the vehicle dynamics-crash model was established in a previous study by the authors (Elkady and Elmarakbi, 2012). The validation is performed to ensure the validity of the model and is accomplished by comparing the mathematical model results with real test data and the results of the former ADAMS model. The validation showed that the mathematical model results are well matched with the other results.

203 2.2 Multi-body occupant model

204 In this section, occupant biodynamic is considered by modelling the occupant mathematically in order to

205 be integrated with the vehicle mathematical model. The occupant model is proposed to be three-body

206 model to capture its dynamic response, rotational events of the chest and head, due to different crash

207 scenarios. The restraint system consists of seat belt, front and side airbags is presented by different

208 spring-damper systems.

209 The occupant biodynamic model shown in Fig. 5 is developed in this study to evaluate the occupant

210 kinematic behaviour in full and offset frontal crash scenarios. The human body model consists of three

211 212

218 219

220 221

bodies with masses m1, m2 and m3. The first body (lower body/pelvis) with mass m1, represents the legs and the pelvic area of the occupant and it is considered to have a translation motion in the longitudinal direction and rotation motions (pitching, rolling and yawing) with the vehicle body. The second body (middle body/chest), with mass m2, represents the occupant's abdominal area, the thorax area and the arms, and it is considered to have a translation motion in the longitudinal direction and a rotation motion around the pivot between the lower and middle bodies (pivot 1). The third body (upper body/head), with mass m3, represents the head and neck of the occupant and it is considered to have a translation motion in the longitudinal direction and a rotational motion around the pivot between the middle and upper bodies (pivot 2).

Direction of impact

Back of the

Seatbelt

Frontal airbag

Bottom of " the seat

Steering wheel/dashboard

Fig. 5 Multi-body occupant model.

A rotational coil spring is proposed at each pivot to represent the joint stiffness between the pelvic area and the abdominal area and between the thorax area and the neck/head area. The seatbelt is represented by two linear spring-damper units between the compartment and the occupant. The frontal and side airbags are each represented by two linear spring-damper units.

226 2.2.1 Equation of motion (EOM) of the human body model

227 Figs. 6 (a), (b), and (c) show the side, top and front views of the occupant model, respectively. POI in Fig.

6(b) means point of impact. For each figure, the positions of the occupant's three bodies are illustrated before and after the crash. Lagrange's equations are used to describe the general motions of the multi-body human model.

235 (c)

Before crash

During crash

Before crash During crash

Fig. 6 Occupant model. (a) Side view. (b) Top view. (c) Frontal view.

The general motions of the multi-body human model are described using Lagrange's equations as follows

A( dE) + + = 0

dt dX1 dx1 dx1 dX1

d, dE , dE dV dD — (—-)--+-+ —-

dt d0, d 0, d 0, d0,

d , dE , dE dV dD

— (—-)--+-+—-

dr d& d0 dq d/

d t dE , dE dV dD

—) -—+T—+-

dt dy2 dy2 dy2 dyy2

d t dE , dE dV dD

— ) --—+ -— + -

dt dy/3 dy3 dy3 dy/3

where E, V and D are the kinetic energy, potential energy and the Rayleigh dissipation function of the system, respectively, x1, 02, 03, y2 and y3 are the longitudinal movement of the occupant's lower

body, the rotational angle of the occupant's middle body about y axis, the rotational angle of the occupant's upper body abouty axis, the rotational angle of the occupant's middle body about x axis and

249 the rotational angle of the occupant's upper body about x axis, respectively, hence, X1 , 62, 63 , y2 and

y/3 are their associated velocities, respectively. The kinetic energy of the system can be written as

; 2 2 V2

m3V3 . I1 / q 2 .12 . -2 X . I2 ( q 2 + n'r2\ + I3 i & 2 , ,#v2

2 + -^(q2+f&2+y2)+-^q2 +y2)+^q2+y2)

where v1, v2 and v3 are the equivalent velocities of the lower, middle and upper bodies of the occupant, respectively, I1,I2 and I3 are the rotational moment of inertia of the lower, middle and upper bodies about the CG of each body, respectively. It is assumed that the rotational moment of inertia of each body

around x, y and z axes are the same. 6, (/ and y/ represent the vehicle body pitching, yawing and

rolling velocities, respectively. The equivalent velocities of the three bodies of the occupant can be calculated as follows

v2=xm+t2i+Zm

where the displacement of the lower body in x direction can be calculated using Fig. 7 as

__at—/-■-

CTHIES^

262 Fig. 7 A schematic diagram of the occupant's lower body movement during impact.

263 X^ = xi + Li[sin(b) - sin(b-0)] - L2[cos(Z-f) - cos(Z)] (8)

264 The velocity of the lower body in x direction can be written as

265 Xmi = xi + L0/cos(b - 0) -L2</sin(Z -f) (9)

266 The displacement and velocity of the lower body in y direction can be calculated as

267 Ymi = L2[sin(Z) - sin(Z-f)] + L3[cos(a) - cos(a + y)] (10)

268 Ymi = L<fcos(Z - f) + L3y/sin(a+y) (11)

269 The displacement and velocity of the lower body in y direction can be calculated as

270 Z^ = z + L [cos(b - 0) - cos(b)] + L3[sin(a + y) - sin(a)] (12)

271 Zm = L1 ¿sinb- 0) + Lyy cos(a+y) (13)

272 Substituting Eqs. (9), (11) and (13) in Eq. (7), the equivalent velocity of the lower body can be

273 determined. By repeating the previous steps of these equations (Eqs. (8)-(13)), the equivalent velocities

274 of the middle and upper bodies can be calculated.

275 Where Xm is the resultant longitudinal displacement in x direction, Ym is the resultant vertical

276 displacement in y direction and Zm is the resultant vertical displacement. The subscript 1 is for lower

277 body, 2 is for middle body and 3 is for upper body. L1 is the distance from the vehicle'sy axis to the lower

278 body's CG, L2 is the distance between the point of impact and the CG of the lower body, and L3 is the

279 distance from the vehicle's x axis to the lower body's CG. It is assumed that L1, L2 and L3 are constant

280 due to the insignificant change of their lengths during the crash. fi is the angle between the vertical

281 centreline of the vehicle z axis and the line between the vehicle'sy axis and the CG of the lower body (L1).

282 Zis the angle between the longitudinal centreline of the vehicle x axis and the line between the point of

283 impact and the CG of the lower body (L2). a is the angle between the vertical centreline of the vehicle z

284 axis and the line between the vehicle's x axis and the CG of the lower body (L3).

285 By substituting the equivalent velocities of the three bodies in Eq. (6), the kinetic energy can be

286 obtained. Using Fig. 6 the potential energy of the system can be written as

V = m1 g[h + z + L1 (cos(b - 0) - cos(b))] + m2 g[h + z + L (cos(b - 0) -cos(b)) + ^ cos( 02) -12 (1 - cos( y2))] + m3 g[h + z + L1 (cos(b - 0) -

287 cos(b)) + 12cos( 02) -12(1 - cos(y2)) + ^cos( 03) -13 (1 - cos(y3))] + (14)

\(FkA + Fk 2A2 + Fk 3A3 + Fk A + Fk 5A5 + Fk 6A6 + Fk12 0A12 0 + Fk12yA12y +

F A + F A )

1 k23 0 230 ^ 1 k23yu23y)

288 where h is the vehicle's CG height and z is the vertical displacement of the vehicle body, Fk1, Fk2, Fk3, Fk4,

289 Fk5 and Fk6 are the forces generated from the lower seatbelt spring, the upper seatbelt spring, the lower

290 frontal airbag spring, the upper frontal airbag spring, the lower side airbag spring, the upper side airbag

291 spring, respectively. Fk12e and Fk12v are the forces generated from the rotational spring between the

292 middle and lower body around y and x axes, respectively. Fk23e and Fk23v are the forces generated from

293 the rotational spring between the upper and middle body aroundy and x axes, respectively. S1, A2, A3,

294 A, A and A6 represent the total deflection of the lower seatbelt spring, of the upper seatbelt spring, of

295 the lower frontal airbag spring, of the upper frontal airbag spring, of the lower side airbag spring, of the

296 upper side airbag spring, respectively. A12 0 and A12y , A23 0 and A23y are the deflection of the

297 rotational spring between the lower and middle body around y and x axes and the deflection of the

298 rotational spring between the middle and upper body around y and x axes, respectively.

299 The Rayleigh dissipation function can be written as follow

300 D = 1(FA + FA + FA + FCA + FA + Fc 6^) (15)

301 where Fc1, Fc2, Fc3, Fc4, Fc5 and Fc6 are the forces generated from the lower seatbelt, the upper seatbelt,

302 the lower frontal airbag, the upper frontal airbag, the lower side airbag, and the upper side airbag

303 dampers, respectively. S1, S2, A3, A4, A5, and A6 are the associated velocities of the 81, A2, A3, A4,

304 A and A, respectively.

305 The forces Fki and Fci (i= 1, 2, •••) are calculated as

306 Fi = kA (16)

307 Fa = cd (17)

308 In order to get the components of the Eqs. (1)-(5) the differentiation of the kinetic energy, potential

309 energy and Rayleigh dissipation function are determined. To solve these equations, they need to be

310 re-arranged in an integratable form and then rewritten in a matrix form as follow

311 AB = C (18)

312 B = [j 62 63 y2 y3]T

313 The final form then can be written as

314 B = A~lC (19)

315 Different occupant bodies' responses (x1, 02, 93, y2 and y3) can be determined by solving Eq. (19)

316 numerically.

317 2.2.2 Occupant model validation

318 The occupant model has been validated by comparing its results with the former finite element human

319 model and crash test. To ensure that the input crash data applied to the dummy and the occupant in the

320 finite element model match the input data in the mathematical model, the vehicle decelerations in all

321 cases (mathematical model, finite element model and real test) are compared as depicted in Fig. 8. The

322 same initial crash conditions are adapted in the mathematical model to be the same as in the FE model

323 and the real test. It is observed that the deceleration of the mathematical model shows outstanding

324 agreement with the real test and the finite element model results with respect to peak values and the

325 timing of the curves.

0.08 Time (s)

Fig. 8 Comparisons of the vehicle body deceleration results among a previous finite model, real test and the mathematical model.

Similarly, Fig. 9 shows the chest deceleration-time histories of the real test, finite element and mathematical models. The values and trends of the three different chest deceleration curves are well-matched. The maximum deceleration of the occupant chest in the mathematical model is a slightly lower compared to the real test data, while it is a slightly higher compared to the finite element model. In addition, there is a small shifting in this peak value compared with the other results. This is due to the modelling simplification of the airbag used in the mathematical models.

50 40 30 20 10 0 -10

] ] Real test data Finite element model Mathematical model

/ ,v\ k x -----]

\ y ' i

,-y - - -] \ * \ N \ \ x

A-/N i \

0.08 Time (s)

Fig. 9 Comparisons of the chest deceleration results among a previous finite element model, a real test and 3-body mathematical model.

In the same way, the head deceleration results of the occupant models are presented in Fig. 10. Although the general trends and slopes of the three different results are well matched, there is a small difference in the peak value of the mathematical model compared with both finite element and real test results. A small shifting of the head deceleration peak value is also observed here for both finite element

343 and mathematical models by different values compared with the real test data.

3 40 c

Q 10 0 -10

0 0.04 0.08 0.12 0.16

344 Time (s)

346 Fig. 10 Comparisons of the head deceleration results among a previous finite element model, a real test and a 3-body

347 mathematical model.

348 3 Numerical simulations

349 Seven different cases of VDCS are investigated in this section and their associated results are

350 compared with the free rolling case scenario. These different VDCS cases are described as follows.

351 Case 1: free rolling - in this case the vehicle collides with a barrier/vehicle without applying any types

352 of control.

353 Case 2: ABS - in this case the anti-lock braking system is applied before and during the collision.

354 Case 3: ABS + ASC - the ASC system is integrated with the ABS to increase the vertical normal force

355 on the road (Ori et al., 2011) and hence increase the braking force.

356 Case 4: ABS + frontal active suspension control (FASC) - the ASC system is integrated with the ABS

357 on the front wheels only.

358 Case 5: ABS + anti-pitch control (APC) - the APC system is integrated with the ABS using the ACS to

359 keep the vehicle in a horizontal position before the crash by applying an active force element on the front

360 and rear wheels in upward and downward directions, respectively.

361 Case 6: ABS + UPC - in this case, the vehicle is taken a reverse pitching angle before crash using an

362 ASC system.

363 Case 7: ABS DYC - the braking force is used to be applied to individual wheels to reduce the yawing

364 moment of the vehicle body.

365 3.1 Primary impact results

366 The primary impact simulation results for offset vehicle-to-vehicle crash scenario are demonstrated in

367 this section. The values of different parameters used in numerical simulations are given in Table 1

368 (Alleyne, 1997), where Iyy, Ixx, Izz and Ibzz are the moments of inertia of the vehicle body about y, x and z

369 axes and the moment of inertia of the rotation part of the bumper (the part of the bumper rotated with the

370 non-impacted side of the vehicle due to offset collisions) about z axis at the point of impact, respectively.

371 The effect of the different cases of VDCS on vehicle collision mitigation is also investigated. In addition,

372 the effect of the control systems on the other vehicle (vehicle (b)) is discussed. Fig. 11 shows the

373 impacted side of the front-end structure's deformation-time histories for vehicle (a) for all different VDCS

374 cases. It is noticed that the deformation increased to reach its maximum value (different for each case)

375 and then decreased slightly due to front-end springs rebound. The minimum deformation is obtained in

376 the Case 3 when the ASC is applied along with ABS. The maximum reduction of 50 mm is observed in

377 this case and a reduction of 30 mm is shown in Case 6, while a reduction of about 25 mm is obtained in

378 Cases 2, 4 and 5 compared with the free rolling case. On the other hand, Case 7 (ABS + DYC) produced

379 a higher deformation with a total reduction of about 15 mm. Although 50 mm is relatively small

380 compared with the total deformation, this reduction may help prevent the compartment to be reached.

381 The integrated control of the ASC with the ABS aims to increase the braking force by increasing the

382 vertical load to obtain a minimum stopping distance. It is worth mentioning that the application of the

383 ASC control system (Case 3) helps reducing the maximum deformation of the front-end structure as

384 shown in Fig. 11. For vehicle (b), the maximum deformation is almost the same with very small and

385 insignificant values for all cases of VDCS, and this means the control systems have no great effect on

386 the front-end deformation of the other vehicle during the offset collision.

Table 1 Values of the different parameters used in primary impact simulations.

Parameter m (kg) 4, (kg • m2) I„ (kg - m2) Iz (kg • m2) Ibzz (kg • m2) W = kSfL

(kN/m)

Value Parameter

Value Parameter Value

kSrR = kSrL

(kN/m) 13.75

cfR = cfL

(N • s/m) 1100

lb (m)

CrR = crL

(N • s/m) 900

lf (m)

la (m)

lr (m) h (m)

1.185 1.580 0.452 1.20

bi = bo (m) 0.8

403 (b)

a 0.70

0.60 0.05

- Case 1: free rolling

......... Case2:ABS

-----Case 3: ABS+ASC

---Case 4: ABS+FASC

- - - Case 5: ABS+APC --Case 6: ABS+UPC

Time (s)

— Case 1: free rolling ......... Case2:ABS ----- Case 3: ABS+ASC

---Case 4: ABS+FASC - - - Case 5: ABS+APC --Case 6: ABS+UPC ~~---

■""""I- • - —-Z^r -

Time (s)

Fig. 11 Deformation of the front-end structure (offset frontal vehicle-to-vehicle impact). (a) Vehicle (a). (b) (Enlarge scale) vehicle (a).

408 The deceleration-time histories of the vehicle body for all cases of vehicle (a) are presented in Fig. 12.

409 The deceleration-time history can be divided into three stages. The first stage represents the increase of

410 the vehicle's deceleration before the front left wheel reaches the barrier. In this stage the highest

411 deceleration value is observed in Case 3. In the other cases, a slight higher deceleration is also noticed

412 compared with the free rolling case. In the second stage, the front left wheel reaches the barrier and

413 stop moving, therefore its braking effects is vanished. At the beginning of this stage a rapid reduction in

414 the vehicle body deceleration occurs (arrow 1, Fig. 12). This deceleration drop does not appear in the

415 free rolling case while there is no applied braking. During the second stage, it is noticed that the

416 minimum deceleration is still in Case 1, while the maximum deceleration is almost the same for all other

417 cases. At the end of this stage, the vehicle stops and starts moving in the opposite direction. In addition,

418 the braking force changes its direction and another drop in the vehicle deceleration is noticed as shown

419 in Fig. 12 (arrow 2). At the third stage, a condition of allowing the front-end springs to be rebounded for

420 a very short time is applied during the simulation analysis. During this stage, the vehicle moves back

421 and the deformation of the front-end decreases as shown in Fig. 12. At the end of this stage, the

422 non-linear front-end springs are deactivated and the vehicle's deceleration suddenly dropped to a value

423 of zero. This fast drop is due to the assumption of immediate stopping the effect front-end springs after

424 a very short time of rebound.

8 10 CD

0 0.02 0.04 0.06 0.08 0.10

425 Time (s)

427 Fig. 12 Vehicle body deceleration (offset frontal vehicle-to-vehicle impact), vehicle (a).

428 An insignificant increase of the vehicle deceleration in all VDCS cases is observed in the other vehicle

429 (b) compared with the free rolling case. The maximum values of the vehicle deceleration in a vehicle (b)

S3BSSESS rfV^

A r grd

Á 2"d

//y / l" - Case 1: free rolling ......... Case2:ABS -----Case3: ABS+ASC ---Case 4: ABS+FASC ---Case 5: ABS+APC --Case 6: ABS+UPC Case 7: ABS+DYC

430 are also almost the same for all the VDCS cases.

431 Fig. 13 shows the vehicle's pitch angle-time histories for all cases of vehicle (a). The VDCS is applied

432 1.5 s before the collision, therefore, the vehicle body impacts the barrier at different values of pitch

433 angles according to each case as shown in Fig. 13. The vehicle's pitch angle then reaches its maximum

434 values (normally after the end of the crash) according to each case. Following this, the pitch angle

435 reduces to reach negative values and then bounces to reach its steady-state condition. In the offset

436 crash scenario, vehicle body pitching angle is generated due to the difference in impact forces between

437 the upper and lower front-end members of the impacted side in the free rolling case. The additional

438 pitching moment is generated from the braking force in the other VDCS cases. The maximum pitch

439 angle is observed in Case 2 followed by Cases 7, 4, 1, 5, 3 and finally Case 6. In Case 6, a notable

440 reduction of about 6.5 deg compared with Case 1 and about 12 deg, compared with Case 2 are

441 observed

-55 10 01

S 4 ■5 2

-2 -4 -6

0 0.3 0.6 0.9 1.2 1.5

444 Fig. 13 Vehicle body pitch angle (offset frontal vehicle-to-vehicle impact), vehicle (a).

445 A rolling moment of the vehicle body is generated during the crash due to the different values of the

446 component of the left frontal springs' forces in y direction and from the friction between the ground and

447 the tyres due to the yaw motion. At the end of the collision, the pitching and rolling moments are ended

448 and the vehicle is controlled by the tyres and suspension forces. The vehicle's rear wheels left the

449 ground during the vehicle pitching and the left wheels (front and rear) left the ground as well during the

450 vehicle rolling. At this moment, three wheels of the vehicle are not contacted with the ground with

451 different distances. This explains the different sudden changes of the vehicle pitching acceleration when

— Case 1: free rolling Case 2: ABS Case 3: ABS+ASC

— ^ ^

\\ ---Case 4: ABS+FASC --- Case5:ABS+APC --Case6: ABS+UPC ■ Case7:ABS+DYC

a / \S

/ p V

--------------/ /, // \\

/ / \ . w

s N ——-^r**^

/ r v -M fc-—_ - ^

each wheel re-contact the ground (look at the arrows referred to Case 1 in Fig. 14).

The vehicle body pitching acceleration is also depicted in Fig. 14 for all seven cases for vehicle (a). The vehicle maximum pitching acceleration is observed in Cases 2, 4 and 7, whilst the lowest value is

detected in case 6 (ABS + UPC). Compared with Case 1 (free rolling) and case 2 (ABS), a reduction of

2 2 about 670 deg/s and about 950 deg/s , respectively, are obtained in Case 6 (ABS + UPC).

0.6 0.9

Time (s)

Fig. 14 Vehicle body pitch acceleration (offset frontal vehicle-to-vehicle impact), vehicle (a).

Similarly, the pitch angle and pitch acceleration-time histories for vehicle (b) are obtained. It is noticed that there is no difference between the results of the seven crash scenarios. That means the different applied cases of the VDCS on vehicle (a) do not affect the pitching event of vehicle (b) in case of offset collision.

Fig. 15 shows the vehicle yaw velocity-time histories for all seven cases of vehicle (a). The vehicle yaw velocity is equal to zero before the crash, then it changes in three different stages: firstly, it increases rapidly to reach its maximum value; secondly, it decreases slowly for a different period of time related to each case; and thirdly it decreases gradually to reach zero. In the first stage, the rapid increase in the yaw velocity is due to the high yawing acceleration (Fig. 16) caused by the one side impacted spring. At the end of the collision, the rear wheels left the ground due to the vehicle pitching and the front-left wheel left the ground due to the vehicle rolling and hence the vehicle is controlled by the front-right wheel only. In the second stage, the decrease in the vehicle's yaw velocity occurred due to the friction force between the front-rear tyre and the ground. The period of this stage is different for each case and it mainly depends on the maximum pitching angle. During the second stage, the front-left

474 wheel re-contacts the ground. Stage 3 begins when the rear wheels start contacting the ground

475 generating yaw moments in the opposite direction. This is causing a reduction of the vehicle yawing

476 velocity with a higher rate than the decreasing of velocity rate in the second stage. Because of the

477 maximum vehicle front-end deformation is observed in Case 1 (free rolling) as shown in Fig. 11, the

478 greatest peak of yaw velocity appears in the same case as shown in Fig. 15. A reduction of the

479 maximum yawing velocity (10 deg/s) is observed in Cases 3 and 6, while a reduction of about 5 deg/s is

480 obtained in the other cases of VDCS.

— 80

"5s 01 T)

* 60 J-»

w 40 >

0 0.3 0.6 0.9 1.2 1.5

481 Time (s)

483 Fig. 15 Vehicle body yaw velocity (offset frontal vehicle-to-vehicle impact), vehicle (a).

484 Vehicle body yaw acceleration-time histories are depicted in Fig. 16. The maximum yaw acceleration

485 is observed in Case 1 (free rolling) and the minimum yaw acceleration is also observed in Cases 3 and

486 6. At the end of the collision, the vehicle is controlled by the front-left wheel only, as mentioned before,

487 trying to hinder the yawing motion. Accordingly, a negative yawing acceleration is generated with

488 different small values related to each case as shown in Fig. 16 (arrow 1). These negative values of the

489 vehicle yaw acceleration increase slowly with time producing two sudden drops of acceleration (arrow 2)

490 once the right-rear wheel and the left-rear wheel re-contact the ground, respectively. These drops are

491 not shown in Case 6 because the rear wheels do not leave the ground in this case. When the vehicle

492 yawing ends and the yaw speed reaches zero, the yaw acceleration returns to zero as well as shown in

493 Fig. 16 (arrow 3).

-c< ise 1: free rolling ise 2: ABS ise 3: ABS+ASC

"■iirK -----c<

" - . ---Case 4: ABS+FASC ---Case 5: ABS+APC --Case 6: ABS+UPC

s. . \ x.....

1 V % X \ %

f v\Y %

N. \ -

•> W \ \ .

/ x X «A

~5b 01 T3

Time (s)

Fig. 16 Vehicle body yaw acceleration (offset frontal vehicle-to-vehicle impact), vehicle (a).

Fig. 17 shows the vehicle body yaw angle-time histories for all cases of vehicle (a). It is found that the maximum yaw angle of 49.3 deg is noticed in Case 2 (ABS) while the minimum yaw angle of 36.8 deg is noticed in Case 6 (ABS + UPC). The maximum value of the vehicle yaw angle depends on the maximum yaw acceleration and the vehicle pitch angle for each case. It is worth mentioning that reducing the maximum vehicle body yaw angle reduces the risk of the car side-impact by any obstacles on the road. Following the yawing analysis, it can be said that the best set of the vehicle dynamic control is to apply Case 6 (ABS + UPC) since the minimum yaw angle and acceleration are obtained in this case.

2. 01 "So fi

Case 1: free rolling Case 2: ABS Case 3: ABS+ASC Case 4: ABS+FASC Case 5: ABS+APC

_---—■ — —--- -

■---

--Case 6: ABS+UPC Case 7: ABS+DYC

0.6 0.9

Time (s)

Fig. 17 Vehicle body yaw angle (offset frontal vehicle-to-vehicle impact), vehicle (a).

The yawing event of the vehicle (b), which is not equipped by the VDCS, is affected by vehicle (a) once different control systems are applied. The maximum yaw velocity of the vehicle (b) is increased in all cases compared with the free rolling case, except in Case 6. It is observed that the maximum yaw acceleration is also increased in all cases compared with the free rolling case by different values related

511 to each case. In the same manner, the maximum yaw angle of the vehicle (b) is increased in all cases by

512 different values (from 1.5 to 2 deg) related to each case, except in Case 6. However, all these values are

513 very small and insignificant.

514 3.2 Secondary impact results

515 The secondary impact simulation results for offset vehicle-to-vehicle crash scenario are demonstrated

516 in this section. The values of different parameters used in numerical simulations are given in Table 2,

517 where ds1, ds2, ds3, ds4, ds5 and ds6 are the Initial slack lengths of the lower seatbelt, upper seatbelt, lower

518 frontal airbag spring, upper frontal airbag spring, lower side airbag spring and upper side airbag spring,

519 respectively. The values m1, m2, m3, l2, l3, k12 and k23 have been taken from (Ilie and Tabacu, 2010). Fig.

520 18 shows the occupant's pelvis relative displacement for vehicle (a). It is shown that it increases forward

521 to reach its maximum position and then returns due to the lower seatbelt springs. It is observed that

522 there are insignificant differences between the values of the maximum relative displacement of the

523 occupant's pelvis. Related to the lower-body deceleration, it is shown that it increases during the

524 collision to reach its maximum values at the end of impact and then reduces after the effect of collision is

525 ended. It observed that the maximum deceleration is almost the same for all cases with very small

526 differences. These small differences mean that the VDCS do have an insignificant effect on the pelvis

527 relative displacement and deceleration.

Table 2 Values of the different parameters used in secondary impact simulations.

Parameter mi(kg) m2 (kg) m3(kg) /2 (m) /3 (m) Li (m) L2 (m) L3 (m)

Value 26.68 46.06 5.52 0.427 0.240 0.30 2.30 0.65

Parameter L4 (m) L5 (m) L6 (m) L7 (m) L8 (m) L9 (m) p(deg) Z(deg)

Value 0.30 0.35 0.45 0.55 0.97 1.10 30 15

Parameter a(deg) Y(deg) Ei (deg) E2 (deg) Pi (deg) P2 (deg) ki2 (N • m/rad)

Value 23 30 15 15 35 43 380

Parameter k23(N • m/rad) ki (N/m) k2 (N/m) k3 (N/m) k4 (N/m) k5 (N/m) k6 (N/m)

Value 200 58,860 39,240 2500 2500 2500 2500

Parameter ci, C2, C3, C4, C5, c6 dsi, ds2 (m) ds3, dS4 (m) ds5 (m) dS6 (m)

Value 20% of the critical damping 0.00 0.05 0.00 0.05

- 0.20

g 0.15

■■3 0.10

5 0.05 0) a

- Case 1: free rolling ......... Case2:ABS -----Case 3: ABS+ASC ---Case 4: ABS+FASC --- Case 5: ABS+APC --Case6: ABS+UPC — Case7:ABS+DYC

0.04 0.06

Time (s)

Fig. 18 Occupant's pelvis displacement (offset frontal vehicle-to-vehicle impact), vehicle (a).

The rotation angle of the occupant's chest abouty axis for all cases of vehicle (a) is shown in Fig. 19. The occupant's chest starts the collision with different rotational angles according to each case. The occupant takes this angle in the period of 1.5 s prior collisions when the VDCS is applied. After that, the

rotational angle of the occupant's chest remains constant for about 0.03 s, then it increased to reach its maximum value after the end of the collision. The maximum rotation angle is observed in Cases 2, 4 and 7 while the minimum one is observed in Case 6 (ABS + UPC). Fig. 20 shows the rotational acceleration about y axis of the occupant's chest. The chest rotational acceleration increases gradually to reach its maximum positive value and then reduces to reach its maximum negative value. The maximum positive rotational acceleration is monitored in Case 1 and the minimum one occurred in Case 5, while the maximum negative rotational acceleration is shown in Case 6 and the minimum is in Cases 2 and 7.

t>0 Ol

t>0 fi O!

to C o

■a 20

- Case 1: free rolling Case 2: ABS Case 3: ABS4-ASC

---Case 4: ABS+FASC - - - Case 5: ABS+APC --Case 6: ABS4-UPC ---Case 7: ABS+DYC

> \ \ \ X N. \\

■y .y X \

/ \ ^ \ \ \ .................\........

— •— ^ \ \ \

0.08 0.12 Time (s)

Fig. 19 Rotational angle of the occupant's chest about y axis (offset frontal vehicle-to-vehicle impact), vehicle (a). 150

Ö "75 05

So -150

.2 -225

4-> CÖ 4->

(§ -300

i 1

__ iCv /

> i/

— Case 1: free rol mg ---

Case3:ABS+ASC Case 4: ABS+FASC X \ n ~jfcf*/

— \ ^ ------J" - -. „

— Case 5: ABS+APC --Case6:ABS+UPC Case 7: ABS+DYC X — - —

---^ ----y

0.08 0.12 Time (s)

Fig. 20 Rotational acceleration of the occupant's chest about y axis (offset frontal vehicle-to-vehicle impact), vehicle (a).

The rotation angle of the occupant's head abouty axis is depicted in Fig. 21. The head rotation angle increases rapidly for a period of time, which occurred during the increase of the chest rotation. And then, it increases fast due to the return of the occupant's chest to reach its peak value (maximum value). The peak value of the head rotational angle is observed in Cases 2, 4 and 7, while the minimum one is

563 detected in Case 6. Fig. 22 shows the rotational acceleration of the occupant's head. The acceleration

564 increases with a different manner according to each case to reach its maximum value. These maximum

565 values occurred in different time related to each case. In other words, the maximum acceleration in

566 Cases 1, 3 and 6 occurs approximately at 0.07 s, while in the other cases it occurs approximately at 0.08

567 s. The minimum negative acceleration is observed in Cases 2 and 7, while the maximum negative

568 values are seen in Cases 1 and 6.

569 Time (s)

571 Fig. 21 Rotational angle of the occupant's head about y axis (offset frontal vehicle-to-vehicle impact), vehicle (a).

574 Fig. 22 Rotational acceleration of the occupant's head about y axis (offset frontal vehicle-to-vehicle impact), vehicle (a).

575 The rotation angle about x axis of the occupant's chest for all cases of vehicle (a) is depicted in Fig.

576 23. When the occupant's chest reaches its maximum rotational angle, it stays in this position for a

577 period of time while the vehicle rotates around the point of impact. The maximum rotation angle is

578 observed in Case 1 (free rolling) while the minimum angle is observed in Cases 3 and 6 (ABS + ASC

and ABS + UPC). Fig. 24 shows the rotational acceleration of the occupant's chest about x axis for all 6 cases for vehicle (a). The first sudden change in this acceleration is due to the activation of the side airbag, while the second one is due to the reverse braking force (arrows 1 and 2, respectively). The third sudden change of the chest acceleration (arrow 3) is due to the deactivation of the vehicle's front-end springs, which causes a sudden decrease of the vehicle pitching, yawing and rolling. The maximum positive rotational acceleration of the occupant's chest about x axis is observed in Cases 1 and 7, while the minimum value occurs in Case 3. The maximum negative rotational acceleration happens in Cases 1 and 4 and the minimum is observed in Case 3. These negative acceleration values occur due to the force generated by the lower spring-damper system of the side airbag.

DO 01 T3

Case 1: free rolling Case 2: ABS Case3:ABS+ASC Case 4: ABS+FASC Case 5: ABS+APC Case 6: ABS+UPC Case 7: ABS+DYC

0.08 0.12 Time (s)

Fig. 23 Rotational angle of the occupant's chest about x axis (offset frontal vehicle-to-vehicle impact), vehicle (a)

"5b <v "Ö

\i " ; *

jT / s // -- Vs. i)

2/ ' N ' V>N

.......................4 Är X x. N \ x-\

- ......... "ase 1: free roll !lase2:ABS ing J? \ \ \ W \

----- Case 3: ABS+ASC ---Case 4: ABS+FASC --- Case 5: ABS+APC --Case 6: ABS+UPC Case 7: ABS+DYC

0.08 0.12 Time (s)

594 Fig. 24 Rotational acceleration of the occupant's chest about x axis (offset frontal vehicle-to-vehicle impact), vehicle (a).

595 The rotation angle about x axis of the occupant's head for vehicle (a) is shown in Fig. 25. At the

600 601 602

beginning of the collision, while the chest takes a positive acceleration and starts rotating towards the vehicle's side door, the head takes a different negative small rotation value related to each case, all these values are close to 5 deg. The positive maximum value of the head rotational angle is observed in Case 6, while the minimum peak angle is seen in Cases 2, 3, 4 and 7. Fig. 26 shows the rotational acceleration about x axis of the occupant's head for all cases. The effect of the reverse braking force is observed at the end of the collision (arrow 1 in Fig. 26). The maximum positive acceleration (in the period from 0.06 to 0.10 s) is almost the same for all cases, while the maximum negative acceleration (in the period from 0.10 to 0.16 s), caused by the side airbag force, is observed in Case 1 with relatively a higher value. The minimum negative acceleration is detected in Cases 2, 4, 5 and 7.

00 tu ■a

00 fi CO

"Öl C o

Case 1: free rolling Case2:ABS Case 3: ABS+ASC Case 4: ABS+FASC Case 5: ABS+APC Case 6: ABS+UPC Case 7: ABS+DYC

0.08 0.12 Time (s)

Fig. 25 Rotational angle of the occupant's head about x axis (offset frontal vehicle-to-vehicle impact), vehicle (a).

40 b rH

« -20

Case 1: free rolling Case 2: ABS Case3: ABS+ASC

---Case 5: ABS+APC --Case 6: ABS+UPC ---Case 7: ABS+DYC

\__________i-'—

/ - . ------ _1_._

—— - —^-- —

M ..................... 1 i

\ N 1 .

\ t...........

Y / 1 i

Y t V;

Time (s)

Fig. 26 Rotational acceleration of the occupant's head about x axis (offset frontal vehicle-to-vehicle impact), vehicle (a).

620 621 622

628 629

It is shown that the occupant's pelvis relative displacement and deceleration for vehicle (b) are insignificantly affected by the application of VDCS on the other vehicle (vehicle (a)). There are very small and insignificant increases, especially on the peak values, for all cases compared with the free rolling case.

The occupant's chest rotational angle for vehicle (b) and its acceleration about y axis are also obtained. It observed that there are no changes in the rotational angle; however, there are small variations among the different cases on the occupant's chest acceleration from 0.13 to 0.15 s. These variations are also very small and insignificant.

The occupant's head rotational angle abouty axis for the occupant in vehicle (b) is gained. It is shown that there are very small differences of the maximum rotational angle according to the different cases. Fig. 27 shows the occupant's head rotational acceleration abouty axis for all cases. From this figure, a clear difference in the head rotational acceleration is detected at 0.135 s. When the VDCS is applied, the maximum head rotational acceleration becomes higher than the one in the free rolling case with different values from 5000 to 15000 deg/s2 related to each case; and the maximum head rotational acceleration is shown in Case 2.

55 45 35 25

■ffi

g-15 S "25

Pi -35

ase 1: free rolling ase2:ABS

......... G \

----- Case 3: ABS+ASC ---Case 4: ABS+FASC -•- Case5:ABS+APC --Case 6: ABS+UPC ---Case 7: ABS+DYC

0.08 0.12 Time (s)

Fig. 27 Rotational acceleration of the occupant's head about y axis (vehicle offset frontal vehicle-to-vehicle impact), vehicle (b).

The occupant's chest rotational angle about x axis for vehicle (b) is recorded. Compared with the free rolling case, the rotational angle of the chest is increased by small values from about 0.2 deg in Case 6

635 to about 2 degs in Cases 2 and 4. The occupant's chest acceleration about the x axis showed very small

636 increases of the chest rotational acceleration when the VDCS were applied at the periods from 0.04 to

637 0.09 s and from 0.13 to 0.15 s. This increase in the chest rotational acceleration ranges between 300 to

638 800 deg/s2, however, these are not significant values.

639 The maximum occupant's head rotational angle about x axis is also increased when any of the VDCS

640 is applied. This increase ranges between 0.2 to 1.0 deg, and this is not a significant value. The

641 maximum head rotational angle is observed in Case 2, while the minimum value is detected in Case 1.

642 The maximum positive acceleration of the occupant's head about x axis is almost the same. However,

643 the maximum negative head rotational acceleration is increased when the VDCS are applied. In Case 6

644 the head rotational acceleration is increased by about 5000 deg/s2, while the highest increase value is

645 observed in Case 2 by about 15000 deg/s2.

646 4 Conclusions

647 Development of a new 6-DOF vehicle dynamics/crash mathematical model and three

648 dimensional-three-mass occupant mathematical model have been represented to study the effect of

649 vehicle dynamic control systems (VDCS) on vehicle crash at offset frontal vehicle-to-vehicle collision.

650 The models presented here would be very useful in the early design stages for assessing the crash

651 worthiness performance of the vehicle and for selecting appropriate vehicle parameters. From the

652 numerical simulations, it can be said that the VDCS can improve the vehicle crash situation and the

653 occupant behaviour. The different cases applied in this paper have a different effect on the vehicle and

654 its occupant. It is shown that the crash event gets worse related to the vehicle (b), based on higher

655 values of vehicle deceleration, pitching angle and acceleration, etc. However, these higher values are

656 very small and insignificant

657 Acknowledgments

658 The authors would like to thank the Egyptian government and the Faculty of Engineering, Ain Shams

659 University for supporting this research. We also acknowledge with sadness, the contribution of Prof.

660 Dave Crolla who has passed away during the period of this research.

661 662

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725 Mustafa Elkady is an assistant professor of mechanical engineering at Lebanese International

726 University (LIU). He received a competition grant from the Egyptian government (~ £100,000 for 3 years)

727 for his PhD. He obtained his PhD in mechanical engineering at the Department of Computing,

728 Engineering and Technology, University of Sunderland, UK (2012). Prior to this he was a teaching

729 assistant in mechanical engineering at the Automotive Department, Ain Shams University, Egypt. He

730 obtained his Master degree in automotive engineering at Ain Shams University, Egypt (2004). His

731 research interests include mathematical modelling analysis, advanced dynamics, vehicle dynamics,

732 crash-worthiness, vehicle safety and impact biomechanics, vehicle engine controls and energy-efficient

733 using lightweight materials. His research outcomes are realized as evident from his over 20 publications,

734 he has published the book, Enhancement of Vehicle Crash/Occupant Safety: Mathematical Modelling.

737 Ahmed Elmarakbi obtained his PhD in mechanical engineering from the University of Toronto, Canada

738 (2004). After successful postdoctoral fellowships in Canada and Japan, he moved to the University of

739 Sunderland, UK in 2007, where he is, currently, a professor of automotive composites. His research

740 interests lie in the area of energy-efficient and safe vehicles (EESVs) including advanced composite

741 materials (e.g., grapheme) for automotive applications and low carbon vehicles. His work outcomes are

742 recognized both nationally and internationally as evident from his 70+ plenary lectures, invited talks and

743 presentations; 130+ peer-reviewed research papers. Most recently (2013), he has published the book:

744 Advanced Composite Materials for Automotive Applications: Structural Integrity and Crash-worthiness,

745 with Wiley, UK. He has 15 years of experience managing national and international projects, including

746 multi-disciplinary collaborative projects with Europe, USA, Canada, China, Japan, and Brazil. He has

747 received many prestigious awards and grants worldwide, including EU Graphene Flagship,

748 Horizon2020, EPSRC, NSERC, JSPS, OGS, FP7, and several fellowships. He is expert reviewer for

749 FP7 and EPSRC, member of several professional bodies; editorial-board member of high-impact

750 international journals; organizer of international conferences and reviewer for conferences and many

751 high-impact journals. He is also founder Editor-in-Chief of International Journal of Automotive

752 Composites. He has an extensive track record of collaboration with the automotive industry and

753 world-class academic institutions over the last 15 years and he is currently a member of the EU

754 Graphene Flagship.

757 John MacIntyre is the dean of the Faculty of Applied Sciences, and Pro Vice Chancellor at the

758 University of Sunderland. He has worked at the University of Sunderland since 1992, having graduated

759 from the University with a First Class Honours Degree in combined science (computer science and

760 physiology). He then went on to complete a PhD in applied artificial intelligence, focusing on the use of

761 neural networks in predictive maintenance, which was awarded in 1996. During 1990s John established

762 a research centre for adaptive systems at the university, which became recognized by the UK

763 government as a centre of excellence for applied research in adaptive computing and artificial

764 intelligence. The centre undertook many projects working with and for external organizations in industry,

765 science and academia, and for three years ran the smart software for decision makers programme on

766 behalf of the Department of Trade and Industry. He has successfully supervised PhDs in fields ranging

767 from neural networks, hybrid systems, and bioinformatics through to lean manufacturing, predictive

768 maintenance, and business and maintenance strategies. He went on to become associate dean, and

769 then the dean of the School of Computing, Engineering and Technology, covering computer science

770 and engineering. In 2008 he became the dean of the Faculty of Applied Science, and in 2010 Pro Vice

771 Chancellor of the University.

773 Mohammad Alhariri is a research assistant in the Department of Computing, Engineering and

774 Technology and a PhD student in automotive engineering in the University of Sunderland. His research

775 interests lie in the area of safety in passenger-vehicle. His current work focuses on developing a novel

776 controller for vehicles dynamic systems aiming for better energy absorption resulting from vehicle frontal

777 crashes.