非独立悬架汽车的建模与仿真
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q
ρ
stand for bodies centrifugal forces.
Now, center of mass matrix is
1 1 1 2 B(ZC − ZD )e1 + R( X C + X D )e1 M = 0 1 3 3 B(Z A − Z B )e1 + R( X A + X B )e1 2
汽车独立悬架麦弗逊式独立悬架扭力梁式非独立悬架双叉臂式独立悬架四连杆独立悬架多连杆独立悬架双横臂式独立悬架独立悬架扭力梁式半独立悬架双连杆独立悬架
2010 Asia-Pacific Conference on Power Electronics and Design
Modeling and Simulation of Non-independent Suspension Vehicle
(5) Where,
F1 =m1V2源自ρ，F2 =
m2V
2
ρ
，
and
F3 =
m3V 2
1 F = (0,0,0,2k s 2 q4 + cs 2 q4 , k s 2 Bs22 q5 + cΦ 2 q5 , 2 (4) 1 2 T 2k s1q6 + cs1q6 , k s1 Bs1q7 + cΦ1q7 ) 2
1 0 ( − m g + Z + Z )e 0 3 + ( X C + X D ) e 2 − F1 e 2 1 C D 0 0 F = − m2 g e 3 − F2 e 2 0 3 0 (− m3 g + Z A + Z B )e 3 + ( X A + X B )e 2 − F3 e 2
978-0-7695-4045-0/10 $26.00 © 2010 IEEE DOI 10.1109/APPED.2010.31
0
P = diag ( p 1 , p 2 , p 3 ) are the system’s slide axis and
revolution axis vector matrix. The system has 7 DOF, and the generalized freedom array is
k s 2 respectively stand for the front and rear single side
suspension linear stiffness. Bs1 , Bs 2 respectively for effective distance of the front and rear suspension spring, cs1 and cs 2 stand for front and rear suspension linear damps. cΦ1 and cΦ 2 stand for front and rear suspension roll damps separatly. Then the model system inner restraint force matrix:
localization and direction are shown in Fig.1 (H0, (H1
，e
e ) and
1
) are coincided.
2 e3
2 e2 2 e1
H2 XC ZC
e3 3
H3
e3 2
XA
e
1 3
e
e31
ZA
1 2
H1(H0)
XD ZD
1 e1
I.
INTRODUCTION
q = (q1 , q2 , q3 , q4 , q5 , q6 , q7 )T
For
(1)
，
1
，
2
，
3
q1 = V , q1 = 0 , then the model has 6DOF. During calculation process, sin qi = qi , cos qi = 1 , where i = 3,5,7 . The mass matrix m and the central inertia tensor
Liu Jinxia
College of Mechanical and Electroin Engneering
Shandong University of Science and Technology, SUST Qingdao, China xiar_liu@
0
Abstract—In this paper, six DOF model has been established for non-independent suspension vehicle with Robertson - Widenborg multi-body dynamics method. On this basis, Yaw velocity gain of a heavy vehicle was simulated by Matlab. The simulation results verified the model is reasonable. After furthe simulation, it indicates the model has theory significant for researching the handling and stability and designing suspension system and the structure layout of this type vehicle. Keywords—vehicle; non-independent suspension; rigid multi-body dynamics; simulation
ZA = (
0 m v2 R bm2v2 ( R + h) 1 b mg + ( 3 + + ks1Bs21q7 ) / B)e3 2L ρ Lρ 2 ,
matrix J respectively:
m = diag (m1 , m2 , m3 ) J = diag ( J 1 , J 2 , J 3 )
(2) (3)
93
B. The inner forces The system inner force comes from H2 and H3.
k s1 ,
XB
ZB
The structure of non-independent suspension is that the two sides wheels of a vehicle are mounted on a whole axle,and the axle connected with frame through the suspention. This type suspension structure is simple, low cost, maintenance easy, and can provide reliable transmission power, so widely used in heavy-duty trucks, passenger cars and some other general cars. These vehicles play an important role in the national economy. Its stability studies should pay sufficient attention to. In this paper, considering the characteristics of non-independent suspension it has established non-independent suspension vehicle multi-body dynamic model based on the Robertson- Widenborg Multi-body dynamics method, and simulated a heavy-duty truck. II. BUILDING THE MODEL
Figure 1. Non-indupendent suspension vehicle dynamics model.
C1 is located at the center of front axle and C3 is at the center of rear axle; C2 is above the center of sprung mass h1; the distance between axle and roll axis is h ; a and b stand for the distance of automobile center of mass to front and rear axles, where a+b=L; assume front tread is equal to rear tread named B; the radius of tire is R. Articulations H1, H2 and H3 are separately between B0 and B1, B1 and B2, B2 and B3. Slide axis and revolution axis vector array of H1, H2, H3 individually:
(6)
C. The external forces The external forces include gravity, ground facing tire action as well as centrifugal force. Z A , Z B , Z C and Z D respectively stand for four tires radial forces. g stands for gravity acceleration. ρ is the travel radius. Then
ground; (H1 e ), (H2 e ) and (H3 e ) are local coordinate systems, separately fixed on B1, B2, B3; the origin of H1 is located at the crossing point of the automobile center of mass perpendicular and the line between rear axle center and front axle center; the origin of H2 is at the crossing point of automobile center of mass perpendicular and the roll axis; the origin of H3 is at the center of rear axle. At the initial time, coordinate systems
k 1 = (e1 , e 2 ,0) , p1 = (0,0, e 3 ) , k 2 = (e 3 ,0) , p 2 = (0, e1 ) , k 3 = (e 3 ,0) , p 3 = (0, e1 ) ,
So
2 3 3
0
0
1
2
k = diag (k 1 , k 2 , k 3 )
and
A. Model hypothesis The automobile is composed of 3 rigid bodies[1], shown in fig.1. The rear axle is the first rigid body named B1, the suspension mass is B2, and the front axle is B3. The center of mass rigid body Bi is Ci, and the mass is mi, where i=1,2,3; Take the ground as the total inertia reference base, named B0. (H0, e ) is the inertial coordinate system, fixed on the
ρ
stand for bodies centrifugal forces.
Now, center of mass matrix is
1 1 1 2 B(ZC − ZD )e1 + R( X C + X D )e1 M = 0 1 3 3 B(Z A − Z B )e1 + R( X A + X B )e1 2
汽车独立悬架麦弗逊式独立悬架扭力梁式非独立悬架双叉臂式独立悬架四连杆独立悬架多连杆独立悬架双横臂式独立悬架独立悬架扭力梁式半独立悬架双连杆独立悬架
2010 Asia-Pacific Conference on Power Electronics and Design
Modeling and Simulation of Non-independent Suspension Vehicle
(5) Where,
F1 =m1V2源自ρ，F2 =
m2V
2
ρ
，
and
F3 =
m3V 2
1 F = (0,0,0,2k s 2 q4 + cs 2 q4 , k s 2 Bs22 q5 + cΦ 2 q5 , 2 (4) 1 2 T 2k s1q6 + cs1q6 , k s1 Bs1q7 + cΦ1q7 ) 2
1 0 ( − m g + Z + Z )e 0 3 + ( X C + X D ) e 2 − F1 e 2 1 C D 0 0 F = − m2 g e 3 − F2 e 2 0 3 0 (− m3 g + Z A + Z B )e 3 + ( X A + X B )e 2 − F3 e 2
978-0-7695-4045-0/10 $26.00 © 2010 IEEE DOI 10.1109/APPED.2010.31
0
P = diag ( p 1 , p 2 , p 3 ) are the system’s slide axis and
revolution axis vector matrix. The system has 7 DOF, and the generalized freedom array is
k s 2 respectively stand for the front and rear single side
suspension linear stiffness. Bs1 , Bs 2 respectively for effective distance of the front and rear suspension spring, cs1 and cs 2 stand for front and rear suspension linear damps. cΦ1 and cΦ 2 stand for front and rear suspension roll damps separatly. Then the model system inner restraint force matrix:
localization and direction are shown in Fig.1 (H0, (H1
，e
e ) and
1
) are coincided.
2 e3
2 e2 2 e1
H2 XC ZC
e3 3
H3
e3 2
XA
e
1 3
e
e31
ZA
1 2
H1(H0)
XD ZD
1 e1
I.
INTRODUCTION
q = (q1 , q2 , q3 , q4 , q5 , q6 , q7 )T
For
(1)
，
1
，
2
，
3
q1 = V , q1 = 0 , then the model has 6DOF. During calculation process, sin qi = qi , cos qi = 1 , where i = 3,5,7 . The mass matrix m and the central inertia tensor
Liu Jinxia
College of Mechanical and Electroin Engneering
Shandong University of Science and Technology, SUST Qingdao, China xiar_liu@
0
Abstract—In this paper, six DOF model has been established for non-independent suspension vehicle with Robertson - Widenborg multi-body dynamics method. On this basis, Yaw velocity gain of a heavy vehicle was simulated by Matlab. The simulation results verified the model is reasonable. After furthe simulation, it indicates the model has theory significant for researching the handling and stability and designing suspension system and the structure layout of this type vehicle. Keywords—vehicle; non-independent suspension; rigid multi-body dynamics; simulation
ZA = (
0 m v2 R bm2v2 ( R + h) 1 b mg + ( 3 + + ks1Bs21q7 ) / B)e3 2L ρ Lρ 2 ,
matrix J respectively:
m = diag (m1 , m2 , m3 ) J = diag ( J 1 , J 2 , J 3 )
(2) (3)
93
B. The inner forces The system inner force comes from H2 and H3.
k s1 ,
XB
ZB
The structure of non-independent suspension is that the two sides wheels of a vehicle are mounted on a whole axle,and the axle connected with frame through the suspention. This type suspension structure is simple, low cost, maintenance easy, and can provide reliable transmission power, so widely used in heavy-duty trucks, passenger cars and some other general cars. These vehicles play an important role in the national economy. Its stability studies should pay sufficient attention to. In this paper, considering the characteristics of non-independent suspension it has established non-independent suspension vehicle multi-body dynamic model based on the Robertson- Widenborg Multi-body dynamics method, and simulated a heavy-duty truck. II. BUILDING THE MODEL
Figure 1. Non-indupendent suspension vehicle dynamics model.
C1 is located at the center of front axle and C3 is at the center of rear axle; C2 is above the center of sprung mass h1; the distance between axle and roll axis is h ; a and b stand for the distance of automobile center of mass to front and rear axles, where a+b=L; assume front tread is equal to rear tread named B; the radius of tire is R. Articulations H1, H2 and H3 are separately between B0 and B1, B1 and B2, B2 and B3. Slide axis and revolution axis vector array of H1, H2, H3 individually:
(6)
C. The external forces The external forces include gravity, ground facing tire action as well as centrifugal force. Z A , Z B , Z C and Z D respectively stand for four tires radial forces. g stands for gravity acceleration. ρ is the travel radius. Then
ground; (H1 e ), (H2 e ) and (H3 e ) are local coordinate systems, separately fixed on B1, B2, B3; the origin of H1 is located at the crossing point of the automobile center of mass perpendicular and the line between rear axle center and front axle center; the origin of H2 is at the crossing point of automobile center of mass perpendicular and the roll axis; the origin of H3 is at the center of rear axle. At the initial time, coordinate systems
k 1 = (e1 , e 2 ,0) , p1 = (0,0, e 3 ) , k 2 = (e 3 ,0) , p 2 = (0, e1 ) , k 3 = (e 3 ,0) , p 3 = (0, e1 ) ,
So
2 3 3
0
0
1
2
k = diag (k 1 , k 2 , k 3 )
and
A. Model hypothesis The automobile is composed of 3 rigid bodies[1], shown in fig.1. The rear axle is the first rigid body named B1, the suspension mass is B2, and the front axle is B3. The center of mass rigid body Bi is Ci, and the mass is mi, where i=1,2,3; Take the ground as the total inertia reference base, named B0. (H0, e ) is the inertial coordinate system, fixed on the