4569846498

222 Multibody Systems Approach to Vehicle Dynamics
⎡A
⎢
⎢
A
⎣⎢
A
Cx
Cy
Cz
⎤ ⎡ 372.
059 ⎤ ⎡ 161.445 ⎤ ⎡ 210.
614 ⎤
⎥ ⎢
⎥ ⎢
⎥
27 893.260 583.
447
⎥
⎢
28
476.707
⎥
mm/s
⎢
⎥ ⎢ ⎥ ⎢
⎥
2
⎦⎥
⎣⎢
6109.169 ⎦⎥
⎣⎢
2653.
479⎦⎥
⎣⎢
3455.
690 ⎦⎥
(4.220)
⎡A
⎢
⎢
A
⎣⎢
A
Gx
Gy
Gz
{A D } 1 {A DA } 1 { 3 } 1 {V D } 1 { 3 } 1 {R DA } 1 (4.221)
⎡A
⎢
⎢
A
⎣⎢
A
(4.223)
{A G } 1 {A GE } 1 { 2 } 1 {V G } 1 { 2 } 1 {R GE } 1 (4.224)
⎤ ⎡ 0 ⎤ ⎡0 0 0 ⎤ ⎡115⎤
⎡ 0 ⎤
⎥ ⎢
⎥ ⎢
⎥
41
375.058 0 0 11.
791
⎥ ⎢
275
⎥
⎢
41
481.177
⎥
mm/s
⎢
⎥ ⎢
⎥ ⎢ ⎥ ⎢
⎥
2
⎦⎥
⎣⎢
1354.093 ⎦⎥
⎣⎢
0 11. 791 0 ⎦⎥
⎣⎢
9
⎦⎥
⎣⎢
1888.
432 ⎦⎥
(4.225)
{A H } 1 {A HJ } 1 { 5 } 1 {V H } 1 { 5 } 1 {R HJ } 1 (4.226)
⎡A
⎢
⎢
A
⎣⎢
A
Dx
Dy
Dz
Hx
Hy
Hz
⎤ ⎡ 96. 030 ⎤ ⎡ 0 1.
145 0 ⎤ ⎡115
⎥ ⎢
⎥ ⎢
⎥
⎥
47
281.651 1. 145 0 18.
819
⎢
239
⎢
⎥ ⎢
⎥ ⎢
⎦⎥
⎣⎢
1576.804 ⎦⎥
⎣⎢
0 18.
819 0 ⎦⎥
⎣⎢
15
⎡ 177.
625 ⎤
⎢
47
432.261
⎥
mm/s
⎢
⎥
2
⎣⎢
2920.
973 ⎦⎥
3
⎤ ⎡9. 602 10 ⎤ ⎡ 0 1. 843 0.
06466⎤
⎡ 0 ⎤
⎥ ⎢
⎥ ⎢
⎥ ⎢
⎥
⎥
⎢45
743.094 ⎥ 1. 843 0 23.
361 229
⎢
⎥ ⎢ ⎥
⎦⎥
⎢
⎥
⎣
1605.022
⎦ ⎣⎢
0. 06466 23.
361 0 ⎦⎥
⎣⎢
9
⎦⎥
⎡ 422.
619 ⎤
⎢
45
953.343
⎥
mm/s
⎢
⎥
2
⎣⎢
3744.
647 ⎦⎥
(4.227)
The acceleration vector {A P } 1 is already available from the initial bump
analysis and the solution of equation (4.215). In summary the acceleration
vectors for the moving points are as follows:
{A C } T 1 [210.614 28 476.707 3455.690] mm/s 2
{A D } T 1 [177.625 47 432.261 2920.973] mm/s 2
{A G } T 1 [0.0 41 481.177 1888.432] mm/s 2
{A H } T 1 [422.619 45 953.343 3744.647] mm/s 2
{A P } T 1 [558.211 36 163.671 0.0] mm/s 2
Having found the acceleration {A C } 1 at the bottom of the damper unit we
can now proceed to carry out a separate analysis of the unit to find the components
of acceleration acting between Bodies 6 and 7.
As with the velocity analysis, this phase of the acceleration analysis
can be facilitated by the modelling of three coincident points, C 3 on Body 3,