4569846498

Modelling and analysis of suspension systems 211
{V G } 1 {V GE } 1 { 2 } 1 {R GE } 1 (4.147)
⎡V
⎢
⎢
V
⎣⎢
V
Gx
Gy
Gz
(4.148)
{V H } 1 {V HJ } 1 { 5 } 1 {R HJ } 1 (4.149)
2
⎡VHx
⎤ ⎡ 0 1.1062 3.881 10
⎤ ⎡ 0 ⎤ ⎡252.524⎤
⎢
V
⎥ ⎢
⎥
⎢ Hy ⎥
⎢ 1.1062 0 14.121
⎢
⎥ 229
⎥
⎢
112.968
⎥
mm/s
⎢ ⎥ ⎢ ⎥
⎣⎢
VHz
⎦⎥
⎢
2
⎣
3.881 10 14.121 0 ⎥
⎦ ⎣⎢
9
⎦⎥
⎣⎢
3219.588 ⎦⎥
(4.150)
The velocity vector {V P } 1 is already available. In summary the velocity
vectors for the moving points are as follows:
T
{ VC
} [ 120.555 435.157 1979.499 ] mm/s
1
T
{ VD}
[ 204.345 112.260 3355.321 ] mm/s
1
T
{ VG
} [0.0 110.394 3373.150] mm/s
1
T
{ VH
} [ 252.524 112.968 3219.588 ] mm/s
1
T
{ V } [166.468 108.859 3366.0] mm/s
P
⎤ ⎡0
0 0 ⎤ ⎡115⎤
⎡ 0 ⎤
⎥ ⎢
⎥ ⎢
⎥
0 0 12.266
275
⎥
⎢
110.394
⎥
mm/s
⎢
⎥ ⎢ ⎥ ⎢ ⎥
⎦⎥
⎣⎢
0 12.
266 0 ⎦⎥
⎣⎢
9
⎦⎥
⎣⎢
3373.150⎦⎥
1
Having found the velocity {V C } 1 at the bottom of the spring damper unit
point C we can now proceed to carry out a separate analysis of the unit to
find the sliding component of velocity acting along the axis C–I. For this
phase of the analysis we introduce two new bodies, Body 6 and Body 7, to
represent the upper and lower part of the damper as shown in Figure 4.71.
I
Body 6
Body 7
{ 6 } 1
A
Body 3
B
C 7
C 3
C 6
D
Fig. 4.71
Modelling the damper unit for a velocity analysis