4569846498

Modelling and analysis of suspension systems 225
Equation 4 3 6x 9 6y 436 6z 0 (4.250)
The four equations can now be set up in matrix form ready for solution:
⎡ 3 0 436 9
⎤ ⎡ A s ⎤ ⎡ 669.564 ⎤
⎢
9 436 0 3
⎥ ⎢
⎥ ⎢
28 592.484
⎥
⎢
⎥ ⎢
6x
⎥ ⎢ ⎥
(4.251)
⎢436 9 3 0 ⎥ ⎢6y
⎥ ⎢ 3838.594⎥
⎢
⎥ ⎢ ⎥ ⎢ ⎥
⎣ 0 3 9 436⎦
⎣6z
⎦ ⎣ 0 ⎦
Solving equation (4.251) yields the following answers for the four
unknowns:
A s 7.457 s 2
6x 65.730 rad/s 2
6y 1.147 rad/s 2
6z 0.483 rad/s 2
This gives us the last two angular acceleration vectors for the upper and
lower damper bodies:
T
6 1
T
7 1
{ } [ 65.730 1.147 0.483 ] rad/s
{ } [ 65.730 1.147 0.483 ] rad/s
From equation (4.240) we now have
{A C6C7 } 1 2{ 6 } 1 {V C6C7 } 1 A s {R CI } 1 (4.252)
⎡879.162⎤
⎡ 3 ⎤ ⎡ 856.791
⎤
{ A C C } 1 ⎢
3626.702
⎥
7.457
⎢
9
⎥
⎢
3559.589
⎥
mm/s
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
⎣⎢
80.457
⎦⎥
⎣⎢
436⎦⎥
⎣⎢
3331.709⎦⎥
6 7
2
(4.253)
A comparison of the angular accelerations found from the preceding calculations
and those found using an equivalent MSC.ADAMS model is
shown in Table 4.12.
2
2
Table 4.12 Comparison of angular acceleration vectors computed by theory and
MSC.ADAMS
Body
Angular acceleration vectors
Theory
MSC.ADAMS
x (rad/s 2 ) y (rad/s 2 ) z (rad/s 2 ) x (rad/s 2 ) y (rad/s 2 ) z (rad/s 2 )
2 11.790 0.0 0.0 11.791 0.0 0.0
3 18.819 0.0 1.145 18.823 0.0 1.146
4 29.386 3.737 20.847 29.395 3.737 20.840
5 23.361 0.065 1.843 23.384 0.157 2.053
6 65.730 1.147 0.483 57.204 2.663 0.449
7 65.730 1.147 0.483 57.204 2.663 0.449