03
Mec hanical Translation Systems:
1.tr
+l
sl
,/,t"
,) "+ ,H
J/i
rl,)
(&J
{s)
* ,'trdk :
.fx -* /i(.r"
{c}
F ig. Net
Network elements of mechanical
./'s:
B{
r;
-
,kf
^Sr",
* .*f I)2 x
,\-,/ )
* t)
-
#{oxo *J).v)
tran
lranslation system
Example:
Fig. Multiple element mechanical system
Fig. Corresponding mechanical network
tal
{fr}
For node a:
For node &:
the system ouiput is *:p.
:
Ths trsnstbr I'unction$ 61 "s.lF
and S: xt/-,q, are nbtuined by s*lving tl:e equ*ti$ns firr this syst*m.
:
"r1
-s3
;{6 fur spring J{3
r tro fur spring ,q
-
r{
**Ax*bu
*./
fmcrx
: il - t;# finr mag$ T{?
x4 m *3 : l'n f*r rna$s ,{'fI
"Xr
$ :'t* :
Jft
-.grwState euations:
h-
[-
sFMechanical Rotational Systems:
3?:Jm*J&:*J#3S
Id -
$.
vk
ff{&* *
Ss}
'
* 8{m* * {'}J.} * .s{^s$- * ^sS;"}
Fig. Network elements of mechanical
rotational system
Example:
{8,
",r;
Fig. Multiple element rotational system
n,l
Fig. Corresponding rotational network
w
lrr 1,
'Node
l:
Nsde 2:
Node 3:
r,:? ur:ff
S,
**
Ga #1#363-&9&:s.3
rsrs?*
EFFECTIYE IVIOMEilIT SF INERTIA II'NB DAMPING OF
TRAII1I
A GE'[R
Fig. Representation of a gear train
f&
d, l,
Fig. Corresponding mechanical network
S:nilillber
of teeth $n eflch Sser
al*.D0: veloci$ of eaehgeer
n*: ratio of {rpeed ef drivirg rhaft}l{*peed of driven shaft}
$
:
trilSuXar
positi*n
r
The equations describing th* rystem nre
{d0r * frffir * rr : 1"
: $: *
na:e)1
u
ul2 02 lfi
{o2S2 * 1l2ffi3 + }e gr
T2 * ,tuTr
-' :9
-na
Th* equatio$$ sarr be combined to prcduce
{ r,
\
L*t
*4)rro,
*
{ r.*+}oor *
fiil
nu
n;l
\
&q
*4 +*na
Beq
- Bt ++
na
TZ