Page 326 - Mechanical Engineers' Handbook (Volume 2)

4 Standard Forms for Linear Models 317

3
Figure 9 An idealized model of a milling machine: (a) lumped-element model, (b) system graph.

1
v and T Rƒ r
2
p
R
there are now five equations in the five unknowns , , v, T , and ƒ . Combining these
p
r
1
2
equations to eliminate all of the unknowns except v yields, after some manipulation,
3
2
d v d v dv
a a a a v bT
3 3 2 2 1 0 1
dt dt dt
where
JK K
a Jm a Bb mK b
1
1
3
R 2 R
BK
a Jb mB a Kb
2
0
R 2
Differentiating yields the desired I/O equation