EML 6267 Assignment #3 Spring 2009
Please remember to put your name on your assignment.
Due: Monday, 2/16
1.
(60 pts.) Complete problem 1 from chapter 3 of the text. For part f), use plot limits of
zero to 60000 rpm and zero to 10 mm.
a)
Calculate the directional orientation factor. Using this value, compute and plot the
real and imaginary parts (in m/N) of the oriented frequency response function vs.
frequency (in Hz).
The directional orientation factor is found by first projecting the force,
F
, into the
u
direction, and then projecting that result into the
x
direction.
()
(
)
( ) ( )
671
.
0
35
cos
35
70
cos
cos
cos
=
−
=
−
=
α
β
µ
The oriented frequency response function is the product of the directional
orientation factor and the single degree of freedom frequency response for this
system. It is written as:
( )
⋅
+
−
⋅
−
−
=
2
2
2
2
2
1
2
1
r
r
r
i
r
k
FRF
orient
ζ
, where
n
r
ω
=
and
m
k
n
=
. The result is shown in Fig. s.3.1.b. This figure was produced using
e_3_1_a.m.
0
200
400
600
800
1000
2
0
2
x 10
7
Real (m/N)
0
200
400
600
800
1000
4
2
0
x 10
7
Frequency (Hz)
Imag (m/N)
Figure s.3.1.b: Oriented frequency response function.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documentb)
Determine the minimum value of the real part of the oriented frequency response
function and the corresponding chatter frequency. Calculate
b
lim,crit
.
For a single degree of freedom system, we can calculate the minimum value of
the real part of the frequency response function using:
()
ζ
+
−
=
1
4
1
Re
min
k
FRF
. For this example, the minimum value of the real
part of the oriented frequency response function is then:
4
10
6
.
1
1
4
Re
min
−
×
−
=
+
−
=
µ
k
FRF
orient
mm/N,
where we’ve converted from m/N to mm/N. The corresponding chatter frequency
is approximated as:
( )
5
.
528
1
=
+
=
n
c
f
f
Hz. This result is confirmed in
e_3_1_a.m using the M
ATLAB
®
min
command. The critical stability limit is
determined using:
[]
1
.
2
10
6
.
1
1500
2
1
Re
min
2
1
4
crit
lim,
=
×
−
⋅
⋅
−
=
⋅
−
=
−
orient
s
FRF
K
b
mm.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Schmitz
 µ, 0 m, Microphone, 3 mm, 2 2 K, 0 kg

Click to edit the document details