ME 352  Machine Design I
Name of Student
______________________________
Fall Semester 2011
Lab Section Number
___________________________
Homework No. 10 (30 points). Due at the beginning of lecture on Wednesday, November 16th.
Problem 1.
Solve Problem 15.26, see page 746, using: (i) The Exact Solution; (ii) The Dunkerley
approximation; and (iii) The RayleighRitz approximation.
Problem 2.
Solve Problem 15.27, see page 747, using the Dunkerley approximation.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2
Solution to Problem 1.
A steel shaft is simply supported by two rolling element bearings at A and B as
shown in Figure 1. The length of the shaft is 1.45 m and two flywheels with weight
1
2
W
W
300 N
=
=
are rigidly attached to the shaft at the locations shown. One flywheel is 0.35 m to the right of the left
bearing at A and the other flywheel is 0.35 m to the left of the right bearing at B. The weight of the shaft
can be neglected. The influence coefficients are
5
11
a
12.600 x10
cm/N
−
=
and
5
21
a
9.250 x10
cm/N.
−
=
(i) Determine the first and second critical speeds of the shaft using the exact solution.
(ii) Determine the first critical speed using the Dunkerley approximation and RayleighRitz equation.
Figure 1. A Steel Shaft Simply Supported by Two Rolling Element Bearings.
The exact solutions for the first and second critical speeds of the shaft can be written as
2
11
1
22
2
11
1
22
2
11
22
12
21
1
2
2
2
1
2
( a
m
a
m )
( a
m
a
m )
4 ( a
a
a
a
) m m
1
1
,
ω
ω
2
+
±
+
−
−
=
(1)
From the symmetry of the loading, the influence coefficients
5
11
22
a
a
12.600 x10
cm/N
−
=
=
(2)
From Maxwell's reciprocity theorem, the influence coefficients
5
12
21
a
a
9.250 x10
cm/N
−
=
=
(3)
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Machine Design, 2 m, 5 sec, 0.60 m, 22 M, 1.45 m

Click to edit the document details