Page 165 - Marks Calculation for Machine Design

P1: Rakesh
January 4, 2005
14:16
Brown.cls
Brown˙C03
U.S. Customary ADVANCED LOADINGS SI/Metric 147
Step 2. Using Eq. (3.31) calculate the maxi- Step 2. Using Eq. (3.31) calculate the maxi-
mum pressure (p max ). mum pressure (p max ).
2F 2F
p max = p max =
πbL πbL
2(32,500 lb) 65,000 lb 2(147,500 N) 295,000 N
= = = =
π(0.11 in)(4in) 1.38 in 2 π(0.0028 m)(0.1m) 0.00088 m 2
= 47,025 lb/in 2 = 335,400, 000 N/m 2
= 47.0 kpsi = 335.4MPa
Step 3. As Poisson’s ratio (ν) for the steel Step 3. As Poisson’s ratio (ν) for the steel
wheels is close to the 0.3 used to graph the wheels is close to the 0.3 used to graph the
principal stress equations in Fig. 3.12, assume principal stress equations in Fig. 3.12, assume
the maximum shear stress occurs at 0.75b and the maximum shear stress occurs at 0.75b and
is 0.3 p max . Therefore, using the value for the is 0.3 p max . Therefore, using the value for the
maximum pressure found in Step 2, the maxi- maximum pressure found in Step 2, the maxi-
mum shear stress (τ max ) is mum shear stress (τ max ) is

τ max = 0.3p max = (0.3)(47.0 kpsi) τ max = 0.3p max = (0.3)(335.4MPa)
= 14.1 kpsi = 100.6MPa

Step 4. Using Eq. (3.40), calculate the factor- Step 4. Using Eq. (3.40), calculate the factor-
of-safety (n) for the design as of-safety (n) for the design as
τ max 1 τ max 1
= =
S y n S y n
2 2
1 14.1 kpsi 2 (14.1) 1 100.6MPa 2 (100.6)
= = = 0.47 = = = 0.48
n 60 kpsi 60 n 420 MPa 420
2 2
1 1
n = = 2.13 n = = 2.09
0.47 0.48
The design is safe by a factor of 2. The design is safe by a factor of 2.

3.4 ROTATIONAL LOADING

Rotational loading occurs when a machine element, such as a flywheel, sawblade, or turbine
is spinning about a stationary axis at very high speed. Depending on the complexity of the
machine element, the stresses developed must be analyzed to determine if the design is
safe. It is appropriate here in Chap. 3 to limit the discussion to the basic rotating machine
element: the thin solid disk. Other types of rotating machine elements, such as flywheels,
will be discussed in a later chapter.
The geometry of a thin rotating disk is shown in Fig. 3.13,