Page 46 - Shigley's Mechanical Engineering Design

bud29281_ch01_002-030.qxd 11/11/2009 5:35 pm Page 21 pinnacle s-171:Desktop Folder:Temp Work:Don't Delete (Jobs):MHDQ196/Budynas:

Introduction to Mechanical Engineering Design 21
The previous example represented an absolute tolerance system. Statistically, gap
dimensions near the gap limits are rare events. Using a statistical tolerance system, the
7
probability that the gap falls within a given limit is determined. This probability deals
with the statistical distributions of the individual dimensions. For example, if the distri-
butions of the dimensions in the previous example were normal and the tolerances, t, were
given in terms of standard deviations of the dimension distribution, the standard devia-
2
tion of the gap ¯w would be t w = t . However, this assumes a normal distribution
all
for the individual dimensions, a rare occurrence. To find the distribution of w and/or the
probability of observing values of w within certain limits requires a computer simulation
in most cases. Monte Carlo computer simulations are used to determine the distribution
of w by the following approach:
1 Generate an instance for each dimension in the problem by selecting the value of
each dimension based on its probability distribution.
2 Calculate w using the values of the dimensions obtained in step 1.
3 Repeat steps 1 and 2 N times to generate the distribution of w. As the number of
trials increases, the reliability of the distribution increases.

1–14 Units

In the symbolic units equation for Newton’s second law, F ma,
F = MLT −2 (1–6)
F stands for force, M for mass, L for length, and T for time. Units chosen for any three
of these quantities are called base units. The first three having been chosen, the fourth
unit is called a derived unit. When force, length, and time are chosen as base units, the
mass is the derived unit and the system that results is called a gravitational system of
units. When mass, length, and time are chosen as base units, force is the derived unit
and the system that results is called an absolute system of units.
In some English-speaking countries, the U.S. customary foot-pound-second system
(fps) and the inch-pound-second system (ips) are the two standard gravitational systems
most used by engineers. In the fps system the unit of mass is

FT 2 (pound-force)(second) 2 2
M = = = lbf · s /ft = slug (1–7)
L foot
Thus, length, time, and force are the three base units in the fps gravitational system.
The unit of force in the fps system is the pound, more properly the pound-force. We
shall often abbreviate this unit as lbf; the abbreviation lb is permissible however, since
we shall be dealing only with the U.S. customary gravitational system. In some branches
of engineering it is useful to represent 1000 lbf as a kilopound and to abbreviate it as
kip. Note: In Eq. (1–7) the derived unit of mass in the fps gravitational system is the
2
lbf · s /ft and is called a slug; there is no abbreviation for slug.
The unit of mass in the ips gravitational system is
FT 2 (pound-force)(second) 2 2
M = = = lbf · s /in (1–8)
L inch
2
The mass unit lbf · s /in has no official name.

7 See Chapter 20 for a description of the statistical terminology.