Machinery Vibration: Alignment

Appendix C: Formulas

Overview

6400 mils = 360

400 grads = 360

1 radian = 57.2957795

1 second = 4.848137 x 10 -6 radians

1 degree = .0174533 radians

1 degree = 17.77778 mils

1 grad = 0.9

1 grad = .01570797 radians

1 mil = 0.05625

1 mil = 3.375 minutes

1 mil = 202.5 seconds

1 inch = 25.4 millimeters

1 mil = .001 inch (one thousandth of an inch or one milli-inch)

If shaft sag is known, then the first lateral (bending) critical speed can be calculated:

critical RPM = 950

L

=

Length, inches

S

=

sag, mils


Figure C.1

A radian (rad) is the central angle subtended by an arc equal to the radius of a circle. Since an arc equal to the circumference of a circle subtends an angle of 360 , and since the circumference equals 2 ? times the radius r, then:

  • 2 ? rad = 360 = 1 rev

The area of any triangle is equal to one-half the product of the base times the altitude to that base. See Fig. C.2. The formula is:

  • A = 1/2 bh


Figure C.2: Triangle showing base and altitude.

where

A

=

area

b

=

base

h

=

height, or altitude


Figure C.3

The sum of the three interior angles of any triangle is 180 . The formula is:

  • A + B + C = 180

where A, B, and C are the three interior angles of the...

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