Page 143 - Intro Predictive Maintenance

134 An Introduction to Predictive Maintenance

(lbf/in). Machine-trains have three stiffness properties that must be considered in
vibration analysis: shaft stiffness, vertical stiffness, and horizontal stiffness.

Shaft Stiffness. Most machine-trains used in industry have flexible shafts and rela-
tively long spans between bearing-support points. As a result, these shafts tend to flex
in normal operation. Three factors determine the amount of flex and mode shape that
these shafts have in normal operation: shaft diameter, shaft material properties, and
span length. A small-diameter shaft with a long span will obviously flex more than
one with a larger diameter or shorter span.

Vertical Stiffness. The rotor-bearing support structure of a machine typically has more
stiffness in the vertical plane than in the horizontal plane. Generally, the structural
rigidity of a bearing-support structure is much greater in the vertical plane. The full
weight of and the dynamic forces generated by the rotating element are fully sup-
ported by a pedestal cross-section that provides maximum stiffness.

In typical rotating machinery, the vibration profile generated by a normal machine
contains lower amplitudes in the vertical plane. In most cases, this lower profile can
be directly attributed to the difference in stiffness of the vertical plane when compared
to the horizontal plane.

Horizontal Stiffness. Most bearing pedestals have more freedom in the horizontal
direction than in the vertical. In most applications, the vertical height of the pedestal
is much greater than the horizontal cross-section. As a result, the entire pedestal can
flex in the horizontal plane as the machine rotates.

This lower stiffness generally results in higher vibration levels in the horizontal plane.
This is especially true when the machine is subjected to abnormal modes of operation
or when the machine is unbalanced or misaligned.

Damping
Damping is a means of reducing velocity through resistance to motion, in particular
by forcing an object through a liquid or gas, or along another body. Units of damping
are often given as pounds per inch per second (lbf/in/sec, which is also expressed as
lbf-sec/in).

The boundary conditions established by the machine design determine the freedom of
movement permitted within the machine-train. A basic understanding of this concept
is essential for vibration analysis. Free vibration refers to the vibration of a damped
(as well as undamped) system of masses with motion entirely influenced by their
potential energy. Forced vibration occurs when motion is sustained or driven by an
applied periodic force in either damped or undamped systems. The following sections
discuss free and forced vibration for both damped and undamped systems.

Free Vibration—Undamped. To understand the interactions of mass and stiffness,
consider the case of undamped free vibration of a single mass that only moves