An introduction to predictive maintenance - part 4 pdf

quency would be indicated as 4X, or four times the running speed. In addition, because

some malfunctions tend to occur at specific frequencies, it helps to segregate certain

classes of malfunctions from others.

Note, however, that the frequency/malfunction relationship is not mutually exclusive,

and a specific mechanical problem cannot definitely be attributed to a unique fre￾quency. Although frequency is a very important piece of information with regard to

isolating machinery malfunctions, it is only one part of the total picture. It is neces￾sary to evaluate all data before arriving at a conclusion.

Amplitude

Amplitude refers to the maximum value of a motion or vibration. This value can be

represented in terms of displacement (mils), velocity (inches per second), or acceler￾ation (inches per second squared), each of which is discussed in more detail in the

Maximum Vibration Measurement section that follows.

Amplitude can be measured as the sum of all the forces causing vibrations within a

piece of machinery (broadband), as discrete measurements for the individual forces

(component), or for individual user-selected forces (narrowband). Broadband, com￾ponent, and narrowband are discussed in the Measurement Classifications section that

follows. Also discussed in this section are the common curve elements: peak-to-peak,

zero-to-peak, and root-mean-square.

Maximum Vibration Measurement. The maximum value of a vibration, or amplitude,

is expressed as displacement, velocity, or acceleration. Most of the microprocessor￾based, frequency-domain vibration systems will convert the acquired data to the desired

form. Because industrial vibration-severity standards are typically expressed in one of

these terms, it is necessary to have a clear understanding of their relationship.

Displacement. Displacement is the actual change in distance or position of an object

relative to a reference point and is usually expressed in units of mils, 0.001 inch. For

example, displacement is the actual radial or axial movement of the shaft in relation

to the normal centerline, usually using the machine housing as the stationary refer￾ence. Vibration data, such as shaft displacement measurements acquired using a prox￾imity probe or displacement transducer, should always be expressed in terms of mils,

peak-to-peak.

Velocity. Velocity is defined as the time rate of change of displacement (i.e., the first

derivative, or X

.

) and is usually expressed as inches per second (ips). In simple

terms, velocity is a description of how fast a vibration component is moving rather

than how far, which is described by displacement.

Used in conjunction with zero-to-peak (PK) terms, velocity is the best representation

of the true energy generated by a machine when relative or bearing cap-data are used.

dX

dt

130 An Introduction to Predictive Maintenance

[Note: Most vibration-monitoring programs rely on data acquired from machine

housing or bearing caps.] In most cases, peak velocity values are used with vibration

data between 0 and 1,000 Hz. These data are acquired with microprocessor-based,

frequency-domain systems.

Acceleration. Acceleration is defined as the time rate of change of velocity (i.e.,

second derivative of displacement, or X¨) and is expressed in units of inches per

second squared (in/sec2

). Vibration frequencies above 1,000 Hz should always be

expressed as acceleration.

Acceleration is commonly expressed in terms of the gravitational constant, g, which

is 32.17 ft/sec2

. In vibration-analysis applications, acceleration is typically expressed

in terms of g-RMS or g-PK. These are the best measures of the force generated by a

machine, a group of components, or one of its components.

Measurement Classifications. There are at least three classifications of amplitude

measurements used in vibration analysis: broadband, narrowband, and component.

Broadband or overall. The total energy of all vibration components generated by a

machine is reflected by broadband, or overall, amplitude measurements. The normal

convention for expressing the frequency range of broadband energy is a filtered range

between 10 to 10,000 Hz, or 600 to 600,000 cpm. Because most vibration-severity

charts are based on this filtered broadband, caution should be exercised to ensure that

collected data are consistent with the charts.

Narrowband. Narrowband amplitude measurements refer to those that result from

monitoring the energy generated by a user-selected group of vibration frequencies.

Generally, this amplitude represents the energy generated by a filtered band of vibra￾tion components, failure mode, or forcing functions. For example, the total energy

generated by flow instability can be captured using a filtered narrowband around the

vane or blade-passing frequency.

Component. The energy generated by a unique machine component, motion, or other

forcing function can yield its own amplitude measurement. For example, the energy

generated by the rotational speed of a shaft, gear set meshing, or similar machine com￾ponents produces discrete vibration components whose amplitude can be measured.

Common Elements of Curves. All vibration amplitude curves, which can represent

displacement, velocity, or acceleration, have common elements that can be used to

describe the function. These common elements are peak-to-peak, zero-to-peak, and

root-mean-square, each of which are illustrated in Figure 7–11.

Peak-to-peak. As illustrated in Figure 7–11, the peak-to-peak amplitude (2A, where

A is the zero-to-peak) reflects the total amplitude generated by a machine, a group of

components, or one of its components. This depends on whether the data gathered are

d X

dt

2

2

Vibration Monitoring and Analysis 131

broadband, narrowband, or component. The unit of measurement is useful when the

analyst needs to know the total displacement or maximum energy produced by the

machine’s vibration profile.

Technically, peak-to-peak values should be used in conjunction with actual shaft￾displacement data, which are measured with a proximity or displacement transducer.

Peak-to-peak terms should not be used for vibration data acquired using either

relative vibration data from bearing caps or when using a velocity or acceleration

transducer. The only exception is when vibration levels must be compared to vibra￾tion-severity charts based on peak-to-peak values.

Zero-to-peak. Zero-to-peak (A), or simply peak, values are equal to one half of the

peak-to-peak value. In general, relative vibration data acquired using a velocity trans￾ducer are expressed in terms of peak.

Root-mean-square. Root-mean-square (RMS) is the statistical average value of the

amplitude generated by a machine, one of its components, or a group of components.

Referring to Figure 7–11, RMS is equal to 0.707 of the zero-to-peak value, A. Nor￾mally, RMS data are used in conjunction with relative vibration data acquired using

an accelerometer or expressed in terms of acceleration.

7.5 MACHINE DYNAMICS

The primary reasons for vibration-profile variations are the dynamics of the machine,

which are affected by mass, stiffness, damping, and degrees of freedom; however, care

132 An Introduction to Predictive Maintenance

Figure 7–11 Relationship of vibration amplitude.

must be taken because the vibration profile and energy levels generated by a machine

may vary depending on the location and orientation of the measurement.

7.5.1 Mass, Stiffness, and Damping

The three primary factors that determine the normal vibration energy levels and the

resulting vibration profiles are mass, stiffness, and damping. Every machine-train is

designed with a dynamic support system that is based on the following: the mass of

the dynamic component(s), specific support system stiffness, and a specific amount of

damping.

Mass

Mass is the property that describes how much material is present. Dynamically, the

property describes how an unrestricted body resists the application of an external

force. Simply stated, the greater the mass, the greater the force required to accelerate

it. Mass is obtained by dividing the weight of a body (e.g., rotor assembly) by the

local acceleration of gravity, g.

The English system of units is complicated compared to the metric system. In the

English system, the units of mass are pounds-mass (lbm) and the units of weight are

pounds-force (lbf). By definition, a weight (i.e., force) of one lbf equals the force pro￾duced by one lbm under the acceleration of gravity. Therefore, the constant, gc, which

has the same numerical value as g (32.17) and units of lbm-ft/lbf-sec2

, is used in the

definition of weight:

Therefore,

Therefore,

Stiffness

Stiffness is a spring-like property that describes the level of resisting force that results

when a body changes in length. Units of stiffness are often given as pounds per inch

Mass Weight lbf

ft

lbm ft

lbf

= =¥ = lbm *

sec

*

*sec

g

g

c

2

2

Mass Weight = * g

g

c

Weight Mass = * g

gc

Vibration Monitoring and Analysis 133