Page 107 - Instrumentation Reference Book 3E

6 Vibration

P. H. SYDENHAM

6.1 Introduction realistic object may need up to six sensors, one for
each degree of freedom.
6.1.1 Physical considerations In practice some degrees of freedom may be
nominally constrained (but are they really?), pos-
Vibration is the oscillatory motion of objects. sibly eliminating the need for some of the six
Several different measurable parameters may be sensors. Practical installation should always con-
of interest: relative position, velocity, acceler- tain a test that evaluates the degree of actual
ation, jerk (the derivative of acceleration), and constraint because sensors will often produce
dynamic force being those most generally desired. some level of output for the directions of vibra-
For each parameter it may be the instant- tion they are not primarily measuring. This is
aneous value, the average value, or some other called their cross-axis coupling factor, transverse
descriptor that is needed. Accuracy of the order response, or some such terminology.
of 1 part in 100 is generally all that is called for. In many installations the resultant of the
Vibration, in the general sense, occurs as peri- motion vector may lie in a constant fixed direc-
odic oscillation, as random motion, or as transient tion with time. In such cases, in principle, only
motion, the latter more normally being referred one sensor will be required provided it can be
to as shock when the transient is large in ampli- mounted to sense in that direction. If not, as is
tude and brief in duration. often the case, more than one unit will be
Vibration can occur in linear or rotational required, the collective signals then being com-
forms of motion, the two being termed respect- bined to produce the single resultant.
ively translational or torsional vibrations. In The potential frequency spectrum of vibration
many ways the basic understanding of each is parameters extends, as shown in Figure 6.2, from
similar because a rotational system also concerns very slow motions through frequencies experi-
displacements. Translational forms are outlined enced in machine tools and similar mechanical
in the following description. There will usually structures to the supersonic megahertz fre-
exist an equivalent rotational system for all quencies of ultrasound. It is not possible to cover
arrangements described. this range with general-purpose sensors. Each
In vibration measurement it is important to
decide whether or not a physically attached fl
mechanical sensor can be used, corresponding to a
contacting or non-contacting technique.
Adequate measurement of vibration can be a
most complex problem. The requirement is to
determine features of motion of a point, or an
extended object, in space relative to a reference
framework; see Figure 6.1.
A point in space has three degrees of freedom.
It can translate in one or more of three directions
when referred to the Cartesian coordinate system.
Rotation of a point has no meaning in this case.
Thus to monitor free motion of a point object Cartesian
requires three measurement sensing channels. coordinate
framework
If the object of interest has significant physical
size it must be treated as an extended object in --I )
which the rotations about each of the three axes, ::;:::;ts
described above, provide a further three degrees Figure 6.1 Possiblemotions of an extended object in
of freedom. Thus to monitor the free motion of a mace relative to a Cartesian framework.