Page 302 - Machinery Component Maintenance
P. 302
284 Machinery Component Maintenance and Repair
A solution may be found in a statistical approach. Since the various
unbalance errors are vectors and may have different angular directions,
they add to each other vectorially, not arithmetically. If certain errors
have opposite angular directions, they actually subtract, thus resulting in
a smaller total error than assumed above.
To determine the probable maximum error, the root of the sum of the
squares (RSS) method should be used. This statistical method requires
that the individual errors (U, to U4) each be squared, then added and the
square root drawn of the total. In the aforementioned example, the com-
putation would look as follows:
= J32 + 0.12 + 0.12 + 32
= 4.25 (g in.)
Now the operator is allowed a working tolerance of 10 - 4.25 = 5.75
g in., or 50 percent more than when the unbalance errors were added
arithmetically. If this still presents a problem, a more sensitive machine
may be needed, or the rotor may have to be trim- or field-balanced after
assembly. Under certain conditions “biasing” of the arbor may help.
This method is described in the third subheading down.
Balancing the Arbor
Since residual unbalance in the arbor itself is one of the factors in the
error analysis, every arbor should be carefully balanced and periodically
checked. If the arbor has a keyway, it should be of the same length as the
final assembly key and be filled completely during balancing with a half-
key (split lengthwise) for rotors of North American origin, with a full
key for rotors of European origin (see also Figure 6-22 and Figure 6-23).
If the arbor has a nut, the arbor should be balanced first without it. Then
the nut should be added and any residual unbalance corrected in the nut.
The nut should be checked in several angular positions to make sure it
stays in balance. If it does not, its locating surface must be corrected.
Special Design Features
If the arbor is to be used on a horizontal balancing machine with end-
drive, one arbor face must be provided with a pilot and bolt hole circle to