T-119
Figure 13-8 shows a constrained gear system in which a rack is meshed. The heavy
line in Figure 13-8 corresponds to the belt in Figure 13-7. If the length of the belt cannot
be evenly divided by circular pitch then the system does not work. It is described by
Equation (13-15).
z1q 1 z2(180 +q1) a
–––– + ––––––––––– + –––– = integer
(13-15)
180 180 p m
Fig. 13-7 Constrained Gear System
Fig. 13-8
Constrained Gear System
Containing a Rack
SECTION 14 BACKLASH
Up to this point the discussion has implied that there is no backlash. If the gears are
of standard tooth proportion design and operate on standard center distance they would
function ideally with neither backlash nor jamming.
Backlash is provided for a variety of reasons and cannot be designated without
consideration of machining conditions. The general purpose of backlash is to prevent
gears from jamming by making contact on both sides of their teeth simultaneously. A
small amount of backlash is also desirable to provide for lubricant space and differential
expansion between the gear components and the housing. Any error in machining which
tends to increase the possibility of jamming makes it necessary to increase the amount of
backlash by at least as much as the possible cumulative errors. Consequently, the smaller
the amount of backlash, the more accurate must be the machining of the gears. Runout of
both gears, errors in profile, pitch, tooth thickness, helix angle and center distance – all
are factors to consider in the specification of the amount of backlash. On the other hand,
excessive backlash is objectionable, particularly if the drive is frequently reversing or if
there is an overrunning load. The amount of backlash must not be excessive for the
requirements of the job, but it should be sufficient so that machining costs are not higher
than necessary.
q1
z1
q2
z2
z2
z3
q1
z1
a
z2
z2
Rack
