tooth numbers below a critical value are
automatically undercut in the generating process. The limiting number of teeth in a gear
meshing with a rack is given by the expression:
Nc =
2
(19)
sin²f
This indicates the minimum number of teeth free of undercutting decreases with increasing Pressure angle. For 14½º the value of Nc is 32, and for 20° it is 18. Thus, 200 pressure angle gears with low numbers of teeth have the advantage of much less undercutting and, therefore, are both stronger and smoother acting.
4.9 Enlarged Pinions
Undercutting of pinion teeth is undesirable because
of losses of strength, contact ratio and smoothness of
action. The seventy of these faults depends upon how far below N, the tooth number is.
Undercutting for the first few numbers is small and in many applications its adverse
effects can be neglected.
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For very small numbers of teeth, such as ten and smaller, and for high-precision
applications, undercutting should be avoided. This is achieved by pinion enlargement (or
correction as often termed), wherein the pinion teeth, still generated with a standard
cutter, are shifted radially ourward to form a full involute tooth free of undercut The
tooth is enlarged both radially and circumferentially. Comparison of a tooth form before
and after enlargement is shown in Figure 1.18. The details of enlarged pinion design, mating gear design and, in general, profile-shifted gears is a large and involved subject beyond the scope of this writing. References 1, 3, 5 and 6 offer additional information. For measurement and inspection Figure 1.18 Comparison of such gears, in particular, consult reference 5. |
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4.10 Backlash Calculation
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 and 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 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.
In order to obtain the amount of backlash
desired, it is necessary to decrease tooth thickness (see Figure 1.19). This decrease must
almost always be greater than the desired backlash because of
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