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errors. However, this combination is not necessarily simple since many of the transmission-error sources are identical to those associated with variable backlash. In addition, transmission error varies between maximum lead and lag values. Details of the integration are beyond the scope of this coverage, but can be found in Reference 5. The basic equation for the peak value is:

(peak) IPE = E_i = ±(E_T + B_c )                                                                       (51)
                                      2

where:
B_c = backlash constant with rotation
E_T = transmission error (± peak value)

12.4 Control of Backlash

In the many cases in which it is necessary to minimize backlash, a proper control must be chosen. The direct approach of narrowing all allowances and tolerances on sources is effective. Accordingly, precision gear qualities are specified, particularly with regard to testing radius (tooth thickness) and TCE. However, there are practical limitations since cost increases exponentially with precision. Some method of circumventing extremes of precision must be used. An alternate means of controlling backlash is to use adjustable centers or to spring-load the gears by one of several different designs. In this regard, the spring-loaded scissor gear has particular merit since all backlash is continually eliminated. However, it is limited to low torque applications. Consult Reference 5 for an in-depth coverage of various types of backlash control and elimination schemes. 

12.5 Control of Transmission Error

The methods available for controlling transmission error are much more limited than the means for controlling backlash. The most effective is the direct control of errors by specification of close tolerances. This means precision categories for TCE, TTCE, and for installation components such as shafting and ball bearings.
     In special cases, such as when the gear ratio of the mesh is unity, it is possible to calibrate the gears to match pitchline runouts to provide cancellation of error. However, besides being costly and not foolproof, this method is very limited since it requires not only a 1:1 gear ratio, but also identical runout errors for both gears.

13.0 GEAR STRENGTH AND DURABILITY

Gear failure can occur due to tooth breakage or surface failure in the form of fatigue and wear. The first is referred to as tooth strength and the latter as durability. Strength is determined in terms of tooth-beam stresses for both static and dynamic conditions, following well established formulas and procedures. Durability ratings are evaluated in terms of surface stresses including the influence not only of dynamics, but also of material combinations, lubrication and a considerable number of empirically derived factors.

13.1 Bending Tooth Strength

Tooth loading produces stresses that can ultimately result in tooth breakage. This is not a prevalent

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