Page 51 - Gear Technology Solutions

publications, invented the same tooth profile independent from Wildhaber in
1956. The contributions of both scientists are honored today by calling this
system Wildhaber-Novikov gears.

Ernest Wildhaber is the father of modern gear theory. His pioneering contribu-
tions have been invaluable for the development of today’s gear calculation and
manufacturing processes.

4.2 News about Hypoid Gears?

The question of whether hypoid gearsets which are designed and manufac-
tured today are based on a precise theory or if their basis is rather approxi-
mated is discussed and analyzed in this chapter. As an opening statement it
can be affirmed that hypoid gearsets with a non-generated gear member and
parallel depth teeth have a mathematically exact base geometry (refer to Fig-
ure 12). Also, hypoids with tapered depth teeth which use a helical motion dur-
ing pinion generation have this mathematically exact base geometry if the ring
gear is non-generated.

A generalized law of gearing was interpreted by Errichello and Stadtfeld [1]
and reads: Conjugate gears transmit uniform rotary motion from one shaft to
another by means of gear teeth. The common normal to the profiles of these
teeth, at all points of contact, must pass through a fixed-point P in the common
connecting line that intersects the two shaft axes and is normal to the pitch el-
ement.

The topics of this chapter are structured accordingly in:

▪ The three fundamental laws of gearing
▪ Perfect conjugacy
▪ Real world applications
▪ Transmission design
▪ Heat treatment, lapping and grinding

4.3 The Three Fundamental Laws of Gearing

The first fundamental law of gearing ng • VS = 0 also implies |N1 x R1| = i • |N2
xR2|, where i is the constant transmission ratio. The three cases in Figure 2
visualize the problem of non-constant ratio and are noncompliant with the first
gearing law because of a ratio change from case to case. This problem led
Leonard Euler to discover the involute tooth profile. A simplistic mathematical
approach teaches that the effective radius vector R remains unchanged while

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