ISSN 1068-798X, Russian Engineering Research, 2017, Vol. 37, No. 7, pp. 603–607. © Allerton Press, Inc., 2017.
Original Russian Text © A.S. Kalashnikov, P.A. Kalashnikov, N.V. Khomyakova, 2017, published in Vestnik Mashinostroeniya, 2017, No. 4, pp. 57–62.
Cutting-Head Optimization to Improve the Reliability
of Conical and Hypoid Gears
A. S. Kalashnikov*, P. A. Kalashnikov, and N. V. Khomyakova
Moscow State Manufacturing University (MAMI), Moscow, Russia
Abstract—The use of one- and two-sided cutting heads to ensure that the longitudinal tooth curvature resem-
bles logarithmic and Archimedes spirals is considered. The influence of such shaping on the operational reli-
ability of conical and hypoid gears with round teeth is assessed.
Keywords: conical gears, hypoid gears, longitudinal tooth curvature, flexural strength, logarithmic spirals,
Archimedes spirals, contact spot, bench tests, road tests
Conical and hypoid gears used in the heavy-duty
transmissions of buses, cars, and trucks must satisfy
high requirements in terms of the precision and sur-
face roughness of the gear teeth and also the opera-
tional reliability. Conical and hypoid gears with round
teeth are most commonly used in industry. The tooth
height declines uniformly from the external diameter
to the vertex of the splitting cone.
The shaping of curvilinear tooth is a very complex
operation. The teeth of conical and hypoid gears are
cut by the engagement of teeth of the virtual generating
gear 1 and teeth of the machined gear 2 (Fig. 1). The
teeth of the pinion and gears of rolling transmissions,
as well as the pinion of semirolling transmissions, are
cut by the linear working edges of cutters 3 in cutting
The rotation of head 2 and cradle 5 of the machine
tool reproduces the rolling motion and forms the
octoid profile of the teeth and the longitudinal tooth
curvature whose radius is equal to the generating
radius of the cutting head.
The shaping system for the lateral surfaces of circu-
lar teeth with variable height is approximate. There-
fore, even conical and hypoid gears that are precisely
manufactured and assembled do not always ensure the
required operational reliability [1, 2].
As a rule, three operations are used for the final
tooth cutting in conical and hypoid gears of precision
class 6–7 according to State Standard GOST 1758–81,
before chemicothermal treatment. Two-sided cutting
is used for the driven gear, which has more teeth than
the driving gear (pinion). Both sides of the troughs
between the circular teeth of gear 1 (convex and con-
cave) are machined simultaneously by the two-sided
cutting head with internal 2 and external 3 cutters
(Fig. 2a). The trough width is constant over the whole
tooth length. The convex side of the teeth in the piston 1
is cut by one-sided cutting heads with internal cutters 2,
while the concave side is cut by heads with external
cutters 3 (Fig. 2b). The trough between the pinion
teeth is of variable width: smaller at the internal diam-
eter and larger at the external diameter, or vice versa.
The rate of narrowing of the trough depends on the
longitudinal curvature and the tooth inclination.
We know that the geometric parameter s of the
tooth engagement that have the greatest influence on
the flexural strength of the gear systems are the round-
ing radius at the base of the tooth, the quality of tooth
shaping, and the longitudinal curvature of the teeth
Fig. 1. Tooth cutting for conical and hypoid gears.