Abstract: According to the fundamental of gear mesh dynamic incentives and
elastohydrodynamic lubrication theory, this paper establishes a mathematical model of constraint
multi objective optimization, which seeks the minimum of time-varying stiffness excitation of
gear mesh, the maximum of minimum oil film thickness (the minimum reciprocal) in tooth space,
and the minimum of total volume of transmission at the same time. This paper improves present
particle swarm optimization of two- objective optimization and shows a design of constraint
three-objective optimization. It also programs optimization by Matlab and analyzes examples. The
optimization process and result show that, in less than one range, when more number of teeth,
larger positive modification coefficient and appropriate pressure angle are adopted, the amplitude
of fundamental harmonic in the tooth mesh spectrogram of synthetical stiffness is enlarged, and
the capacity and cost performance are increased effectively while the gear powertrain system
resists vibration of internal incentives.

Key words: time-varying stiffness of gear mesh, minimum oil film thickness in tooth space;
constraint three-objective optimization