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This study has revealed by taking nondimensional measures that the vibrational characteristics, basically the behaviour of stiffness, of helical gear pairs whose transverse and overlap contact ratios are invariant are identical. The feature is colligated correspondingly at the point on the contact ratio domain by the coordinate of their transverse and overlap contact ratio. By the colligation, the charts have been proposed as named the performance diagram on vibration, which indicate the level of vibration of a pair by contour lines on the contact ratio domain, after the vibrations of helical gear pairs are calculated by a developed simulator. The work has established the method of easy design and improvement for the lower vibration helical gear pair by a cursory glance at these proposed diagrams.

Energy optimal control theory (EOC) is applied to the energy flow control of a hybrid electric vehicle. Since the differential equation is solved analytically, the control law can be easily implemented in real time. Because the objective function is described in power form that permits negative value, not only the energy consumption is minimized but also the energy regeneration by the motor is maximized. In the simulation for the 10-mode driving, it is shown that the fuel cost of EOC is 15% lower than the rule based control (RBC).