The Study Of Contact Stiffness And Damping Of An EHL Lubricated Spur Gear Pair

The gear tooth surface will deform under a certain working condition, which contributes to the gear vibration. Gears often working under the elastohydrodynamic lubrication(EHL) conditions, besides the deformation of oil film thickness, the oil film will cause the energy dissipation during the dynamic contact due to the viscous effect. It is has significant theoretical significance and practical value to study the oil film stiffness and damping and to develop analytical and numerical contact stiffness, oil film stiffness and damping calculation models.The main contents of this paper are shown as follows:(1) The Hertz minimum deformation equation and the Yang-Sun load-deformation equation are applied to derive the contact stiffness equation. Effects of working condition on the contact stiffness are also studied. Results show that the magnitude of the value of contact stiffness obtained by Yang-Sun model is similar with than that of obtained by Hertz theory, the linearization of the contact force-penetration relation is reasonable.(2) The steady line contact EHL model is developed, and four methods to predict oil film stiffness are proposed, i.e. the minimum film thickness method, the central film thickness method, the global method and the average film thickness method. After compare the results of four methods, this paper studies effects of working condition, surface roughness and starved lubrication degree on the oil film stiffness. And the results show that the oil film stiffness evaluated by four methods are similar under a certain working condition. An increase of the load, or a decrease of the rolling speed would cause an increase of the oil film stiffness. The magnitude of the oil film stiffness is generally two or three orders higher than that of the contact stiffness under the same working condition.(3) Based on the transient line contact EHL model, the contact-vibration model is developed, and two methods are proposed to evaluate oil film damping. Meanwhile the time varying characters of the contact-vibration system and effects of the working condition on the oil film damping are also studied. Results show that the dynamic response of the contact-vibration system is corresponds well to the single degree of freedom vibration model. In terms of the harmonic vibration case, the oil film damping is independent of the amplitude and the frequency of the sinusoidal load exaction. As the normal load and rolling speed increasing, the oil film damping decreases.(4) Taking the FZG test spur gear pair as the research project, and combining the proposed calculation models of contact stiffness, oil film stiffness and damping, this paper studies the variations of the contact stiffness, oil film stiffness and damping during the whole meshing period. And results show that contact stiffness of a spur gear is hardly effected by working conditions, which is mainly determined by the material properties. Oil film stiffness of a spur gear has a relationship with working conditions, which increases with the increasing input torque and decreasing rotation speed. Meanwhile, the oil film damping decreases with the increasing input torque and the increasing rotation speed. What’s more, under the same working condition, different types of coefficient of shifting can lead to variations of normal load, equivalent radius and rolling speed along LOA, so that the oil film stiffness varies along LOA.