In the cylindrical gear transmission system of hybrid electric vehicle, due to the need of lubrication and the manufacturing accuracy and installation error of gear teeth, the backlash in the system can not be avoided. In addition, there are many pairs of cylindrical gears meshing at the same time in the compound planetary gear mechanism of the system, which makes its transmission system a typical nonlinear system. Due to the existence of clearance, the transmission system will have impact in the process of starting and braking, and the resulting dynamic load, especially when the rotation direction of the transmission system changes, its dynamic load is often much greater than the dynamic static load. If the influence of clearance in the transmission mechanism is not considered, overload and damage accidents may occur. Experience shows that the clearance of the transmission system increases continuously in long-term operation, because the wear (such as cylindrical gear or clutch) increases with time. Therefore, to study the nonlinear dynamic characteristics of cylindrical gear transmission system, it is necessary to consider not only the time-varying meshing stiffness, but also the backlash in the system.
It is studied that due to the existence of cylindrical gear tooth side clearance, in the user-defined interval, taking the origin of displacement difference as the coordinate, the stiffness and damping can be parameterized independently. In the elastic damping tooth side clearance, there is the largest parameter. In the case of tooth side clearance or not, the contact stiffness K and contact damping B define the stiffness and damping of the element. The clearance L is an interval, and its center is the zero displacement difference between the two elements, Neutral position. In the tooth side clearance section, this element has clearance stiffness K L and clearance damping B L, which are different from contact stiffness K and contact damping B, as shown in the figure:
Therefore, the clearance of cylindrical gear meshing from tension to compression can be simulated and calculated. When there is no reaction force in the gap interval, when simulating the characteristic curve with gap, K L and B L are equal to zero. Therefore, the internal force fi, elastic force FK and damping force FC generated in the model are:
