The stiffness matrix of the rolling bearing connects the relative displacement and deflection of the inner raceway to the center of the outer raceway, which is obtained by the ratio of the non-linear force to the deformation displacement curve during operation.Regardless of friction moment, the bearing rotates freely around the Z-axis.The coefficient is obtained from the actual bearing structure model and can take into account the high nonlinearity caused by internal clearance, bearing preload and eccentric effect at high speed of rotation.
The stiffness submatrix of the rolling bearing is expressed as:
For non-linear components, the stiffness is related to the actual displacement, which needs to be solved by an iterative method.
In order to improve bearing support rigidity and ensure transmission accuracy, certain preload force is usually applied to inner and outer rings during bearing installation to eliminate clearance in bearings.Pre-tension force can express a force or a corresponding displacement. Spring gaskets are often used in the transmission to apply a certain amount of Pre-tension on the outer ring.It is difficult to determine a reasonable preload due to the complex operating conditions of the transmission, large changes in load and speed, and the influence of lubrication and heat dissipation conditions.In engineering, the preload is usually determined according to the axial force under full load condition, and ultimately the bearing life and vibration noise value need to be verified by experiment to prevent excessive preload.
In order to obtain better gear engagement characteristics and overall dynamic characteristics in the gearbox, the preload of the support bearing is usually adjusted to obtain the required support stiffness.Since the transmission spindles, countershafts and differentials studied are all supported by tapered roller bearings, only the pretension and stiffness of tapered roller bearings are discussed here.