The mathematical phenomenological mapping in non-linear dynamics of spur gear pair and radial ball bearing due to the variable stiffness

• Mathematical phenomenological mapping in non-linear dynamics.
• Non-linear dynamics of machine elements and systems.
• Vibration of spur gear pair and ball bearing.
• Stiffness functions for gear pair and ball bearings.
• Reduction the machine elements dynamics to the one-degree of freedom dynamics model.

In this paper the philosophy of mathematical phenomenological mapping has been applied to the non-linear dynamics of spur gears and radial ball bearings. The spur gear pair dynamics and rolling element bearing dynamics are analyzed separately, but with a tendency to reduce the both of the systems to the same mathematical model. The different reasonable assumptions are taken in every of these analyzes, but they do not have significant influence to the accuracy of the results. The systems are reduced to the single degree of freedom dynamics model. The total gear stiffness and ball bearing stiffness are recognized as the main influent factor of vibration behavior of these machine elements. Therefore, the special attention was paid to the new approach and procedure for stiffness solving and related problems. A single spur gear pair dynamics is solved and the results for total gear stiffness and vibration are shown. The conclusions emphasize the importance of described parallel analyzes in order to reduce the calculation time in solving different phenomena with usage of the principle of mathematical phenomenology.