Mathematical Model of Reducer Step Vibration
Keywords:
Gear, Gear Bearing, Reducer, Vibration, Slippage, Gear TeethAbstract
Purpose: To improve the reliability of fine-module gear reducers, various mathematical models have been developed which
calculate the reducer vibration taking into account certain manufacturing errors. However, these models ignore teeth slippage.
The purpose of this study is building a mathematical model of reducer vibration which takes into account the teeth slippage and
determining the spectral composition of the forces caused by the slippage. Results: The developed mathematical model has shown
that, taking into account the variable slippage velocity, the disturbing force of the slippage occurring during the interaction of
the working tooth profiles is modulated in frequency. The slippage contributes to the gear vibration spectrum. The spectrum
contains not only the harmonics from the disturbing forces caused by manufacturing inaccuracies in the rolling support elements,
gearings and slippage, but also the combinatory harmonics from these forces and the stiffness fluctuations. Practical importance:
The proposed mathematical model allows you to accurately calculate the vibration and the dynamic loads in the element contact
zones. You can also estimate the gearbox operational life and reliability of the reducer much more accurately. At the design stage,
this model helps to normalize the slippage and eliminate technological errors in the elements to achieve the desired service life
of the device.