A time-varying friction moment calculation method of an angular contact ball bearing with the waviness error

Angular contact ball bearings (ACBs) are extensively applied in various mechanical rotational systems. Most of current works are focused on time-invariant calculation methods of the ACBs with and without the waviness. This work proposes a time-varying calculation method for computing the friction moment of an ACB. This method considers the variations of the contact forces between the contact parts of ACB. In this method, the rolling friction moments caused by the elastic material hysteresis, slipping friction moments produced by the differential ones, slipping moment generated by the sliding friction between the cage and ring, and viscous friction moments engendered by the gas–oil mixture are formulated. The friction moments of ACB with the waviness on the single part and all parts are analyzed. The friction moments from the previous time-invariant and proposed time-varying methods are discussed to show the superiorities of proposed method. The effects of the waviness amplitude, shaft velocity, radial force, and waviness order on the time-varying friction moment of the ACB are discussed. The simulation results indicate that the proposed time-varying method can offer a more reasonable and precise approach to study the time-varying friction moments of the ACBs.