| Rolling element bearing(REB)is widely used in the rotational machine owing to its low friction coefficient and load-carrying capacity.REB,as a crucial and fundamental part,is subjected to the alternative stress between the raceways and the rolling elements under working condition,resulting in the contact material flaking,i.e.,fatigue spall.The passing process of the rolling element over the spall zone,especially when it rolls into and exits from the spall zone,will excite the dynamic de-stressing and re-stressing process of the rolling element in the spall zone due to the sharp change of the contact form between the rolling element and the spall zone,and then induce the sudden change of bearing’s contact stiffness,finally result in the dual-impulse behavior in the vibration signal.The profile and time interval of the dual-impulse characteristic and the phase information included in the dual-impulse characteristic signal are directly relevant to the size and the angular position of the spall zone,shaft speed,and radial load,etc.It is worth noting that the dual-impulse time spacing(DITS)provides a novel reliable approach for quantification diagnosis,spall damage severity evaluation,and remaining useful life prediction of REB.As a result,it is concluded that investigating the excitation mechanism of dual-impulse behavior due to rolling element-spall zone contact and realizing the accurate objective quantitative evaluation of spall damage severity are meaningful and valuable for theoretical research of REB and practical engineering application.This thesis is focused on the dual-impulse-based dynamic mechanism modeling and quantitative estimation algorithm of the spall zone size of the REB.The investigation on the contact excitation mechanism between the rolling element and spalled raceway is conducted,the piecewise function formulas for describing the additional displacement and contact force due to the rolling element-spall contact are developed,the impact force induced by the strike of the rolling ball on the trailing edge of the spall zone and the timevarying contact stiffness are derived,and the equivalent contact model between the rolling element and the inner and outer race under Elastohydrodynamic Lubrication(EHL)is established,a dynamic model of dual-impulse behavior based on the additional displacement coupling the additional contact force is proposed,a dynamic model of dualimpulse behavior of ball bearing with a raceway spall under EHL is established,a dynamic model of dual-impulse behavior of ball bearing with a raceway spall based on the time-varying contact stiffness is developed,and a novel analytical model for spall size estimation based on the two adjacent peak time spacing is proposed,the main contributions of this paper are organized as follows:1)The dual-impulse characteristic induced by the localized surface spall can not be accurately described by the current dynamic model based on the time-varying displacement model produced by the rolling element-spall contact.To address this issue,the dynamic and kinematic investigations for the ball-spall contact are performed,the formula of impact force is derived,and the additional displacement and contact force model are optimized.As a result,a dynamic model of dual-impulse behavior of ball bearing with a spall on inner or outer race coupling the additional displacement and contact force is proposed.2)The coupling effects between the EHL and ball bearing vibration can not be accurately described by the current dual-impulse-based dynamic model of ball bearing with a localized surface spall on inner or outer race.To address this issue,the piecewise function formulas for modeling additional displacement and contact force are proposed considering the impact force excited by the strike of the ball on the trailing edge of the spall zone,the equivalent contact model of rolling element-raceway contact under EHL is proposed,and finally a dynamic model coupling the additional displacement and contact force for dual-impulse behavior of ball bearing with a localized surface spall under EHL is proposed.An experimental validation is carried out and shows agreement with the numerical results obtained by the proposed model.3)The conventional approach for solving the contact stiffness of health REB is no longer fit for the non Hertzian contact between the rolling element and the spall zone.To overcome this limitation,the geometric relationship of rolling element-spall zone contact is investigated and analyzed,a train of analytical equations are established for solving time-varying contact stiffness,and a dynamic model based on the additional displacement and contact force excitation for dual-impulse behavior of localized spalled ball bearing is proposed.In addition,the validity of the proposed model was validated.4)It is hardly possible for the existing algorithm to accurately determine the entry position of the rolling element into the spall zone,and the current estimating methods are also complex and less accurate.To address this issue,the dynamic and kinematic analyses of multi-event excitations excited by the passing process of the ball over the spall zone are conducted,the analytical equations for describing the ball-spall contact at the critical position when the ball rolls over the spall zone is derived,and an analytical model for estimating the spall size based on the adjacent peak time spacing is proposed.In addition,the accuracy of the proposed estimation model is validated by the experimental results.It can be concluded from the modeling based on the dual-impulse behavior and corresponding experimental validations that a theoretical foundation can be laid for revealing dual-impulse characteristics excited by non-linear excitation mechanism of rolling element-spall contact,damage severity assessment,and quantitative diagnosis of REB. |
