For　the　quantitative　fault　diagnosis　of　rolling　element　bearings,　a　nonlinear　vibration　model　for　fault　severity　assessment　of　rolling　element　bearings　is　established　in　this　study.　The　outer　race　defect　size　parameter　is　introduced　into　the　dynamic　model,　and　vibration　response　signals　of　rolling　element　bearings　under　different　fault　sizes　are　simulated.　The　signals　are　analyzed　quantitatively　to　observe　the　relationship　between　vibration　responses　and　fault　sizes.　The　impact　points　when　the　ball　rolls　onto　and　away　from　the　defect　are　identified　from　the　vibration　response　signals.　Next,　the　impact　characteristic　that　reflects　the　fault　severity　in　rolling　element　bearings　is　obtained　from　the　time　interval　between　two　impact　points.　When　the　width　of　the　bearing　fault　is　small,　the　signals　are　presented　as　clear　single　impact.　The　signals　gradually　become　double　impacts　with　increasing　size　of　defects.　The　vibration　signals　of　a　rolling　element　bearings　test　rig　are　measured　for　different　outer　race　fault　sizes.　The　experimental　results　agree　well　with　the　results　from　simulations.　These　results　are　useful　for　understanding　the　vibration　response　mechanism　of　rolling　element　bearings　under　various　degrees　of　fault　severity.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.