Planetary gearboxes have lots of advantages and are widely used in mechanical transmission systems of many fields.However,severe work conditions result in many failures of planetary gearboxes,so it is necessary to develop their fault diagnosis methods.Traditional fault diagnosis methods of planetary gearboxes based on vibration signals have limitations to identify their early and weak faults,so a new fault diagnosis method based on their ring gears’tooth root strain signals was proposed and the action mechanism of planetary gearbox’s typical faults on their tooth root strain of ring gear was discussed here.Firstly,the modeling method of the tooth root strain of ring gear was analyzed,and the model of the tooth root strain of ring gear was decomposed into the planetary wheelring gear meshing force model,the ring gear tooth form coefficient model and the load between teeth sharing coefficient model.Secondly,the planetary wheelring gear meshing force was calculated with the torsional model of planetary gearboxes,the ring gear tooth form coefficient was derived with the mechanics of materials,and the load between teeth sharing coefficeient of internal meshing was analyzed.Finally,the effects of the faults of planetary gearboxes on the meshing stiffness were studied,and the variation laws of tooth root strain of ring gear under typical faults were computed with the model of the toothroot strain of ring gear.The modeling simulation results showed that faults of different types,different positions and different intensities have different influences on the tooth root strain signals of ring gear and the proposed fault diagnosis method of planetary gearboxes based on tooth root strain is feasible theoretically.