As for ultra-precision grinding of difficult-to-process thin-walled complex components with ball-end grinding wheels,interference is easy to occur.According to screw theory and grinding kinematics,a mathematical model is established to investigate the interference and grinding characteristics of the ball-end wheel.The relationship between grinding wheel inclination angle,C axis rotation angle,grinding position angle and grinding wheel wear are analyzed.As the grinding wheel inclination angle increases,the C axis rotatable range decreases and the grinding position angle increases.The grinding position angle and wheel radius wear show a negative correlation with the C axis rotation angle.Therefore,a trajectory planning criteria for increasing grinding speed as much as possible under the premise of avoiding interference is proposed to design the grinding trajectory.Then grinding point distribution on the ball-end wheel is calculated,and the grinding characteristics,grinding speed and maximum undeformed chip thickness,are investigated.Finally,a complex structural component can be ground without interference,and surface roughness and profile accuracy are improved to 40.2 nm and 0.399 μm,compared with 556 nm and 3.427 μm before ultra-precision grinding.The mathematical model can provide theoretical guidance for the analysis of interference and grinding characteristics in complex components grinding to improve its grinding quality.