Abstract: An optimization design method of vibration reduction for ease-off modification based hypoid gears was proposed to improve dynamic performances of automobile drive pinion axle． The modified pinion were represented by a sum of two vector functions determining the tooth of conjugate and the pinion normal ease-off deviations ，which were expressed by both predesigned transmission error function and tooth profile modification curves． Mes-hing stiffness was obtained with tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA)． Based on force analysis of the meshing position，the bending-torsional-axial coupling dynamic lumped mass model for hy-poid gears was established，and the vibration response of the system was obtained by solving the differential equa-tion of motion with numerical method． The best ease-off deviations were determined by a optimizing minimal mean square value of normal vibration． Besides，influences of stiffness curve shape and amplitude caused by modifica-tion on the dynamic performance of the system were explored． A numerical example shows that excessive modifica-tion leads to decrease of meshing stiffness，which are responsible for the increase of normal vibration． In case of a little differences in value of average meshing stiffness for the modified tooth surfaces，the shape is more sensitive to vibration than the amplitude for stiffness curve． After the optimal ease-off modification，the vibration of system is obviously reduced． Besides，the average meshing stiffness decreases a little and main frequency in the stiffness curve is meshing frequency，and there is no frequency doubling component． When the amplitude of load transmis-sion error (ALTE) decreases and the high frequency component in the curve increases，the vibration may not be reduced，and ALTE can basically reflect the variation tendency of vibration with loads．

Key words: hypoid gear, ease-off modification, vibration, meshing stiffness, loaded transmission error, loaded tooth contact analysis