By utilizing lumped-mass method

the torsion-vibration mechanics model of the main transmission system of rolling mill is established.Furthermore

the differential equations of the torsion-vibration model are established by taking damping into consideration.Then complex mode analysis is converted into an issue of solving the nonlinear generalized eigenvalue problem

and the solution is conducted in MATLAB

and the vibration form differences of system at every point is analyzed when the complex mode component factor is respectively plural and real number.By using the complex mode of system

the differential equations of the torsion-vibration model are decoupled

the basis of analysis torsion vibration response of main transmission system is provided.