On the linear section of the Hangzhou -Shenzhen passenger rail line, there exists alternating side grinding on the linear rails. When the EMU passes through the grinding section, the truck will be swayed in an unstable state. This paper studies this problem from the perspective of wheel-rail dynamics of long trains, and gives some harnessing measures about the alternating side grinding. By building a simulation model of trains based on MATLAB/SIMULINK software, the operation of the EMU through the existence of pure rolling line offset straight rail is carried out. It is found that the formation of alternate side grinding of the rail is affected by the wheel-to-pure rolling line offset. When the rail is unevenly worn due to factors such as asymmetric grinding, the pure rolling line of the wheel pair on the rail will be offset, which will cause the periodic polarization phenomenon of the train wheel pair, thus eventually leading to the overall lateral low-frequency shaking of the long trains.