Vibration energy harvesters (VEHs) convert mechanical energy of unpowered freight wagons into electricity and unlock more smart devices to improve operating conditions. In this paper, the nut-screw-based mechanically-driven VEHs (MD-VEHs) along with several mechanical motion rectifiers (MMRs) are proposed and compared in nonlinear railway freight system. Firstly, the working principles of harvesters with non-MMR, half-wave and full-wave MMRs are researched, and equivalent circuit models are established to better reveal the engagement and disengagement of one-way clutches, followed by the integrated model of wagon-harvester system which studies the suspension vibration response and assesses harvester performance. The harvester equivalent circuit model is validated on a horizontal test bench, and presents a good consistency with test data. In addition, the effects of harvester equivalent damping and inertia on performance are explored systematically. The analysis results indicate that full-wave MMR presents the best power performance under the same parameter configuration. The increase of flywheel inertia will decrease the power generation capacity of non-MMR configuration, but further enhance those of half-wave and full-wave MMRs and narrow the performance gap between both. This analysis based on system coupling will be instructive for the engineering design and application of railway VEHs.