Biodiesel has wide application prospects due to its good power performance, fuel economy and emission reduction. Experimental studies have found that the measured engine vibration presents an N-shaped nonlinear trend with the increase of the biodiesel proportion in blends, which cannot be explained solely based on the combustion characteristics of blended fuels. To study the mechanisms for this nonlinear trend of engine vibration, a two-degree-of-freedom nonlinear model of piston–cylinder system was established and verified to analyse the correspondence between in-cylinder combustion behaviour and engine dynamic responses. By correlating simulation results with measured signals, it is found that the root cause of the nonlinear vibration trend is the coupling effect of in-cylinder pressure and piston inertial force. The time integral of piston lateral force in the interval from combustion top dead centre (TDC) to the subsequent piston slap ultimately determines the trend of liner vibrations. These key findings pave the fundamentals for the vibration analysis of engines fuelled with other alternative fuels, which is important for improve engine operation performances including reliability assessment and NVH control.
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