Abstract: Considering the variable inertia of the reciprocating parts,free torsional vibration characteristics of crankshaft are studied.Based on instantaneous kinetic energy equivalent principle,a kind of accurate calculating method of single-cylinder diesel engine's variable inertia is presented.Free torsional vibration differential equations of the single-and multi-cylinder diesel engine crankshaft systems are established,and torsional vibration characteristics of the system are also analyzed theoretically.Numerical calculation of the free vibration of a certain multi-cylinder diesel engine is completed.The results indicate that the introduction of variable inertia has a great effect on the torsional vibration characteristics,such as the free frequency,critical speed zone,and torsional vibration angular displacement,of the crankshaft system.