Gear mesh stiffness is the foundation of the study on gear dynamics.Taking the spur gear as research object

the finite element model of the spur gear with root crack is established

and the accurate calculation method of gear mesh stiffness is proposed based on the finite element quasi-static analysis principle.Through analysis

the influence rule of crack parameter on gear time-varying meshing stiffness is obtained

the result of numerical calculation shows that

the value of mesh stiffness reduces obviously when the crack appears

the crack parameters（the crack length and the crack direction） have a significant effect on gear mesh stiffness

and the crack length plays an important role

the reduce of gear stiffness depends on the meshing position of gear

the value of stiffness reduces quickly when the gear meshing position is at the highest point of single tooth meshing.