Calculation of the Combined Torsional Mesh Stiffness of Spur Gears ...

Strojniški vestnik - Journal of Mechanical Engineering 57(2011)11, 810-818a) b)Fig. 4. Adaptive refining of the mesh at the contact point(s) for the 3D model; a) remeshed contact forsingle contact, b) remeshed contact for double contactThat is the combined torsional mesh stiffness, thedeformation of gear body, teeth and contact zonefor pinion and gear.2 THE COMBINED TORSIONAL MESHSTIFFNESSThe definition of the combined torsionalmesh stiffness K m used in this paper is the quotientof input load T [Nm] and driving gear hub rotationunder load T.E. [rad] [6] to [8]:TKm = TE . . . (1)This definition can be used for the dynamicsimulation of spur gear systems as it directlydescribes the relation between load torque andrelative motion of the gears.In 2001, Jia [2] introduced a commonformula describing the combined torsional meshstiffness by body and tooth bending stiffness. Thissimplification neglects the effect of the appliedtorque on the gearing's stiffness. The results fromthe FE model, however, show that there is aninfluence of the torque on the resulting combinedtorsional mesh stiffness as shown in Fig. 5.The studies of the deformational behaviourof the gear wheels show that the stiffness of gearbody and teeth are almost load-independent whilethe contact deformation is non-linear, as a Hertziancontact occurs between the teeth of the gears. Theinfluence of the applied torque on the component’sstiffness is shown in Fig. 6. The position and widthof the handover region between single and doublecontact zone are also torque-dependent which hasalso been shown previously [1].Fig. 5. Torsional mesh stiffness for a complete mesh cycle with different torque loads (model with 1:1 gearratio, 23 teeth, modulus 6 mm, steel)Calculation of the Combined Torsional Mesh Stiffness of Spur Gears with Two- and Three-DimensionalParametrical FE Models813