Dynamic Characteristic of Gear Drive Error Excitation Shafting Timoshenko Beam Unit

The establishment of dynamic simulation model is completed by RomaxDesigner.In the model, the shafting is treated as a Timoshenko beam unit.The influence of shear strain is considered on the basis of the Euler beam element.

For beam units shown in the figure, if shear deformation is ignored, the tangent O’T offset from the center line should be perpendicular to the normal of the plane Q’R’.Angle gamma represents the angle between tangent O’T of the deformation center line and normal O’N of the deformation surface, and characterizes the deformation of the unit.

Where_represents the deflection of the centerline of the curved surface due to bending deformation, bending moment M and shear force V.According to and W obtained from the following equation:

Where A is a constant Timoshenko shear coefficient determined by the shape of the beam section.For circular sections, a = 9/10.

For free vibrations of beams with identical sections, the Timoshenko beam unit vibration equation is:

For forced vibrations of beams with uniform cross-sections, the Timoshenko beam unit vibration equation is:

Stiffness Matrix:

Quality Matrix:

Where: LnL is one of them: nL is the length of N truncation axis, n axis nD axis interface diameter,