Computer Bending Strength Analysis of Straight and Barrel Teeth under Skew Conditions

The paper presents the results of computer simulation to research the bending stress distribution law at the root of straight and barrel-shaped teeth of spur gearings under conditions of misalignment of the gear axes. It is known that the greatest effect on the load capacity and durability of spur gearings is exerted by the irregular load distribution along the contact lines due to the distortion of the tooth surfaces in meshing, leading to contact area length shortening and edge contact of teeth. This results in a multifold transmission life reduction in terms of contact or bending strength. Spur gears with longitudinal (barrel-shaped) tooth modification allow increasing the durability of spur gears when operating in conditions of gear axis misalignment. In this work, a comparative Finite Element Analysis of the stress-strain state of a straight tooth and a barrel-shaped tooth was carried out underline load at the tooth top and a variable skew angle from 0' to 8'. Computer simulations were performed at ANSYS Mechanical APDL. The line load distribution laws along the longitudinal tooth coordinate were obtained analytically for various skew angles based on the three-dimensional contact problem solution, taking into account tooth volume and contact deformations, as well as edge effects. As a result of computer simulation, figures of the tensile stress distribution in the tooth roots were obtained and a reduction in stresses by 15% was determined using a barrel-shaped modification. The proposed method of strength analysis allows to justify the choice of tooth barrel-shaped longitudinal modification even at the stage of gearing synthesis providing bending stress reduction in the gearing during its operation in conditions of skew of a given degree.