Mesh Stiffness and Its Non-Linearity of a Pair of Spur Gears with Machining Errors, Assembly Errors and Tooth Modifications

Abstract

Three-dimensional (3D), finite element method (FEM) and face-contact model of gear teeth are combined with mathematical programming method to do loaded tooth contact analysis (LTCA) and mesh stiflhess (MS) calculation of a pair of spur gears with machining errors (ME), assembly errors (AE) and tooth modifications (TM). MS of the gears without ME, AE and TM are calculated by the presented method and compared with the results calculated by Ishikawa's equations. It is found that the two results are agreement with each other roughly. Also, tooth contact pattern and root strains of gears with AE are calculated and compared with the measured ones. It is found that the calculated results are agreement with the measured ones well. Then, MS of a pair of spur gears with ME, AE and TM are analyzed with the presented method and effects of ME, AE and TM on MS of the gears are investigated. It is found that ME, AE and TM reduce MS of the gears greatly. It is also found that MS is a 6-order non-linear function of the loaded torque; a 2-order non-linear function of the misalignment error on the plane of action; 2-order non-linear function of the machining errors and a 3-order non-linear function of the quantity of lead crowning. These non-linear relationships of the MS shall be used for exact vibration analysis of a pair of gears with ME, AE and TM in the future research.