Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications

This paper presents three-dimensional (3-D), finite element methods (FEM) to conduct surface contact stress (SCS) and root bending stress (RBS) calculations of a pair of spur gears with machining errors (ME), assembly errors (AE) and tooth modifications (TM). In this paper, firstly positions of a pair of parallel-shaft spur gears with ME, AE and TM are defined in a 3-D coordinate system. Then tooth contact of the pair of gears is assumed on a reference face around the geometrical contact line. This tooth contact on the reference face is called face-contact model of the gears. With this face-contact model, contact reference points on the reference face of one gear are assumed firstly, then a geometrical method that can consider the effects of ME, AE and TM on tooth contact is presented to find the responsive contact reference points on tooth surface of the second gear (the mating gear). Deformation influence coefficients of the pairs of contact points are calculated by 3-D, FEM and loaded tooth contact analysis (LTCA) of the pair of gears with ME, AE and TM is conducted by mathematical programming method. FEM programs are developed to do LTCA, tooth load, SCS and RBS calculations of the pair of spur gears with ME, AE and TM automatically in a personal computer. Tooth contact lengths of a pair of spur gears with lead crowning are calculated by the programs and compared with the measured results. Also, tooth contact pattern and root stains of a pair of spur gears with AE are analyzed by the programs and compared with experimental results. It is found that the calculated results are agreement with the measured ones well. Finally, an example of calculating the real SCS and RBS of a pair of spur gears with ME, AE and TM is given in the paper. It is found that ME, AE and TM exert great effects on SCS and RBS of the gears. SCS and RBS of the same pair of gears are also calculated by ISO and JGMA standards for comparing with the FEM results.