Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gears

Abstract

Abstract This paper quantitatively investigates effects of machining errors (ME), assembly errors (AE) and tooth modifications (TM) on loading capacity, load-sharing ratio (LSR) and transmission error (TE) of a pair of spur gears by using special-developed finite element method (FEM) software in a personal computer. Tooth surface contact stress (TSCS) and tooth root bending stress (TRBS) of a pair of spur gears with ME, AE and TM are analyzed by the FEM software. Effects of ME, AE and TM on TSCS and TRBS are also defined as “Influence factors” and the influence factors of ME, AE and TM on TSCS and TRBS are calculated quantitatively. It is found that misalignment error of gear shafts on the plane of action of the spur gears exerts great effects on TSCS and TRBS while misalignment error of gear shafts on the vertical plane of the plane of action almost exerts no effects on TSCS and TRBS. It is also found that ME and lead crowning have greater effects on TSCS and TRBS. When the maximum tooth surface machining error is 40 μm, influence factor of ME on TSCS and TRBS are about 2.2 and 1.5. When quantity of lead crowning is 40 μm, influence factor of lead crowning on TSCS and TRBS are about 2.0 and 1.4. These influence factors can be used as references when ISO standards are used for tooth surface contact strength and root bending strength calculations of a pair of spur gears with ME, AE and TM. Methods for LSR calculation of a pair of spur gears with ME, AE and TM are also presented in this paper. Effects of ME, AE and TM on LSR are analyzed quantitatively. It is found that ME has greater effect on LSR. When the maximum tooth surface machining error is greater than 10 μm, double pair tooth-contact shall become single pair tooth-contact for sake of the effect of ME. This means that when ME on tooth surface is large, outer limit of the single pair tooth-contact area can not be used as the so-called “worst load position”. It is safe and reasonable to use tooth tip as the “worst load position” when to perform tooth bending strength calculation. Methods for TE calculation of a pair of spur gears with ME, AE and TM are also presented in this paper. Effects of ME, AE and TM on TE of the gears are analyzed quantitatively. It is found that ME not only changes waveform of TE easily, but also makes TE greater and greater when ME is increased. AE and TM also make TE greater and greater when they are increased, but do not change waveform of TE.