New method for determining the load distribution and mesh stiffness of internal helical gears

Of all the factors affecting the performance of a gear pair, the load distribution and mesh stiffness (or transmission error) can be considered two of the most important. A new 3-D FE method for determining the load distribution and mesh stiffness of internal helical gears is presented in this paper. It should be emphasized that the key to this new method is that in this method, a set of tooth profile coordinate systems of internal helical gears is ingeniously devised and the matrices of coordinate transformations have been derived. Through coordinate transformations, the load distributions along the contact lines and mesh stiffness of internal helical gears during the whole engagement period can be calculated simultaneously by a personal computer. The CPU time by the present method can be reduced to about 1/n (n is the total contact points on the action plane; in the example of the present paper,n equals 82) of that by general FE calculation. Furthermore, the new method can greatly increase the calculation accuracy because no simplifications are introduced. It may be of some interest to mention that in the ISO/TC 60 there are easy-to-use formulas to evaluate the tooth stiffness, but the formulas are rather crude and imperfect. At the end of the present paper, an actual example is calculated and shows that, in comparison with ISO, the present method is a fast and reliable method. The corresponding personal computer program has been developed by the author. The method presented in this paper can be easily simplified to be used in spur gears or developed to the applicable to bevel gears.