Study On Gearing Theory For Manufacturing Of Epicycloidal Bevel Gears

The straight or skew bevel gears of tempered tooth flank are still widely used in large machine equipment in coal mine, metallurgy and petroleum industries around our country at present. And there exist problems such as lower in carrying capacity, shorter in service life and larger in storage quantity of spare parts. It is an emergent demand for the development in modern heavy machinery to substitute the spiral bevel gears with hardened tooth-surface for the straight or skew bevel gears of tempered tooth flank as earlier as possible to satisfy with the higher requirements in driving velocity and carrying capacity.Spiral bevel gears could get rid of the deformation and errors in heat treatment by cutting a rather thin layer of metal off the gear face with a hardness of HRC 58 to 62 using the scraping technique for harder gear face, have features in higher cutting efficiency for larger and hardened gears, especially apply for heavy machinery, and represent a trend of the spiral bevel gear in the field.Considering the present situation of manufacturing for bigger epicycloidal bevel gears in China, the purposes of the study are to analyze the relationship between gearing properties and contact areas of spiral bevel gears and manufacturing parameters of machining tools in the design and manufacture from the point of gearing theory, to develop compute aided manufacturing system for epicycloidal bevel gears by combining experiential equations in production, to accomplish the complicated design and check process automatically, and to provide theoretical fundaments for raising the manufacturing capability and developing the machining tools for bigger epicycloidal bevel gears.The meshing properties of a pair of gears are determined by the geometrical characteristics of the tooth surfaces. From the mathematic points of view, the relative positions and motions between the cutter head and the workpiece are usually changed continuously with the same rule during the manufacturing for any kinds of metal-cutting machines. As for epicycloidal bevel gear, the relative motion principle between the cutter and the gear blank are the same, though the driving systems for different types of machining tools are different. Based on the point, the paper researched on gearing theory of epicycloidal bevel gears systemically.A mathematical model of the flank for generating gear of epicycloidal bevel gears in manufacture was established. The contact lines of the generating gear was analyzed. When the motion velocity of gearing point on generating surface is equal to the relative velocity to the gearing point on the surface of gear being cut, the relationship were established among the number of gears being manufactured, cutter head radius, cutter position, generating gears radius, spiral angle of reference point and height correction coefficients at the limit point of undercut. The selection method for height correction coefficients in conditions that there was no or little undercut on narrow end for pinion was provided. The paper analyzed the gap distribution between tooth surfaces on two meshing gears along contacting line and deduced approximate equations of minimal gap on meshing tooth surfaces, which could help to judge if there existed diagonal contact.The paper deduced the derivational curvature equations along contact line after analysis on locus of meshing points for epicycloidal bevel gears in different reference systems. A conclusion that spiral bevel gears are in point meshes theoretically but in line meshes approximately In fact was reached, which provided bases for analyzing contact stress on tooth surfaces and using Hertz stress equations to calculate the contact strength.Theoretically, there is no end contact ratio for the spiral bevel gears in point meshes. However, contact ratios including end and axial ones are calculated according to the equivalent virtual gears in application in fact, and there are errors. Contact line equations were constructed based on the locus of meshing points for epicycloidal bevel gears in fixed reference systems in the paper. The formula to calculate the maximum value of contact ratio was formed which could be used to check if the ratio resulted from the equivalent virtual gears were too bigger. The contact locus and the relationship between the contact positions in meshing gear surfaces for the spiral bevel gears were reached after analysis on the locus of meshing points in dynamic reference systems fixed on the gears.An approach was suggesed to establish solid models through which you could check if there existed undercut for pinion, cutter heads were intervened with bigger gear, any rib was left in groove and the shape of gears were shaved. By taking the milling machine for Klingelnberg bevel gears as an objective, an integrated compute aided manufacturing program was developed to accomplish dimensional and parametric calculations, strength check and parameters adjustment.