Meshing Characteristics And Load Capacity Analysis Of Elliptical Bevel Gear

Elliptical bevel gear pair is a typical transmission style of noncircular bear gear,and it incorporates the characteristics of elliptical gear and conic straight gear. This geardrive can be applied to transmit motion and power between intersecting axis, which hasparticular application value in textile machinery, farm machinery and automobiles.Elliptical bevel gear transmission is developing into a direction of high-speed, powertransmission, so researching on meshing characteristics and tooth load capacity ofelliptical bevel has an import theoretical significance.This issue derives from Natural Science Foundation of China, the main purpose isto explore a general calculation method for the meshing characteristics and tooth loadcapacity of elliptical bevel gear, and to solve the intensity check of elliptical bevel gearpair. Aiming at elliptical bevel gear pair, the main research work in this thesis isorganized as follow.According to the spatial gear meshing principles and generating envelope theory,the basic transmission principle was studied. With the meshing coordinates established,the pitch curve formulas and spherical radius formula were deduced, and then the basicstructural parameters including eccentricity ratio of driving gear, module, tooth numberof driving gear, orders of gear pair and tooth width were determined. The blankparameters, cutting tool parameters and the tool path were ascertained and theparametric design of elliptical bevel gear solid model was achieved, so a parametricdesign method was established.On the basis of differential geometry surface and curve theories, the pitch curves ofelliptical bevel gear pair were flattened onto a plane in condition that the spatialgeodesic curvature was equal to planar relative curvature. Then the formulas ofequivalent pitch curves were deduced. Base on the equivalent pitch curves, the pressangle and contact ratio in the meshing process were acquired, and then the influence ofbasic structural parameters to press angle and contact ratio was analyzed.A kind of strength calculation method of elliptical bevel gear was established. Thentooth force analysis was performed and the moments between transmission axes weredetermined. Then the formulas of tangential force, normal force, radial force and axialforce were deduced, meanwhile, the radial force and axial force which are relative tobearing load were analyzed in detail. The regulation that radial force and axial force change with basic structural parameters was discussed, and the lifetime of bearingchecked with an instance. The formulas of synthetic curvature, tooth profile factor andstress correction factor were derived, and the regulation that tooth surface contact stressand tooth root bending stress change with driving gear rotation angle was acquired, sothe weakest tooth in the meshing process was determined. The influence of the basicstructural parameters to tooth strength was analyzed and the general elliptical bevel geartooth strength calculation software was developed with VB programming languageaccording the formulas derived.According to the structural characteristic that elliptical bevel gear evolve into conicstraight gear, the strength calculation method was verified theoretically through thecomparison analysis between results from elliptical bevel gear strength calculationmethod and that from traditional bevel gear calculation method. The finite elementanalysis model was established and the solid model was manufactured with five-axesnumerical controlled milling machine, so the strength calculation method was verifiedthrough finite element analysis and transmission experiment.