Tooth Contact Pattern Analysis And Design Technology Research Of Cycloid Hypoid Gears

The hypoid gears with long epicycloid teeth of uniform depth(cycloid teeth for short) is manufactured by using continuous indexing face-hobbing(FH) method, which requires only two set of cutting machines, two tools and two handlings. Compared with the single indexing face-milling(FM) method which is used to cut hypoid gears with arc taper-shaped teeth, the production efficiency is greatly increased, labor intensity is decreased, and the facilities and tools needed are decreased. This type of gear pair is also featured by smooth transmission, low noise, and strong carrying capacity, etc. So it is particularly suit the automobile industry of mass production, e.g., it is widely applied in axle gear transmission of various kinds of light and heavy trucks and SUVs.With the high-speed development of native automobile industry and daily-closer cooperation with European, US, Korean, and Japanese automobile companies, the manufacturing process of the advanced cycloid teeth hypoid gears and the whole set of machining, measuring, tool-sharpening, tool-adjusting devices are gradually introduced into the domestic large automobile companies, which lead to the widely application of this gear, and deeper comprehension of public. However, due to the historic reason, long period of attention is focused on arc taper-shaped teeth, and lacked for the research of cycloid teeth. And the foreign technological blockade further added to the situation that our domestic design and manufacturing is far behind EU and USA. The basically starting technical situation severely restrains the improvement of independent design and process level. Considering on this, focusing on cycloid hypoid gears and starting from the meshing performance analysis and tooth surface design, this work mainly discusses the following contents:(1) Tooth surface modeling and contact analysis of cycloid hypoid gears. A tooth surface machining simulation method that is applicable for Klingelnberg and Orelikon was established, and on the thought of blade arcs and tool nose arcs, the complete tooth surface model involving the working tooth surface and tooth root transition surface was established. The basic formula of cycloid hypoid gear meshing was deduced based on the principle of differential geometry and the principle of meshing. A new contact ellipse calculation method was proposed, and the geometry model of tooth contact analysis(TCA) was improved. We also proposed a geometric analysis method for edge tooth contact analysis(ETCA) of cycloid hypoid gears. Combining gear geometric analysis and mechanical analysis, the loaded tooth contact analysis(LTCA) model of cycloid hypoid gears was established, based on which we analyzed the contact stress and bending stress and proposed a new calculation method for time-varying meshing stiffness.(2) Tooth surface errors sensitivity analysis and pre-correction of cycloid hypoid gears. With the tooth surface model mentioned above, by applying quantitative disturbance, we analyzed the effect of various processing parameters, such as tool parameters, cutter head parameters, machine setup parameters, and roll modification parameters, on tooth surface errors, and obtained the processing parameter combination that has greater impact on tooth surface topology. Then, a tooth surface error pre-correcting optimization model of cycloidal hyper gears was established, and the variations of those processing parameters were obtained by solving the model with sequence quadratic program(SQP) algorithm.(3) Active tooth surface design of cycloid hypoid gears. Based on conjugate principle, the pinion auxiliary tooth surface that is in line contact with the gear tooth surface and has a parabolic transmission error(TE) is obtained by using the gear as a virtual cutter to generate the pinion under a predesigned motion function, then the pinion target tooth surface is obtained by modifying the pinion auxiliary tooth surface along the contact line with a predesigned contact pattern(CP). Then, an optimization model is proposed which set the adjustments of pinion machining parameters as variables and the least sum of square errors as object, and a weight factor is introduced here to selectively guarantee the meshing performances of a certain side, SQP algorithm is used as a tool to solve this model. This proposed methodology provides a new approach for meshing performances control of face-hobbed hypoid gears that cannot be grind after heat treatment and other typs of gears in double-flank cutting.(4) Real tooth surface contact analysis of cycloid hypoid gears. We explored the actual meshing principle and method by fitting the discrete coordinate points which are measured by high-accurate gear measuring center. Then, we extracted the data points of the meshing tooth, and calculated by controlling the peak point and weight factor to obtain the non-uniform rational b-spline(NURBS) fitting surface expression, that is the digitization tooth surface, and the fitting accuracy was verified. Finaly, the simulation analysis mathematical model of digital tooth meshing was established. Compared with the traditional rolling test, it can obtain the TE curve along with the CP, which presents comprehensively the actual meshing information. An active tooth surface design methodology based on real tooth surfaces for face-hobbed hypoid gears is proposed. Thus, the tooth surface errors of both gear and pinion are all considered by just correcting the pinion surface as in practical production, and no second correction is needed.(5) Tests and comparison analysis verification. The feasibility of above-mentioned methods is demonstrated by using a numerical example of a Klingelnberg-Oerlikon’s Spirac high-speed axle gear set, we carried out tooth cutting, tooth measuring, rolling test and the verification of active tooth surface design. Finally, the results of simulation and tests, and that obtained by the latest Klingelnberg spiral bevel gear design and analysis software(KIMoS5) were compared and analyzed, the results shown the accuracy and feasibility of the tooth surface modeling method, theoretical tooth surface contact analysis method, active tooth surface design method, and the real tooth surface meshing simulation method.