Research On The NC Machining And Error Correcting Technology For Spiral Bevel And Hypoid Gears

As a foundational component in mechanical transmission, spiral bevel and hypoid gearis characteristic of quite a few complexities in space shape, meshing and machining. As aresult of the developing of Numerical Control technology, the flexible machining andsimplifying adjusting are supplied with a way for spiral bevel and hypoid gear. Themachining accuracy of spiral bevel and hypoid gear will be improved greatly with theapplication of NC technology. At present, in the other country just several company grasp thetechnology, in our country the research is just beginning. Therefore, according to thespeciality of NC machining, deep researches are made on the machining theory, digitalprocessing, measure technology, error correcting method in this thesis, whose primarycontent is as follows. The meshing principle and the machining characteristics of the spiral bevel and hypoidgear has been researched deeply. By its local conjugation characteristic, several GLEASONmachining algorithms have been analyzed and deduced. Furthermore, according to theequations of cutting, the parameters of machine settings are calculated. These algorithms arethe foundation of realizing NC machining for spiral bevel and hypoid gear. Based on GLEASON principle and the flexibility characteristics of NC machine tool,two novel algorithms, "the cutter tilt and variable ratio of roll" and "cutter tilt & displacementof pitch point", for manufacturing hypoid pinion are proposed. And the parameters ofmachine settings are calculated. Manufacturing the pinion with a prescribed-size cutter onNC machine tool can be realized, which helps to simplify cutter specifications and realizeerror compensation of the cutter size. Moreover the NC machine tool characteristic offlexible manufacturing is exploited to the full, and the machining accuracy and efficiency isimproved. To analyze the design of tooth surface and its machining quality, according to themachine settings, tooth surface contact analyzing is taken, and the equation of tooth surface isderived. And by equation of the gear's tooth surface and that of the pinion's, the contactpattern and transmission errors curve are got. The algorithm of disperse tooth surface contact analysis is established and deduced,which lays the foundation for the digital measure and analyzing of tooth surface. Firstly thesampling points of tooth surface measurement, mathematics model for spiral bevel andhypoid gear's fitting tooth surface is formularized reversedly by applying principle ofdifferential geometry and Ferguson parameter spline function. And then according to thefixing condition and the "BOX" optimization method for finding extremum with a limitedboundary and conjugation theory, quick solving the contacting point of tooth surface can be IIrealized by changing definition region. An algorithm for finding path of contact, contactpattern and transmission errors is investigated. After the research on the digital measure technology of tooth surface, an errorcompensation method is proposed. In this method, the deviations of a gear's real toothsurface from the theoretical surface along the normal can be determined by coordinatemeasurements at the grid of the surface. Under the Cartesian coordinates, with the applicationof least-square method for an overdetermined system of linear equations, the machinesettings can be calculated, which minimize deviations of a gear's real tooth surface from thetheoretical surface. On the study of the gear's transmission errors, its principle resulted from tooth mismatchand misalignment, is analyzed. And the methods reducing the transmission errors arepresented. The motion optimization method is proposed, by which transmission errors anddiscontinuousness of tooth surface meshing is decreased to minimum. A general NC generating motion transition method was proposed, integrated with themachining technique of spiral bevel a...