| As a very important transmission part, gear has a long history of being applicated byhumans. Gear transmission system is usually applied to transfer the force and movementbetween two shafts. Spiral bevel gear, in particular, it can transfer the force and movment ofintersecting shafts or staggered shafts. Spiral bevel gear can carry heavier load, has smoothtransmission and high efficiency, low noise and small vibration in the process oftransmission. So it is widely used in aviation, automobile, engineering machinery and otherfields.The theoretical tooth profile of bevel gear is spherical involute, a pair of conjugate toothsurfaces with spherical involute profile can achieve meshing correctly, and the instantaneoustransmission ratio is constant. However, in theoretical researches at home and abroad holdthe view that spherical involute is undevelopable, it is diffcult to form a cutting tool edgewith spherical involute, and the design and manufacture of spherical involute are also moredifficult, etc., so approximate proforming methods are used to manufacture the spiral bevelgears in actual production. A pair of gears manufactured with approximate proformingmethods have the problems of point contact at any instant and transmission ratio is notconstant, etc., when they are meshing. In order to guarantee the paired gears meshingcorrectly, need to modify gears machined out. Gear cutting method on the tracing lineadopted in this paper can overcome the above problems, and in theory the precise sphericalinvolute tooth profile can be got so that the principle error is eliminated, gears machinedhave high precision, interchangeable, can guarantee constant transmission ratio and themovement of machine tools and the configuration of cutting tools are simple. In this paper,the mian research contents are as follows:(1) Studied thoroughly the gear cutting method on the tracing line of skew bevel gear.The parameter equation of spherical involute and the tooth surface equation of skew bevelgear were deduced based on the generating process of spherical involute. Studied a methodof calculating pitch cone helix angle by utilizing base cone spiral angle based on the toothsurface equation.With right-handed skew bevel gear as an example, a bevel gear wasdesigned, which module is7and number of teeth is12.(2) The gear cutting movement of concave and convex tooth surface of right-handedskew bevel gear was discussed and analyzed. After calculating, generating-line’s critical length which is46mm and tooth root overcut which is1.461mm were determined, which areused in machining concave and convex tooth surface. Analyzed the machinability of the geardesigned, and the results show that designed gear can be machined by using the existing disccutter with three sides blade.(3) Analyzed the cutter location before gear cutting. Based on the relationship ofvelocity and displacement, related equations of gear cutting movement were deduced.Thetime of each processing stage in the machining process was calculated. According to therequirements of orthogonal polynomial regression design, the gear of nylon material wasmade. Through the measurement of tooth space in small end tooth root of skew bevel gearmachined in gear cutting test, and compared with the theoretical value, verified the validityof gear cutting motion analysis and related equations of gear cutting movement, and thecorrectness of the programs was checked at the same time.(4) The meshes of skew bevel gear’s tooth surface were established and calculated.Used3D-Scanner to scan the machined skew bevel gear. The theoretical models of toothsurface were established by utilizing the macro programs of three-dimensional modelingsoftware CATIA. The practical model of the gear was made in CATIA, and the tooth surfacedeviation of skew bevel gear was measured and analyzed. Used the orthogonal polynomialregression design to construct the mathematical model between the tooth surface deviation ofconcave, convex tooth surface and processing parameters, and the confidence level of themodels is95%and99%respectively.The tooth surface modeling method of skew bevel gear discussed in this paper has thecharacteristics of theory is correct, simple and practical. However, the mathematical modelsconstructed between the tooth surface deviation and processing parameters, which can beused to predict the value of tooth surface deviation of skew bevel gear machined by the gearcutting method on the tracing line, and also can be used as the objective functions tooptimize processing parameters. The research results in this thesis have a certain guidingsignificance to practical production of skew bevel gear. |
