| Spiral bevel gear used to transmit motion and power between intersect axis, comparedto straight bevel gears, spiral bevel gear has many advantages, such as the large toothcontact ratio, higher load capacity, steady transmission, high strength, and insensitive toinstall errors, etc. It is widely used in ships, aviation, defense technology and equipment aswell as automotive, machine tools, construction machinery, mining machinery and othermachinery products. The processing technology of spiral bevel gear has been widelyconcerned. The Gleason Works that founded in1865in the United States is in a leadingposition in bevel gear cutting machines and technology; the spiral bevel gears manufacturedby Gleason Works are the most widely used bevel gears. Due to the inherent Gleasonprocessing principle, The Gleason machines which have complicated machine structure arehard to calculation and adjustment of processing, the machines are one of the most difficultto operate. On the other hand, the principle of “Approximate substitution” and “Locationconjugate” made the tooth surface can not properly engaged, which result too manydisadvantages such as the inexpectant contact area, high-noise and decrease strength,etc. Inorder to improve the gear engagement and obtain better contact area, Machines and toolsneed to be complex adjusted and the gears should be cutting and inspection repeatedly. Thecosts of manufacturing increased, and the production period prolonged, furthermore, thegears should be used in pair. In this way, the tooth profile of spiral bevel gear is not thespherical involutes, so it does not have interchangeable, constant of instantaneoustransmission ratio and other fine features.This study based on the principle of involute gear cutting on the tracing line, using theprinciple can obtain the spiral bevel gears with spherical involute tooth profile. Sphericalinvolute is the theoretical tooth profile of bevel gear; it has all the good characteristics ofinvolute tooth profile. The principle of involute gear cutting on the tracing line provides thecutting methods of spherical involute spiral bevel gears and the design and manufacturingsolutions of the processing equipments. Based on the above works, the situation of contactand engagement of this new type of spherical involute spiral bevel gear were analyzed andstudied in meshing. Meshing characteristics and contact analysis of spiral bevel gear drivehas great influence on the performance of transmission, it has a direct impact on the gearusing and processing, so it is necessary to carry out in-depth research. The main contents ofthis paper include the following aspects:(1) The generating movement of the spherical involute spiral bevel gear tooth surfaces has been studied systematically in this paper. The generating of concave tooth surface andconvex tooth surface both of right-and left-handed spiral bevel gear have been described indetail. On this basis, the mathematical model of the tooth surface has been derived bycoordinate transformation, the right-handed concave tooth surface equation has beenanalyzed from the perspective of meshing theory, the meshing equation, and the contact lineequation and the left-handed convex tooth surface equation were derived. A comparativeanalysis of contact line and tracing line was carried out to prove that the two are the samecurve. This part of research provides support for the tracing line method in theory, and alsoprovides the basis for carrying out research on tooth surfaces and contact analysis.(2) The meshing characteristics of the left and right-handed convex and concave toothsurface were studied, the normal curvature and the principal curvatures of each surfacewere calculated, the main direction also determined. The induced normal curvature of spiralbevel gear tooth surface that line contact in theory were calculated, the expressions whichdescribe the curvature interference limit line and the meshing limit line were derived. Theyall provide the basis for further research to adjust tooth contact area.(3) The method of contact adjustment of spiral bevel gear was proposed in this part,the contact patterns of gears from line-contact changes to point-contact by changing theradius of generating line. The method how to determine the reasonable radius of generatingline was analyzed, and the formula for calculating the radius of the generating line wasderived. After that, the formulas of induced normal curvature which applicable to thepoint-contact conjugate tooth surface were deduced. The works lay the foundation for thetooth contact analysis.(4) The tooth contact analysis method was used to simulating the meshing and contactof gear drives which change to point-contact by changing the radius of generating line. First,the gears should be change into the same coordinate system, and then established contactequation represented by vectors. Second, the contact equation represented by vectors needconverted into numerical formula and MATLAB software was used for solving nonlinearequations. Iterative method is used to solve the nonlinear equations, in order to obtain thereasonable initial value of iteration, the way how to choose reasonable initial value ofiteration was analyzed. Finally, the results of nonlinear equations were plotted in graphical,so the contact trace was obtained. In order to obtain an intuitive contact area, the parametersof the contact ellipse which take instantaneous point as the center were calculated, thecontact region formed by the major axis of contact ellipses was drawed. The results of toothcontact analysis were confirmed by experiment. The actual contact area has been gained, and the difference between simulation and experiment was analyzed.(5) With the purpose of revealing the influence of external factors on the gear contactarea, the influence of installation error on contact area was researched in this paper byestablishing and solving contacts equations that contains the installation error. The effectsof pinion installation error H, gear installation error J, gear shaft deviation V, andaxis angle deviation on location and shape of contact trace were researched and someconclusions were gained. On this basis, further research on comprehensive effects ofinstallation error on contact trace has been analyzed, and then the adjustment rules guidinggear installation were proposed. |
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