A Characteristic Study on Cylindrical Gears with Circular Arc Tooth Traces
|關鍵字:||曲線齒輪;滾齒刀;齒面過切;二次切削;曲率分析;運動誤差;接觸橢圓;接觸應力;curvilinear-tooth gear;hob cutter;tooth undercutting;secondary tooth cutting;curvature analysis;kinematic error;contact ellipse;contact stress|
In general, the tooth surfaces of the curvilinear-tooth gear (cylindrical gears with circular arc tooth trace) are generated by the special machine with gear milling cutters. However, the efficiency of this type of gear generation is lower than that of hobbing. The curvilinear-tooth gear cut by a hob cutter is proposed in this study. Since the generation of gear teeth is a continuous-indexing process, the cutting efficiency of the curvilinear-tooth gear generated by hobbing will be increased substantially. Therefore, the proposed hobbing method is applicable to mass production for the curvilinear-tooth gear. The proposed method by applying a 6-axis CNC hobbing machine to generate the curvilinear-tooth gear is a novel method. The angular velocity of the hob’s swivel must be controllable and correlative with the linear velocity of the axial feeding motion in the process of gear generation. However, the problems of tooth undercutting and secondary cutting of tooth surfaces by a hob cutter in the proposed novel generating process need to be solved. In this study, the geometry of a hob cutter was constructed at first, and then the mathematical model of the curvilinear-tooth gear cut by a hob cutter based on proposed the cutting mechanism for a 6-axis CNC hobbing machine was developed. Sequentially, the theoretical analysis on the tooth undercutting and secondary cutting of the gear teeth in the generating process were also investigated. The method proposed by Litvin was used to analyze the tooth undercutting of the curvilinear-tooth gear. The computer algorithm for investigation on the relationship between the outside diameter of the hob cutter and nominal radius of circular arc tooth trace without secondary cutting was developed. Because the tooth surfaces of the curvilinear-tooth gear are the envelope as two-parameter family of surfaces, literature search for the curvature analysis of the proposed curvilinear-tooth gear is not available. An algorithm for computerized determination of principal curvatures and directions of the curvilinear-tooth gear, as the envelope to two-parameter family of surfaces, was also proposed. Tooth contact analysis was applied to find the contact characteristic of the curvilinear-tooth gear pair such as bearing contacts, kinematic errors, contact ellipses of the curvilinear-tooth gear having center distance assembly errors, horizontal axial- misalignments, and vertical axial misalignments. Finally, The input file for the commercial software, ABAQUS/Standard, was generated automatically by the integrated computer programs. A pair of three-meshing-teeth finite element model was formed to investigate the contact stresses and bending stresses of the curvilinear-tooth gears. The analysis results show that the serious tooth undercutting is at the both-end sections of face width of the curvilinear-tooth gear, and increasing the normal pressure angle or decreasing the outside diameter of the hob cutter can avoid secondary tooth cutting under the same nominal radius of circular arc tooth traces. The KE of the gear pair is not sensitive to axial misalignments because the contact type of the proposed curvilinear-tooth gear pair is in point contacts. The maximum contact stress and bending stress occur when the contact point is near the pitch point, and increasing the nominal radius of circular arc tooth trace reduces the contact stresses and bending stresses.
|Appears in Collections:||Thesis|