Mathematical Model and Tooth Contact Analysis of Cylindrical gears with curvilinear shaped Teeth
|關鍵字:||曲線齒圓柱型齒輪;過切;轉位;運動誤差;接觸比;接觸齒印;cylindrical gears with curvilinear shaped teeth;undercutting;profile-shifted modification;kinematic error;contact ratio;contact pattern|
ABSREACT The contact type of helical gears with parallel axes or spur gears is line contact, and the kinematic errors are sensitive to the gear axial misalignment. The gear set exists axial misalignments, the tooth edge contact will be occurred and this results in stress concentration, vibration and noise. The manufacture of cylindrical gears with curvilinear shaped teeth has been proposed by Liu in 1988. The advantages of curvilinear toothed gears are higher bearing and contacting strength, lower noise, better lubrication condition and no axial thrust forces. In this paper, the mathematical model of curvilinear toothed gears has developed based on the generation mechanism with an imaginary rack-cutter of circular-arc tooth profile. The tooth surface of curvilinear toothed gears can be displayed by using computer graphics and the developed computer simulation program. The right-side and left-side tooth surfaces of curvilinear toothed gears are different and the tooth thickness of central section is larger than those of other sections. According to the developed gear tooth mathematical model, location of the singular point or singular line on tooth surfaces can be obtained by applying the concept of differential geometry and numerical method, i.e. the undercutting of curvilinear toothed gears can be analyzed. In this study, the profile-shifted generation has been also investigated. The undercutting of curvilinear toothed gears can be avoided by using a positive profile-shifted modification during the gear set generation process. The tooth contact analysis technology has been utilized to the investigation on kinematic errors, contact ratios and contact patterns of the gear set under ideal and error assembly conditions. Since the contact type of the curvilinear toothed gear proposed in this paper is point contact, the gear set is not as sensitive to the gear axial misalignments, and the kinematic errors are quite small. The tooth edge contact can be avoided because the contact paths on gear tooth surfaces are located near the central section of face width. The contact ratio of point contact type curvilinear toothed gears is similar to that of spur gears. The contact pattern of curvilinear toothed gears can be obtained by applying the contact surface topology method. It is found that the contact point of the mating tooth surfaces may not be the center of contact ellipses, and the most important design parameter which influences the dimensions of gear contact ellipses is the nominal radius of face mill cutter.
|Appears in Collections:||Thesis|