| 摘要(英) |
Conical gear drives, composed of a spur gear and a shaped conical gear, has the potential to replace the bevel gear for the transmission with a large shaft angle, because of lower required assembly accuracy and low-cost advantage (especially manufactured by powder metallurgy). Conical gear drives have been used most in transmission with a large gear ratio. But in the case of the conical drives with a small gear ratio (smaller than 2), the effective face-width of the conical gear is not enough due to the geometrical limit of tooth pointing and undercutting. On the other hand, the bearing contact between the pinion and the conical gear is localized by selecting the tooth number of the spur gear less than that of the shaper. In such a design, edge contact ocurrs likely due to the contact point locates nearby the undercut limit. Those problems restrict the application of conical gear drives with a small gear ratio in the practice. The purpose of this paper is thus to propose a nonstandard design approach and also to analyze and to validate the assembly error, contact stress and load capacity for the mentioned conical gear drives.
At first some concepts are developed for designing conical gears. The face-width of the conical gear is enlarged by using nonstandard basic rack and the location of the contact point is adjustable by using the concept of the unequal module/unequal pressure angle to design the pinion and the corresponding shaper. Under consideration of the complex relations of the design parameters between the conical gear, the pinion and the shape, design charts are constructed in this paper to obtain a larger effective face-width of the conical gear, and to adjust the location of the contact point near the middle of the face-width. For the purpose of manufacturing on CNC-milling machine, 3D solid models of the conical gearing are generated by using Inventor API program based on the mathematical equations of the tooth surface derived from relations of gear geometry. The generated 3D model are also applied to simulate the location of loaded contact points of conical gear pairs influenced by assembly errors by using interference analysis option of the CAD program. The influence analysis of assembly errors on the location of contact points is also carried out experimentally, and the results validate the feasibility of CAD simulation. The results of analysis showed that the greater the difference of the tooth number between the shaper and the pinion is, the lower the assembly sensitivity is. Moreover, the contact pattern will be much closer to the type of point contact.
To confirm the load capacity of the designed conical gear drive, tooth contact stress is analyzed by using influence coefficient method. The change of contact stress during gear meshing and the distribution of contact stress of engaged teeth at the position of contact begin and conatc end, respectively, are investigated. The analysis results showed that the contact stress is concentrated at the position of contact end and contact begin. Besides, pinions with tip rounding, short linear tip relief and smooth short linear tip relief, respectively, are also considered for loaded tooth contact analysis in the paper. From the analysis results stress concentration can be found at the begin of profile modification of the pinion with tip rounding and short linear tip relief. The pinion with smooth short linear tip relief can reduce the stress concentration, but non-Hertz contact occurs still in the contact region of profile modification. Therefore, the concentrated contact stress can be improved only by applying the tip relief on the conical gear.
Finally, a set of powder metallurgy conical gear pair is mounted it in a gearbox of mower for running test according to the design approach proposed in the paper. The working condition of the mower is simulated by using trimmer line to beat a POM rod. The total load cycle is 106. It is explored from the experiment results that the tooth surfaces of both gears have only slight polishing wear under such a strict load conditions. It can be thus concluded that the proposed design approach for conical gear drives with a small gear ratio can meet the requirements of application for power transmission. |
| 參考文獻 |
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