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基于Frenet標架的渦旋始端型線重構(gòu)與幾何特性分析
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國家自然科學基金資助項目(50965011)和甘肅省自然科學基金資助項目(0710RJZA061、1014RJZA025)


Reconstruction and Geometrical Property of Top Scroll Profile Based on Frenet Frame
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    摘要:

    針對當前型線研究中尚未建立表征修正型線和主體型線固有特性統(tǒng)一模型的問題,建立了基于Frenet標架曲率半徑函數(shù)的渦旋型線通用方程,分別采用零次曲線和一次曲線對渦旋始端型線進行重構(gòu)。定量分析了型線參數(shù)對渦旋始端齒厚的影響,構(gòu)建了基于母線曲率半徑函數(shù)方程的渦旋壓縮腔面積幾何模型,研究了曲率半徑函數(shù)參數(shù)對面積特性的影響。結(jié)果表明:以曲率半徑函數(shù)構(gòu)成渦旋母線的連續(xù)性方程,在設(shè)計階段即能得到完全嚙合型線和完整渦旋齒廓,無需再進行齒端修正;一次曲線重構(gòu)較大的設(shè)計自由度可以使其兼顧渦旋端部齒厚和內(nèi)容積比要求,獲得較零次曲線重構(gòu)綜合性能更為優(yōu)越的渦旋齒。

    Abstract:

    According to the situation that there is no general model to express both main profile and modified top profile, a general integration equation expressed in tangential angle series was established for scroll profile. The start part of profile was reconstructed with zeroth-order curve and firstorder curve, respectively. The influence of parameters of top profile on thickness of scroll tooth was analyzed quantitatively. Furthermore, the geometrical models of area of compression chamber were set up based on curvature radius function of base line. The effect of curvature radius parameters on area property was explored. This study showed that first-order curve construction of top scroll could achieve higher performance by improving volume ratio while maintain reasonable tooth strength. With continuity equation of scroll baseline in form of radius of curvature, a fullymeshed profile and complete tooth profile could be obtained in the stage of machine design, so that there was no need to modify top scroll in later stages. The results could be applied in the scroll profile design.

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劉 濤,鄔再新,芮執(zhí)元.基于Frenet標架的渦旋始端型線重構(gòu)與幾何特性分析[J].農(nóng)業(yè)機械學報,2011,42(2):197-202. Liu Tao, Wu Zaixin, Rui Zhiyuan. Reconstruction and Geometrical Property of Top Scroll Profile Based on Frenet Frame[J]. Transactions of the Chinese Society for Agricultural Machinery,2011,42(2):197-202.

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