小轮为螺旋齿线圆柱齿轮的面齿轮数学模型

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英文篇名：Face Gear Mathematical Model of the Helical Cylindrical Gear 作者：盛伟 ; 冯占荣 ; 王利霞 ; 邹濛 ; 王文轩 英文作者：SHENG Wei;FENG Zhanrong;WANG Lixia;ZOU Meng;WANG Wenxuan;School of Aeronautical Manufacturing Engineering,Nanchang Hangkong University; 关键词：螺旋齿线 ; 圆柱齿轮 ; 面齿轮 ; 数学模型 ; 双圆弧齿轮 英文关键词：helical tooth line;;cylindrical gear;;face gear;;mathematical model;;double arc gear 中文刊名：JXGU 英文刊名：Mechanical Engineer 机构：南昌航空大学航空制造工程学院; 出版日期：2019-02-10 出版单位：机械工程师 年：2019 期：No.332 基金：无损检测教育部重点实验室开放基金(ZD201229010);; 江西省教育厅科学技术研究项目(GJJ160701);; 江西省研究生创新专项资金项目(YC2016026) 语种：中文; 页：JXGU201902002 页数：5 CN：02 ISSN：23-1196/TH 分类号：7-11

摘要

为满足一类面齿轮的初步设计需要,提供一种小轮为任意齿廓的螺旋齿线圆柱齿轮的面齿轮数学模型。首先,基于螺旋齿线圆柱齿轮设计原理,建立了基于任意齿廓的螺旋齿线圆柱齿轮模型I。其次,通过两种不同的方法建立面齿轮的数学模型,其一为根据模型I运用包络法建立面齿轮的刀具齿轮数学模型II;其二为根据螺旋齿线圆柱齿轮的齿条的共轭齿形齿条模型III运用运动学法建立面齿轮的刀具齿轮数学模型II。然后根据刀具齿轮模型,运用运动学法建立面齿轮的刀具齿轮数学模型III。最后以双圆弧齿轮为例,依据面齿轮数学模型建立的思路,推导了基于小轮为双圆弧齿轮的面齿轮的齿面方程,验证了数学模型应用的可行性。研究结果为进一步开展不同齿廓螺旋齿线圆柱齿轮设计及其啮合的面齿轮设计提供数学模型参照,同时也为螺旋齿线圆柱齿轮及其啮合的面齿轮的加工刀具设计提供理论模型参考。
        In order to meet the initial design requirements of a kind of face gear, a face gear mathematical model of a helical cylindrical gear with any tooth profile is provided. Based on the design principle of helical cylindrical gear, a helical cylindrical gear model I with arbitrary tooth profile is established. The mathematical model of face gear is established by two different methods. The first one is the mathematical model II of the face gear based on model I using envelope method. The second one is a conjugate toothed rack model III based on the rack of helical cylindrical gear, and then the kinematics method is used to establish the cutter gear mathematical model II of the face gear. According to the tool gear model, the kinematics method is used to establish the mathematical model III of the face gear. Taking the double arc gear as an example, based on the idea of the mathematical model of face gear, the tooth surface equation of the face gear with double arc tooth profile is deduced. The feasibility of the application of the mathematical model is verified. The results provide a reference for further development of helical cylindrical gear with different profile and design of meshed face gear. It also provides a theoretical model reference for the design of machining tool of helical gear and its meshing face gear.

引文

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