小轮为螺旋齿线圆柱齿轮的面齿轮数学模型  

Face Gear Mathematical Model of the Helical Cylindrical Gear

作　　者：盛伟 冯占荣[1] 王利霞[1] 邹濛 王文轩 SHENG Wei;FENG Zhanrong;WANG Lixia;ZOU Meng;WANG Wenxuan(School of Aeronautical Manufacturing Engineering,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学航空制造工程学院,南昌330063

出　　处：《机械工程师》2019年第2期1-5,共5页Mechanical Engineer

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)

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.

关 键 词：螺旋齿线 圆柱齿轮 面齿轮 数学模型 双圆弧齿轮 

分 类 号：TH132.429[机械工程—机械制造及自动化]