基于共轭原理的棒铣刀铣削直齿齿轮的轨迹规划
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摘要
传统齿轮加工依赖于专用齿轮机床和专用齿轮刀具,小批量多品种齿轮加工时需配备多种齿轮刀具,且齿轮加工柔性差。针对这一问题,采用四轴卧式加工中心和棒铣刀,基于齿条刀具刀刃和齿轮廓线的共轭曲线理论,得到齿轮加工展成原理的数学模型,获得齿面形成的包络线。通过坐标变换,将复杂的包络线变换为棒铣刀的平移运动和齿轮的旋转运动,得到了一种由模数、齿数、齿宽、刀具半径参数驱动的柔性齿轮加工轨迹规划的方法,可实现不同模数齿轮的柔性加工。以直齿齿轮铣削试验为例,验证该轨迹规划方法的有效性。
Gear machining depends on special gear machine tool and special gear cutter, traditional method is not flexible enough for small quantities and multiple varieties of gear processing, has to be equipped with a variety of gear cutting tools. To deal with this situation, four axis horizontal machining center and rod milling cutter are adopted, based on the conjugate curve theory of rack blade and gear profile, mathematical model of gear machining is obtained, then the envelope of the formation of the tooth surface is gained. Through coordinate transformation, the complex envelope is transformed to the translational motion of the rod mill and the rotation of the gear, the method of machining path planning of a flexible gear driven by modulus, tooth number, tooth width and tool radius is obtained, flexible processing of different modulus gears is realized. And the feasibility of the method is verified by the cutting test of spur gear.
Gear machining depends on special gear machine tool and special gear cutter, traditional method is not flexible enough for small quantities and multiple varieties of gear processing, has to be equipped with a variety of gear cutting tools. To deal with this situation, four axis horizontal machining center and rod milling cutter are adopted, based on the conjugate curve theory of rack blade and gear profile, mathematical model of gear machining is obtained, then the envelope of the formation of the tooth surface is gained. Through coordinate transformation, the complex envelope is transformed to the translational motion of the rod mill and the rotation of the gear, the method of machining path planning of a flexible gear driven by modulus, tooth number, tooth width and tool radius is obtained, flexible processing of different modulus gears is realized. And the feasibility of the method is verified by the cutting test of spur gear.
引文
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[2]Chiang Chi-jung,Fong Zhang-hua.Design of form milling cutters with multiple inserts for screw rotors[J].Mechanism and Machine Theory,2010,45:1613-1627.
[3]Mahir Uzun,Ali Inan.Manufacturing the new type concaveconvex profile involute gears modeled by CAD/CAM in CNC milling machines[J].Technical Paper,2015,37:255-261.
[4]Bouquet J,Hensgen L,Klink A,et al.Fast production of gear prototypes-A comparison of technologies[J].Procedia Cirp,2014,14(14):77-82.
[5]Ferenc T R,Zoltan F,Marton M.Evaluation of a mixed CAD gear modeling from time and precidion point of view[J].Procedia Technology,2015,19:28-33.
[6]伍迪,张有忱.基于ANSYS的多齿差摆线齿轮有限元分析[J].机械设计,2009,26(5):40-41.
[7]贵桂生,王乾廷,杜世昌,等.大模数少齿数螺旋齿面的四轴加工与仿真[J].农业机械学报,2004,35(2):150-152.
[8]郝诗明,何静,朱宗铭,等.渐开线齿廓齿轮的精确建模及应力分析[J].湖南农业大学学报,2010,36(1):63-65.
[9]黄贤振,赵庆栋,李少东,等.渐开线圆柱齿轮系统运动精度可靠性分析[J].计算机集成制造系统,2013,20(9):2210-2214.
[10]陈兵奎,梁栋,彭帅,等.共轭曲线齿轮啮合管齿面的几何及接触特性分析[J].西安交通大学学报,2015,49(3):85-94.
[11]刘有余,韩江,夏链.椭圆齿轮滚齿加工三维仿真研究[J].机械设计,2012,29(5):50-53.
[12]杨勇,王时龙,周杰,等.基于自动编程系统的大型滚齿机热误差补偿[J].计算机集成制造系统,2013,19(3):569-576.
[13]Bouzakis K,Michailidis E,Friderikos O.Manufacturing of cylindrical gears by generating cutting processes:A critical synthesis of analysis methods[J].CIRP Annals-Manufacturing Technology,2008,57:676-696.
[14]陈兵奎,梁栋,高艳娥.齿轮传动共轭曲线原理[J].机械工程学报,2014,50(1):130-135.
[15]Litvin F L.齿轮几何学与应用理论[M].国楷,叶凌云,译.上海:上海科学技术出版社,2008.