ZK蜗杆蜗轮的三维造型及有限元仿真分析
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摘要
ZK蜗杆传动具有易于磨削、适合批量生产、承载能力高等优点,是一种值得大力推广的机械传动形式。但是由于相关研究理论的滞后和相关加工工艺的缺乏,该类蜗杆传动在我国并没有得到大规模的推广和使用。近一步完善和深化对ZK蜗杆传动的理论研究,推动我国实现该类型蜗杆传动设计制造的完全自主化十分必要。计算机CAD技术、弹性啮合原理(FCP)、有限元分析(FEA)技术、齿面接触分析(TCA)技术、计算机仿真技术等技术和理论的发展,CAD/CAE/CAM/PDM发展的一体化,使产品设计制造效率大幅度提高,更新换代的步伐加快。本文综合运用上述有关理论和技术,建立了ZK蜗杆蜗轮的数学模型,发展和完善了ZK蜗杆蜗轮的啮合原理,实现了ZK蜗杆蜗轮的三维实体建模和有限元仿真分析。
首先借鉴CAD技术中“特征造型”的思想,提出了“特征齿形”的概念。根据共轭曲面的啮合原理,归纳总结了ZK蜗杆蜗轮不同形式的齿面数学模型,系统地研究了ZK蜗杆蜗轮的特征齿形,从而为蜗杆蜗轮刀具的设计制造、齿形加工精度的控制和检测、蜗杆蜗轮的实体造型等奠定基础。分析了安装误差对于ZK蜗杆齿形误差的影响和影响规律,并且得出了“△a与△f_x成线性关系,近似满足△f_x=△a tanα_0”这一重要结论,从而为实际加工中合理分配和控制加工误差提了供参考依据。
借助于CAD技术,从新的角度阐明了ZK蜗杆过渡曲面的形成原理,推导出了过渡曲面的数学模型。提出了根切判别线的概念,给出了根切判据,并研究了相关参数对根切现象的影响。这对于合理确定刀具参数、制造精密蜗杆副及进行蜗杆副强度分析具有重要的理论意义和实践价值。
根据ZK蜗杆蜗轮的实际切齿原理,基于ActiveX方法,通过Visual Basic操纵AutoCAD,编程实现了ZK蜗杆和蜗轮的切齿仿真。利用切齿仿真得到的仿真齿形验证了磨削蜗杆过程中根切现象及ZK蜗杆过渡曲面的数学模型。
利用ZK型蜗杆蜗轮的特征齿形,采用特征造型的方法在Pro/E中实现了蜗杆蜗轮的三维参数化实体造型,成功解决了具有非线性齿面的ZK型蜗杆蜗轮三维造型问题。将三维模型导入到ANSYS软件中,采用有限元方法进行了三维静态有限元仿真分析。并将有限元分析的结果同空间啮合原理的判断结果进行了比较。
本文的研究工作为ZK蜗杆传动的数字化设计及制造奠定了基础,所采用的研究方法具有推广价值。
The ZK-type worm gear set is well worth using and popularizing, because its precision worm can be ground by a straight-edged grinding wheel. But due to the lag of theoretical research and the lack of practical machining process, it has still not been adopted widely. To further perfect and deepen theoretical study and to realize the independence of its design and manufacture is very necessary and very pressing.Now the period of product upgrade and replacement is shorten for the rapid development of many advanced theories and technologies, such as Computer Aided Design(CAD),Flexible Conjugate Principle, Finite Element Analysis(FEA),Tooth Contact Analysis(TCA),Computer Simulaiton, Intelligent Optimization Methods.The purpose of this thesis is to realize three-dimensional modeling and Finite Element Analysis of ZK-type worm gear set based on further perfecting its conjugate principle.
Firstly, the concept "Feature Profile" was put forward according to "Feature Modeling".The feature profiles of ZK-type worm and worm wheel were systemically studied so as to lay the groundwork for the design and manufacture of machining tools, measuring and control of machining precision, solid modeling.And the effects and effect laws of misalignment on the ZK-worm profile errors were analyzed.
Secondly, from a new angle the generation course of ZK-worm fillet was explained via CAD approach.The mathematical equations of ZK-worm fillet was derived. The concept "Undercutting Eestimation Line" was put forward and the Undercutting Eestimation Criterion was given.The effect of the correlative parameters on the undercutting were studied. These researches are very important to rightly design tools , make precision worm and analyze strength.
Thirdly, according to the real machining of ZK-type worm and worm wheel, the machining simulation of them were realized by Visual Basic operating AutoCAD based on ActiveX. The simulation profiles were used to verify the undercutting and fillet equation of ZK-worm.
Lastly, the three-dimensional solid models of ZK-type worm and worm wheel were made in Pro/E based on their feature profiles.And the Tooth Contact Analysis via Finite Element Method was done in ANSYS.
Researches of this thesis laid the groundwork for the digital design and manufacture of ZK-type worm gear set.
首先借鉴CAD技术中“特征造型”的思想,提出了“特征齿形”的概念。根据共轭曲面的啮合原理,归纳总结了ZK蜗杆蜗轮不同形式的齿面数学模型,系统地研究了ZK蜗杆蜗轮的特征齿形,从而为蜗杆蜗轮刀具的设计制造、齿形加工精度的控制和检测、蜗杆蜗轮的实体造型等奠定基础。分析了安装误差对于ZK蜗杆齿形误差的影响和影响规律,并且得出了“△a与△f_x成线性关系,近似满足△f_x=△a tanα_0”这一重要结论,从而为实际加工中合理分配和控制加工误差提了供参考依据。
借助于CAD技术,从新的角度阐明了ZK蜗杆过渡曲面的形成原理,推导出了过渡曲面的数学模型。提出了根切判别线的概念,给出了根切判据,并研究了相关参数对根切现象的影响。这对于合理确定刀具参数、制造精密蜗杆副及进行蜗杆副强度分析具有重要的理论意义和实践价值。
根据ZK蜗杆蜗轮的实际切齿原理,基于ActiveX方法,通过Visual Basic操纵AutoCAD,编程实现了ZK蜗杆和蜗轮的切齿仿真。利用切齿仿真得到的仿真齿形验证了磨削蜗杆过程中根切现象及ZK蜗杆过渡曲面的数学模型。
利用ZK型蜗杆蜗轮的特征齿形,采用特征造型的方法在Pro/E中实现了蜗杆蜗轮的三维参数化实体造型,成功解决了具有非线性齿面的ZK型蜗杆蜗轮三维造型问题。将三维模型导入到ANSYS软件中,采用有限元方法进行了三维静态有限元仿真分析。并将有限元分析的结果同空间啮合原理的判断结果进行了比较。
本文的研究工作为ZK蜗杆传动的数字化设计及制造奠定了基础,所采用的研究方法具有推广价值。
The ZK-type worm gear set is well worth using and popularizing, because its precision worm can be ground by a straight-edged grinding wheel. But due to the lag of theoretical research and the lack of practical machining process, it has still not been adopted widely. To further perfect and deepen theoretical study and to realize the independence of its design and manufacture is very necessary and very pressing.Now the period of product upgrade and replacement is shorten for the rapid development of many advanced theories and technologies, such as Computer Aided Design(CAD),Flexible Conjugate Principle, Finite Element Analysis(FEA),Tooth Contact Analysis(TCA),Computer Simulaiton, Intelligent Optimization Methods.The purpose of this thesis is to realize three-dimensional modeling and Finite Element Analysis of ZK-type worm gear set based on further perfecting its conjugate principle.
Firstly, the concept "Feature Profile" was put forward according to "Feature Modeling".The feature profiles of ZK-type worm and worm wheel were systemically studied so as to lay the groundwork for the design and manufacture of machining tools, measuring and control of machining precision, solid modeling.And the effects and effect laws of misalignment on the ZK-worm profile errors were analyzed.
Secondly, from a new angle the generation course of ZK-worm fillet was explained via CAD approach.The mathematical equations of ZK-worm fillet was derived. The concept "Undercutting Eestimation Line" was put forward and the Undercutting Eestimation Criterion was given.The effect of the correlative parameters on the undercutting were studied. These researches are very important to rightly design tools , make precision worm and analyze strength.
Thirdly, according to the real machining of ZK-type worm and worm wheel, the machining simulation of them were realized by Visual Basic operating AutoCAD based on ActiveX. The simulation profiles were used to verify the undercutting and fillet equation of ZK-worm.
Lastly, the three-dimensional solid models of ZK-type worm and worm wheel were made in Pro/E based on their feature profiles.And the Tooth Contact Analysis via Finite Element Method was done in ANSYS.
Researches of this thesis laid the groundwork for the digital design and manufacture of ZK-type worm gear set.
引文
1 Faydor L.Litvin.Geometry and Investigation of Klingelnberg-Type Worm Gear Drive[J].Journal of Mechanical Design.2007,129(1):17-22
2 Hong-Sheng Fang,Chung-BiauTsay.Mathematical Model and Bearing Contacts of the ZK-type Worm Gear Set Cut by Oversize Hob Cutters[J].Mech.Mach Theory.1996,31(3):271-282
3 J.Argyris,M.De Donno,F.L.Litvin.Computer program in Visual Basic Language for Simulation of Meshing and Contact of Gear Drives and its Application for Design of Worm Gear Drive[J].Comput.Methods Appl.Mech.Engrg..2000,(189):595-612
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8 吴鸿业,王树国。砂轮直径变化对锥面包络圆柱蜗杆(ZK)齿廓形状影响的研究[J].哈尔滨工业大学报.1985,17(3):112-118
9 赵玉良,杨军,王宇辉.ZK_1蜗杆的齿形误差及其控制[J].重型机械.2000,(5):37-40
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2 Hong-Sheng Fang,Chung-BiauTsay.Mathematical Model and Bearing Contacts of the ZK-type Worm Gear Set Cut by Oversize Hob Cutters[J].Mech.Mach Theory.1996,31(3):271-282
3 J.Argyris,M.De Donno,F.L.Litvin.Computer program in Visual Basic Language for Simulation of Meshing and Contact of Gear Drives and its Application for Design of Worm Gear Drive[J].Comput.Methods Appl.Mech.Engrg..2000,(189):595-612
4 吴鸿业.两次旋转片状锥形刀具轴所加工的曲纹面蜗杆的几何形状[J].哈尔滨工业大学报.1958,(2):70-82
5 王树人.曲纹面圆柱蜗杆传动的研究[J].天津大学报.1981,(3):113-126
6 李特文.齿轮啮合原理(第2版)[M].上海:上海科学技术出版社,1984
7 沈谦,周长秀.ZK型圆柱蜗杆螺旋面方程简析[J]。机械.1990,(6):14-16
8 吴鸿业,王树国。砂轮直径变化对锥面包络圆柱蜗杆(ZK)齿廓形状影响的研究[J].哈尔滨工业大学报.1985,17(3):112-118
9 赵玉良,杨军,王宇辉.ZK_1蜗杆的齿形误差及其控制[J].重型机械.2000,(5):37-40
10 沈谦,周长秀,吴序堂.磨削ZK型蜗杆齿形精度的分析[J].精密制造与自动化.1989,(4):31-32
11 韩云鹏,孟剑锋.ZK蜗杆齿形误差及其控制方法的研究[J].机械工程学报.2004,40(5):178-183
12 韩云鹏,孟剑锋。ZK蜗杆磨削中砂轮廓形的智能化修整[J].中国机械工程.2003,14(16):1377-1380
13 韩云鹏,孟剑锋.ZK蜗杆过渡曲线的研究[J].工具技术.2004,38(1):49-51
14 柴琪.基于三维仿真ZK蜗杆齿形误差的研究[D].山东大学硕士学位论文.2006
15 刘法权.盘状锥面包络圆柱蜗杆传动蜗轮量球测量距的计算[J].机械设计.1990,(4):51-52
16 韩云鹏.ZK蜗杆代替ZI蜗杆的分析和研究[D].山东工业大学硕士学位论文.1991
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