无侧隙双滚子包络环面蜗杆传动的接触分析
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摘要
针对当前机械传动领域对蜗杆传动提出的高精度、高效率、高精度寿命的要求,王进戈教授对各种蜗杆传动形式进行分析研究后,创新地提出了一种新型的无侧隙蜗杆传动形式——双滚子包络环面蜗杆传动。本文以这种新型传动的一种特例——无侧隙双滚柱包络环面蜗杆传动的设计与制造为研究对象,对其啮合理论、几何参数设计、结构设计、三维实体建模、有限元分析展开研究。主要研究内容如下:
依据微分几何和空间齿轮啮合原理,运用运动学法建立了理想状况下双滚柱包络环面蜗杆传动的啮合理论体系。推导了该传动的啮合方程、蜗杆齿面方程等,并导出了诱导法曲率、润滑角、自转角的计算公式。
根据蜗轮副的几何参数,应用Matlab等工程软件,得出了蜗杆的几何特性。根据无侧隙双滚柱包络环面蜗轮副的结构设计,应用三维设计软件Pro/E,完成了蜗轮副的三维实体建模。应用ANSYS与Pro/E之间的直接接口,将Pro/E中生成的几何模型导入ANSYS中,建立了无侧隙双滚柱包络环面蜗轮副的接触有限元模型。
在ANSYS环境中,对蜗轮副的齿间载荷分配以及强度问题进行了详细的研究。得到了齿间载荷分配变化规律以及各种应力云图和变形云图,论证了蜗轮副强度满足设计要求。
最后,对具有安装误差的蜗轮副模型进行了有限元分析,得到相应的应力云图。并对其与理想状态下的等效应力云图做比较分析,研究了各种安装误差对蜗轮副传动影响的程度。这对实际中的安装具有重要指导意义。
After analysis and research of various worm gears, a new kind of zero-backlash worm gear sets, named double-roller enveloping hourglass worm gear , is proposed by Professor Wang Jing-ge. It is applied for the realization of worm-drive with high precision, high efficiency and long life-span of precision in now mechanical transmission field. Zero-backlash double-roller enveloping hourglass worm gear is a kind of special form of the new worm-drive, it’s design and machining are investigated in this paper. This paper investigates the meshing theory, geometry parameter design, structure design, construct three-dimensional solid model and finite element analysis. The content of this research is as follows:
According to the theories of differential geometry and gear meshing, a perfect set of meshing system of the double-roller enveloping hourglass worm gear in an ideal situation is established by applying kinematics method. We deduced the meshing function of this drive and worm tooth surface equations. And, the formulas of contacting parameters which include induced normal curvature, lubrication angle and rotation angle are derived.
According to geometry parameters design of the worm gear, geometry features of the worm is derived with the aid of engineering software such as Matlab. Three-dimensional solid model and the zero-backlash double-roller enveloping hourglass worm gear are constructed with the aid of Pro/E. Using the interface between ANSYS and Pro/E, geometry model of the zero-backlash double-roller enveloping hourglass worm gear which is constructed with Por/E is translated into ANSYS,contact infinite element model of the worm gear have been constructed.
We investigated the load share between gear teeth, stress distribution on contacting-line and strength with the aid of ANSYS, mises stress nephogram and distortion nephogram are derived. All of these works proved strength to satisfy requirement of the design.
Finally,we studied the worm gear model with installations error used finite element analysis,and acquired mises stress nephogram.Through comparative analysis between ideal mises stress nephogram and actual mises stress nephogram,we can find which factor has greatest impact on worm gear’s drive.It has important guide on actual installations.
依据微分几何和空间齿轮啮合原理,运用运动学法建立了理想状况下双滚柱包络环面蜗杆传动的啮合理论体系。推导了该传动的啮合方程、蜗杆齿面方程等,并导出了诱导法曲率、润滑角、自转角的计算公式。
根据蜗轮副的几何参数,应用Matlab等工程软件,得出了蜗杆的几何特性。根据无侧隙双滚柱包络环面蜗轮副的结构设计,应用三维设计软件Pro/E,完成了蜗轮副的三维实体建模。应用ANSYS与Pro/E之间的直接接口,将Pro/E中生成的几何模型导入ANSYS中,建立了无侧隙双滚柱包络环面蜗轮副的接触有限元模型。
在ANSYS环境中,对蜗轮副的齿间载荷分配以及强度问题进行了详细的研究。得到了齿间载荷分配变化规律以及各种应力云图和变形云图,论证了蜗轮副强度满足设计要求。
最后,对具有安装误差的蜗轮副模型进行了有限元分析,得到相应的应力云图。并对其与理想状态下的等效应力云图做比较分析,研究了各种安装误差对蜗轮副传动影响的程度。这对实际中的安装具有重要指导意义。
After analysis and research of various worm gears, a new kind of zero-backlash worm gear sets, named double-roller enveloping hourglass worm gear , is proposed by Professor Wang Jing-ge. It is applied for the realization of worm-drive with high precision, high efficiency and long life-span of precision in now mechanical transmission field. Zero-backlash double-roller enveloping hourglass worm gear is a kind of special form of the new worm-drive, it’s design and machining are investigated in this paper. This paper investigates the meshing theory, geometry parameter design, structure design, construct three-dimensional solid model and finite element analysis. The content of this research is as follows:
According to the theories of differential geometry and gear meshing, a perfect set of meshing system of the double-roller enveloping hourglass worm gear in an ideal situation is established by applying kinematics method. We deduced the meshing function of this drive and worm tooth surface equations. And, the formulas of contacting parameters which include induced normal curvature, lubrication angle and rotation angle are derived.
According to geometry parameters design of the worm gear, geometry features of the worm is derived with the aid of engineering software such as Matlab. Three-dimensional solid model and the zero-backlash double-roller enveloping hourglass worm gear are constructed with the aid of Pro/E. Using the interface between ANSYS and Pro/E, geometry model of the zero-backlash double-roller enveloping hourglass worm gear which is constructed with Por/E is translated into ANSYS,contact infinite element model of the worm gear have been constructed.
We investigated the load share between gear teeth, stress distribution on contacting-line and strength with the aid of ANSYS, mises stress nephogram and distortion nephogram are derived. All of these works proved strength to satisfy requirement of the design.
Finally,we studied the worm gear model with installations error used finite element analysis,and acquired mises stress nephogram.Through comparative analysis between ideal mises stress nephogram and actual mises stress nephogram,we can find which factor has greatest impact on worm gear’s drive.It has important guide on actual installations.
引文
[1]王进戈.滚锥包络环面蜗杆传动[M].成都:四川科学技术出版社,2000.
[2]现代机械传动手册编辑委员会.现代机械传动手册[M].北京:机械工业出版社,2002.
[3] Ted Lumpkin, Tom Wolf. Methods and apparatus for minimizing backlash in a planetary mechanism . Patent: USA,7121973 B2. 2004-5-5.
[4] Brauer, J., Transmission error in anti-backlish conical involute gear transmission:a global-local FE approach[J].Finite Elements in Analysis and design. 2005(41).
[5]钱光瑾.双导程蜗杆传动副[J].新技术新工艺, 1983(5): p. 22-25.
[6]张光辉.侧隙可调式平面包络环面蜗杆传动[P].中国,CN99117383.X, 1999.12.24.
[7] (美)白金汉.威尔德哈卜(Wildharber).蜗轮传动,蜗杆传动文集[M].重庆大学蜗杆传动科研组编译,1976.
[8]洪雷.无侧隙双滚子包络环面蜗杆传动的理论研究[C].西华大学硕士论文,2007.
[9]沈蕴方,容尔谦等.空间啮合原理及SG-71型蜗轮副[M].北京工业出版社, 1983.
[10]钱光瑾.双导程蜗杆副传动[J].新技术新工艺, 1983(5): p. 22-25.
[11]李大庆,邓效忠,张明柱等.数控机床改造中的间隙消除问题研究[J].煤矿机械, 2005(9): p. 114-116.
[12]廉仲.无侧隙齿轮减速机[J].机械电子, 1991(3): p. 36.
[13]高耀东等.ANSYSAS机械工程应用25例[M],北京:电子工业出版社,2007.
[14]王庆五等.ANSYS10.0机械设计高级应用实例[M],北京:机械工业出版社,2006.
[15]周宁.ANSYS机械工程应用实例[M],北京:中国水利水电出版社,2006.
[16]李黎明.ANSYS有限元分析实用教程[M],北京:清华大学出版社,2004.
[17]曾攀.有限元分析及应用[M],北京:清华大学出版社,2004.
[18]吴大任,骆家舜.齿轮啮合理论[M].北京:机械工业出版社, 1984.
[19]张朝晖,李树奎.ANSYS11.0有限元分析理论与工程应用[M].北京:电子工业出版社,2008.
[20]钟日铭.Pro/ENGINEER野火版3.0三维设计[M].北京:机械工业出版社,2006.
[21]胡仁喜.Pro/ENGINEER Wildfire3.0中文版机械设计高级应用实例[M].北京:机械工业出版社,2007.
[22]二代龙震工作室编著. Pro/ENGINEER Wildfire3.0进阶提高[M].北京:电子工业出版社,2007.
[23]凯德设计.精通Pro/ENGINEER实战百例[M],北京:中国青年出版社,2007.
[24]孙江宏等.Pro/ENGINEER Wildfire/2001结构分析与运动仿真[M],北京:中国铁道出版社,2004.
[25]杨玉虎,沈煜,张策等.环面蜗杆类零件实体建模研究[J].天津大学学报,2004.6,37(6):471- 474
[26]孙昌佑,李儒琼,何凤琴.环面蜗杆螺旋线参数建模与齿面生成[J].机械设计与研究,2006.12,22(6):53-56.
[27]秦东兴,秦大同,石万凯.包络环面蜗杆传动的实体建模和几何分析[J].重庆大学学报(自然学版),1998(4):79-83.
[28]王勖成,邵敏编著.有限元基本原理和数值方法[M].清华大学出版社,1995.
[29] Bathe K. J., Finite Element Procedures, Preatice-Hall, Englewood Cliffs, New Jersey, 1996.
[30] Owen D.R.J., Hinton E., Finite Elements in Plasticity, Pineridge Press Limited, Swanson, U. K., 1980.
[31] Bathe, K.J., Wilson, E. L.著,林公豫,罗恩译,有限元分析中的数值方法[M],科学出版社,北京:1985.
[32]宋天霞,邹时智,杨文兵.非线性结构有限元计算[M].华中理工大学出版社,1996.
[33]何君毅,林祥都.工程结构非线性问题的数值解法[M].国防工业出版社,1994.
[34]柴群,万朝燕.基于ANSYS/LS-DYNA的蜗轮蜗杆动态接触分析[J].现代制造工程,2006(11):46-48.
[35]张勇,谢剑刚,王宏波.鼓形齿接触应力的有限元分析[J].机械,2004(4):7-9.
[2]现代机械传动手册编辑委员会.现代机械传动手册[M].北京:机械工业出版社,2002.
[3] Ted Lumpkin, Tom Wolf. Methods and apparatus for minimizing backlash in a planetary mechanism . Patent: USA,7121973 B2. 2004-5-5.
[4] Brauer, J., Transmission error in anti-backlish conical involute gear transmission:a global-local FE approach[J].Finite Elements in Analysis and design. 2005(41).
[5]钱光瑾.双导程蜗杆传动副[J].新技术新工艺, 1983(5): p. 22-25.
[6]张光辉.侧隙可调式平面包络环面蜗杆传动[P].中国,CN99117383.X, 1999.12.24.
[7] (美)白金汉.威尔德哈卜(Wildharber).蜗轮传动,蜗杆传动文集[M].重庆大学蜗杆传动科研组编译,1976.
[8]洪雷.无侧隙双滚子包络环面蜗杆传动的理论研究[C].西华大学硕士论文,2007.
[9]沈蕴方,容尔谦等.空间啮合原理及SG-71型蜗轮副[M].北京工业出版社, 1983.
[10]钱光瑾.双导程蜗杆副传动[J].新技术新工艺, 1983(5): p. 22-25.
[11]李大庆,邓效忠,张明柱等.数控机床改造中的间隙消除问题研究[J].煤矿机械, 2005(9): p. 114-116.
[12]廉仲.无侧隙齿轮减速机[J].机械电子, 1991(3): p. 36.
[13]高耀东等.ANSYSAS机械工程应用25例[M],北京:电子工业出版社,2007.
[14]王庆五等.ANSYS10.0机械设计高级应用实例[M],北京:机械工业出版社,2006.
[15]周宁.ANSYS机械工程应用实例[M],北京:中国水利水电出版社,2006.
[16]李黎明.ANSYS有限元分析实用教程[M],北京:清华大学出版社,2004.
[17]曾攀.有限元分析及应用[M],北京:清华大学出版社,2004.
[18]吴大任,骆家舜.齿轮啮合理论[M].北京:机械工业出版社, 1984.
[19]张朝晖,李树奎.ANSYS11.0有限元分析理论与工程应用[M].北京:电子工业出版社,2008.
[20]钟日铭.Pro/ENGINEER野火版3.0三维设计[M].北京:机械工业出版社,2006.
[21]胡仁喜.Pro/ENGINEER Wildfire3.0中文版机械设计高级应用实例[M].北京:机械工业出版社,2007.
[22]二代龙震工作室编著. Pro/ENGINEER Wildfire3.0进阶提高[M].北京:电子工业出版社,2007.
[23]凯德设计.精通Pro/ENGINEER实战百例[M],北京:中国青年出版社,2007.
[24]孙江宏等.Pro/ENGINEER Wildfire/2001结构分析与运动仿真[M],北京:中国铁道出版社,2004.
[25]杨玉虎,沈煜,张策等.环面蜗杆类零件实体建模研究[J].天津大学学报,2004.6,37(6):471- 474
[26]孙昌佑,李儒琼,何凤琴.环面蜗杆螺旋线参数建模与齿面生成[J].机械设计与研究,2006.12,22(6):53-56.
[27]秦东兴,秦大同,石万凯.包络环面蜗杆传动的实体建模和几何分析[J].重庆大学学报(自然学版),1998(4):79-83.
[28]王勖成,邵敏编著.有限元基本原理和数值方法[M].清华大学出版社,1995.
[29] Bathe K. J., Finite Element Procedures, Preatice-Hall, Englewood Cliffs, New Jersey, 1996.
[30] Owen D.R.J., Hinton E., Finite Elements in Plasticity, Pineridge Press Limited, Swanson, U. K., 1980.
[31] Bathe, K.J., Wilson, E. L.著,林公豫,罗恩译,有限元分析中的数值方法[M],科学出版社,北京:1985.
[32]宋天霞,邹时智,杨文兵.非线性结构有限元计算[M].华中理工大学出版社,1996.
[33]何君毅,林祥都.工程结构非线性问题的数值解法[M].国防工业出版社,1994.
[34]柴群,万朝燕.基于ANSYS/LS-DYNA的蜗轮蜗杆动态接触分析[J].现代制造工程,2006(11):46-48.
[35]张勇,谢剑刚,王宏波.鼓形齿接触应力的有限元分析[J].机械,2004(4):7-9.