螺旋锥齿轮副大轮齿顶线倒角加工方法的研究
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摘要
齿轮传动是最重要的机械传动形式,螺旋锥齿轮因具有良好的传动性能而得到广泛应用,尤其是在汽车的后桥中普遍采用螺旋锥齿轮传动。为避免渐开线齿面被碰毛,降低噪声和冲击,螺旋锥齿轮的齿端和外锥面齿顶线常需要进行倒角。然而,现在仅限于对齿轮的端面齿形采用机械加工方法进行倒角加工,而齿顶线的倒角是靠工人手工操作砂轮来完成。
为解决该技术难题,本文在林汉元高工申报的专利的基础之上,展开对汽车螺旋锥齿轮副中大轮外锥面齿顶线倒角加工方法的研究,主要工作如下:
基于汽车螺旋锥齿轮副中的大轮采用的半滚切法加工原理,建立了大轮面锥和切齿刀具内、外刀片切削刃轨迹面的数学方程;通过空间坐标变换矩阵和方程联立,推导出大轮的内、外齿顶线方程,为倒角轨迹的推导提供了理论基础。
建立了大轮齿顶线的摆线连续分度法倒角加工的数学模型;推导出倒角刀具的实际运动轨迹,同时获得加工误差和所需要的轴向进给量。
建立了倒角刀具设计的数学模型,将其转化为一个有约束优化问题,进而利用MATLAB中的优化程序包,搜索出最佳的设计变量,最终得到倒角刀具的位置和刀具半径。
最后,给出一个具体的计算实例。用数值结果和动画仿真验证了上述理论和方法的可行性。
Gearing is one of the most important mechanical transmissions. Spiral bevel and hypoid gear is widely used for its good transmission performance, especially in the automobile rear axle. To avoid the failure of involute tooth surface, reduce noise and collision, the tooth profile and addendum lines often need to be chamfered. Up to now, the chamfering has been limited to the tooth profile in mechanical manufacturing. For the chamfering of addendum lines, it is often completed by hand with wheel grinding. In this thesis, the addendum lines’chamfering for the driven gear in spiral bevel and hypoid gear transmission of automobile is studied based on the patent by Lin Hanyuan, and following works have been carried out.
According to the principle of generating-forming method, the equations of face cone and blades trace of gear-cutting tool are obtained for the driven gear. Base on the coordinate transformation matrix and the combination of above equations, the equations of inside and outside addendum lines is deduced, which lays the theoretical foundation of chamfering trace.
The mathematical model of addendum lines' chamfering is proposed in the continuous indexing method for the driven gear. The equations of chamfering trace are deduced, and eventually processing errors and the axial feed depth are obtained. The mathematical model of chamfering tool is proposed. The problem is transformed into constrained optimization, which can be solved by use of MATLAB optimization function to find the optimal solution of design variables. Eventually the location and radius of chamfering tool is obtained.
Finally, a specific example is given. The feasibility of the theoretical method is proved through the theoretical results and the animation.
为解决该技术难题,本文在林汉元高工申报的专利的基础之上,展开对汽车螺旋锥齿轮副中大轮外锥面齿顶线倒角加工方法的研究,主要工作如下:
基于汽车螺旋锥齿轮副中的大轮采用的半滚切法加工原理,建立了大轮面锥和切齿刀具内、外刀片切削刃轨迹面的数学方程;通过空间坐标变换矩阵和方程联立,推导出大轮的内、外齿顶线方程,为倒角轨迹的推导提供了理论基础。
建立了大轮齿顶线的摆线连续分度法倒角加工的数学模型;推导出倒角刀具的实际运动轨迹,同时获得加工误差和所需要的轴向进给量。
建立了倒角刀具设计的数学模型,将其转化为一个有约束优化问题,进而利用MATLAB中的优化程序包,搜索出最佳的设计变量,最终得到倒角刀具的位置和刀具半径。
最后,给出一个具体的计算实例。用数值结果和动画仿真验证了上述理论和方法的可行性。
Gearing is one of the most important mechanical transmissions. Spiral bevel and hypoid gear is widely used for its good transmission performance, especially in the automobile rear axle. To avoid the failure of involute tooth surface, reduce noise and collision, the tooth profile and addendum lines often need to be chamfered. Up to now, the chamfering has been limited to the tooth profile in mechanical manufacturing. For the chamfering of addendum lines, it is often completed by hand with wheel grinding. In this thesis, the addendum lines’chamfering for the driven gear in spiral bevel and hypoid gear transmission of automobile is studied based on the patent by Lin Hanyuan, and following works have been carried out.
According to the principle of generating-forming method, the equations of face cone and blades trace of gear-cutting tool are obtained for the driven gear. Base on the coordinate transformation matrix and the combination of above equations, the equations of inside and outside addendum lines is deduced, which lays the theoretical foundation of chamfering trace.
The mathematical model of addendum lines' chamfering is proposed in the continuous indexing method for the driven gear. The equations of chamfering trace are deduced, and eventually processing errors and the axial feed depth are obtained. The mathematical model of chamfering tool is proposed. The problem is transformed into constrained optimization, which can be solved by use of MATLAB optimization function to find the optimal solution of design variables. Eventually the location and radius of chamfering tool is obtained.
Finally, a specific example is given. The feasibility of the theoretical method is proved through the theoretical results and the animation.
引文
[1]唐定国,陈国民,齿轮传动技术的现状和展望,机械工程学报,1993,29(5):35~42
[2]王声堂,杨歧华,蒋荣孝,21世纪齿轮行业发展战略的建议,机械传动,1999,23(1):46~49
[3]郭晓东,郑昌启,林超,锥齿轮设计制造现代应用技术的研究,重庆大学学报,1993,16(1):37~44
[4] Ernest Wildhaber,Basic Relationship of Hypoid Gears,American Machinist,1946,(2)
[5] Ernest Wildhaber,Basic Relationship of Hypoid Gears-II,American Machinist,1946,(2)
[6] Ernest Wildhaber,Basic Relationship of Hypoid Gears-III,American Machinist,1946,(3)
[7]黄天铭,梁锡昌,齿轮加工技术的现状及进展,机械工艺师,1990,(4):29~31
[8]王统,齿轮技术进步梗概及未来发展趋势,机械制造,1990,(4):10~13
[9]徐鸿根,齿轮制造技术的发展动态,制造技术与机床,1994,(9):43~45
[10]西安交通大学机制教研室齿轮研究组,弧齿锥齿轮和准双曲线齿轮加工调整原理,上海:上海科学技术出版社,1979
[11]郑昌启,弧齿锥齿轮和准双曲面齿轮,北京:机械工业出版社,1988
[12]曾韬,螺旋锥齿轮设计与加工,黑龙江:哈尔滨工业大学出版社,1989
[13]董学朱,准双曲面齿轮切齿调整计算法的改进(一),齿轮,1985,9(6):1~4
[14]董学朱,准双曲面齿轮切齿调整计算法的改进(二),齿轮,1986,10(1):40~43
[15]周凯红,王元勋,李春植等,格利森圆弧螺旋锥齿轮副的实体造型方法,计算机仿真,2003,20(8):97~99
[16]房怀英,洪尚任,杨建红,克林贝格螺旋锥齿轮的建模与仿真,华侨大学学报,2004,25(1):67~70
[17]王军,曹雪梅,周彦伟等,弧齿锥齿轮的三维仿真,工具技术,2003,37(9):20~22
[18]熊越东,王太勇,张威,螺旋锥齿轮数控加工3维仿真研究,制造业自动化,2005,27(6):21~23
[19]熊越东,基于虚拟现实技术的螺旋锥齿轮CNC加工仿真理论与方法研究,[博士学位论文],天津大学,2004
[20] S.H. Suh a,*, W.S. Jih b, H.D. Hong,Sculptured surface machining of spiral bevel gears with CNC milling,International Journal of Machine Tools & Manufacture,2001,41:830~855
[21]李建刚,吴序堂,贺敬良等,CNC铣齿机床加工曲线齿锥齿轮仿真系统的研究,系统仿真学报,2003,15(4):499~501
[22]郭晓东,张明德,梁伟,基于AutoCAD的锥齿轮切齿过程仿真及软件开发,现代制造工程,2002,(10):34~36
[23]舒卫真,CHAN CY,黄晓宇,在螺旋锥齿轮数控磨齿机上磨成形法加工的齿轮,制造业自动化,2004,26(8):31~33
[24]刘鸪然,在数控磨齿机上螺旋锥齿轮及准双曲齿轮刀倾半展成法的实现,精密制造与自动化,2005,(1):47~49
[25]刘鹄然,刘志峰,陈良玉,在普通数控铣床上用连续展成法加工螺旋锥齿轮,组合机床与自动化加工技术,2004,(1):94~95
[26]李必文,肖金凤,廖卫献,齿轮倒角刀的CAD/CAM,机械设计与制造工程,2002,31(4):32~33
[27]牛占文,刘仁龙,郭伟,齿轮曲面倒角刀具几何建模与调整仿真,天津大学学报,2006,39(1):58~62
[28]何培兴,王斌,卧式车床低噪声齿轮的设计及制造技术,机械设计与制造工程,2000,20(2):68~70
[29]北京齿轮厂,螺旋锥齿轮,北京:科学出版社,1974
[30]刘惟信,圆锥齿轮与双曲面齿轮传动,北京:人民交通出版社,1980
[31]申永胜,机械原理教程,北京:清华大学出版社,1999
[32]长春第一汽车制造厂工艺处机械加工试验室,圆弧齿伞齿轮加工手册,吉林:吉林人民出版社,1980
[33]齿轮手册编委会,齿轮手册,北京:机械工业出版社,2001
[34]天津齿轮机床研究所,西安交通大学,格利森锥齿轮技术资料译文集,北京:机械工业出版社,1986
[35]郑昌启,弧齿锥齿轮和准双曲面齿轮(——啮合原理,齿坯设计、加工调整和齿面分析计算原理),北京:机械工业出版社,1988
[36]李敦信,包润阁等,锥齿轮加工简化计算,北京:机械工业出版社,1986
[37]西安交通大学机制教研室齿轮研究组,弧齿锥齿轮和准双曲线齿轮——加工调整原理,上海:上海科学技术出版社,1979
[38]王树人,齿轮啮合理论简明教程,天津:天津大学出版社,2005
[39]张启先,空间机构的分析与综合(上册),北京:机械工业出版社,1984
[40]傅则绍,微分几何与齿轮啮合理论,东营:石油大学出版社,1999
[41]叶元烈,机械优化理论与设计,北京:中国计量出版社,2000
[42]飞思科技产品研发中心,MATLAB6.5辅助优化计算与设计,北京:电子工业出版社,2003
[43]张志涌,徐彦琴等,MATLAB教程:基于6.X版本,北京:北京航空航天大学出版社,2001
[44]张志涌,精通MATLAB,北京:北京航空航天大学出版社,2003
[45]关治,陈景良,数值计算方法,北京:清华大学出版社,1990
[46]刘德贵,郭富印等,FORTRAN算法汇编,北京:国防工业出版社,1982
[47]侯永涛,黄娟等,SolidWorks机械设计实用教程,北京:化学工业出版社,2006
[48]江洪,SolidWorks建模实例解析,北京:机械工业出版社,2005
[49]崔海萍,SolidWorks 2006中文版标准实例教程,北京:机械工业出版社,2005
[2]王声堂,杨歧华,蒋荣孝,21世纪齿轮行业发展战略的建议,机械传动,1999,23(1):46~49
[3]郭晓东,郑昌启,林超,锥齿轮设计制造现代应用技术的研究,重庆大学学报,1993,16(1):37~44
[4] Ernest Wildhaber,Basic Relationship of Hypoid Gears,American Machinist,1946,(2)
[5] Ernest Wildhaber,Basic Relationship of Hypoid Gears-II,American Machinist,1946,(2)
[6] Ernest Wildhaber,Basic Relationship of Hypoid Gears-III,American Machinist,1946,(3)
[7]黄天铭,梁锡昌,齿轮加工技术的现状及进展,机械工艺师,1990,(4):29~31
[8]王统,齿轮技术进步梗概及未来发展趋势,机械制造,1990,(4):10~13
[9]徐鸿根,齿轮制造技术的发展动态,制造技术与机床,1994,(9):43~45
[10]西安交通大学机制教研室齿轮研究组,弧齿锥齿轮和准双曲线齿轮加工调整原理,上海:上海科学技术出版社,1979
[11]郑昌启,弧齿锥齿轮和准双曲面齿轮,北京:机械工业出版社,1988
[12]曾韬,螺旋锥齿轮设计与加工,黑龙江:哈尔滨工业大学出版社,1989
[13]董学朱,准双曲面齿轮切齿调整计算法的改进(一),齿轮,1985,9(6):1~4
[14]董学朱,准双曲面齿轮切齿调整计算法的改进(二),齿轮,1986,10(1):40~43
[15]周凯红,王元勋,李春植等,格利森圆弧螺旋锥齿轮副的实体造型方法,计算机仿真,2003,20(8):97~99
[16]房怀英,洪尚任,杨建红,克林贝格螺旋锥齿轮的建模与仿真,华侨大学学报,2004,25(1):67~70
[17]王军,曹雪梅,周彦伟等,弧齿锥齿轮的三维仿真,工具技术,2003,37(9):20~22
[18]熊越东,王太勇,张威,螺旋锥齿轮数控加工3维仿真研究,制造业自动化,2005,27(6):21~23
[19]熊越东,基于虚拟现实技术的螺旋锥齿轮CNC加工仿真理论与方法研究,[博士学位论文],天津大学,2004
[20] S.H. Suh a,*, W.S. Jih b, H.D. Hong,Sculptured surface machining of spiral bevel gears with CNC milling,International Journal of Machine Tools & Manufacture,2001,41:830~855
[21]李建刚,吴序堂,贺敬良等,CNC铣齿机床加工曲线齿锥齿轮仿真系统的研究,系统仿真学报,2003,15(4):499~501
[22]郭晓东,张明德,梁伟,基于AutoCAD的锥齿轮切齿过程仿真及软件开发,现代制造工程,2002,(10):34~36
[23]舒卫真,CHAN CY,黄晓宇,在螺旋锥齿轮数控磨齿机上磨成形法加工的齿轮,制造业自动化,2004,26(8):31~33
[24]刘鸪然,在数控磨齿机上螺旋锥齿轮及准双曲齿轮刀倾半展成法的实现,精密制造与自动化,2005,(1):47~49
[25]刘鹄然,刘志峰,陈良玉,在普通数控铣床上用连续展成法加工螺旋锥齿轮,组合机床与自动化加工技术,2004,(1):94~95
[26]李必文,肖金凤,廖卫献,齿轮倒角刀的CAD/CAM,机械设计与制造工程,2002,31(4):32~33
[27]牛占文,刘仁龙,郭伟,齿轮曲面倒角刀具几何建模与调整仿真,天津大学学报,2006,39(1):58~62
[28]何培兴,王斌,卧式车床低噪声齿轮的设计及制造技术,机械设计与制造工程,2000,20(2):68~70
[29]北京齿轮厂,螺旋锥齿轮,北京:科学出版社,1974
[30]刘惟信,圆锥齿轮与双曲面齿轮传动,北京:人民交通出版社,1980
[31]申永胜,机械原理教程,北京:清华大学出版社,1999
[32]长春第一汽车制造厂工艺处机械加工试验室,圆弧齿伞齿轮加工手册,吉林:吉林人民出版社,1980
[33]齿轮手册编委会,齿轮手册,北京:机械工业出版社,2001
[34]天津齿轮机床研究所,西安交通大学,格利森锥齿轮技术资料译文集,北京:机械工业出版社,1986
[35]郑昌启,弧齿锥齿轮和准双曲面齿轮(——啮合原理,齿坯设计、加工调整和齿面分析计算原理),北京:机械工业出版社,1988
[36]李敦信,包润阁等,锥齿轮加工简化计算,北京:机械工业出版社,1986
[37]西安交通大学机制教研室齿轮研究组,弧齿锥齿轮和准双曲线齿轮——加工调整原理,上海:上海科学技术出版社,1979
[38]王树人,齿轮啮合理论简明教程,天津:天津大学出版社,2005
[39]张启先,空间机构的分析与综合(上册),北京:机械工业出版社,1984
[40]傅则绍,微分几何与齿轮啮合理论,东营:石油大学出版社,1999
[41]叶元烈,机械优化理论与设计,北京:中国计量出版社,2000
[42]飞思科技产品研发中心,MATLAB6.5辅助优化计算与设计,北京:电子工业出版社,2003
[43]张志涌,徐彦琴等,MATLAB教程:基于6.X版本,北京:北京航空航天大学出版社,2001
[44]张志涌,精通MATLAB,北京:北京航空航天大学出版社,2003
[45]关治,陈景良,数值计算方法,北京:清华大学出版社,1990
[46]刘德贵,郭富印等,FORTRAN算法汇编,北京:国防工业出版社,1982
[47]侯永涛,黄娟等,SolidWorks机械设计实用教程,北京:化学工业出版社,2006
[48]江洪,SolidWorks建模实例解析,北京:机械工业出版社,2005
[49]崔海萍,SolidWorks 2006中文版标准实例教程,北京:机械工业出版社,2005