移动基圆变齿厚齿轮齿面研究及动力学仿真分析
|
摘要
研究了一种新型的变齿厚齿轮——移动基圆变齿厚齿轮,它和传统的利用轴向变位形成的变齿厚齿轮在成型原理上有着本质的区别。因为,根据齿轮的基本原理,当一个齿轮有变位系数时,齿轮的齿顶高、齿根高、齿厚和槽宽都将发生变化,当沿齿轮的轴向添加一组有规律的变位系数时,齿轮在沿轴向各端面的齿厚有规律的变化,即形成了传统的变厚齿轮,而传统的变厚齿轮在齿厚变厚的同时,其各端面的齿顶高、齿根高也都随之变化,这就导致传统的变厚齿轮从小端到大端其齿顶圆直径逐渐增大,即沿径向看传统的变厚齿轮是有一个锥度的,这样在沿轴向调隙时就有可能产生干涉,不能完全调隙。而本文研究的移动基圆变齿厚齿轮就解决了这个问题,它的成型原理是:沿着齿轮的轴向,生成变厚齿轮各端面齿廓渐开线的基圆的位置有规律的变化,即:其基圆的圆心形成的直线与变厚齿轮的轴线并不重合,而是和轴线形成一定的夹角,这样变厚齿轮的齿厚就沿着中间端面向一边逐渐变厚或变薄。由于各端节面上变位系数为零或相同,所以在齿厚变厚的同时,其各端面的齿顶高、齿根高也相同,即各端面的齿顶圆直径相同,这样在调隙过程中就不会产生干涉,能达到完全调隙的目的。
本文的研究内容如下:
①研究了移动基圆变齿厚齿轮的成型原理、几何特点,将其与传统的变齿厚齿轮相比较,体现了移动基圆变齿厚齿轮的优点;根据齿轮的基本原理,提出移动基圆变齿厚直齿轮的插齿、滚齿加工方法以及用标准齿条刀具的加工方法。
②结合齿条刀具加工移动基圆变齿厚直齿轮的加工方法,根据齿轮啮合原理,由齿条刀具的齿面方程推导出移动基圆变齿厚直齿轮的齿面方程;并利用Matlab编程对移动基圆变齿厚直齿轮的齿面进行仿真,将得到的各点的坐标值导入Pro/E中,建立其精确的三维模型。
③利用前面推导出的齿面方程,根据齿面接触分析的基本原理,建立移动基圆变齿厚直齿轮传动副接触的数学模型,用Matlab编程对其求解,得到其齿面上的接触点和接触迹线,实现了接触分析的可视化。
④利用Adams软件,建立了该齿轮传动的动力学模型,对其进行动力学仿真分析,得到了其啮合力曲线,并将其与标准直齿轮传动产生齿侧间隙后的啮合力曲线相比较,体现了调隙的优越性。
Studied a new type of involute beveloid gear which was formed base on the movement of base circle.It has essential differences with the traditional involute beveloid gear in establishment principle.According to the basic principles of gear,when a gear with modification coefficient ,the tooth addendum, tooth dedendum, tooth thickness and space width of the gear will change.If it have a cluster of regular modification coefficients along the axialdirection of the gear,the thickness of tooth will change with regular,this constitute the traditional involute beveloid gear.However, with the changing of tooth thickness,the tooth addendum and tooth dedendum will change,then it lead to the tip diameter of involute beveloid gear will be stepup from the small end face to big end face,then the involute beveloid gear will be a conicity. So,it will have interference when regulating the backlash.But this new type of involute beveloid gear which was formed base on the movement of base circle could solve this problem.The basic establishment principle of this new type involute beveloid gear is that the base circle move ragularly along the axialdirection of the gear.So,the line formed by centers of base circles is misalign with axialdirection of the gear.Then the tooth thickness of involute beveloid gear is gradually getting thickening or thinning from the middle head face to another side.Because there is no modification coefficient, the tooth addendum and tooth dedendum will be same,then it will have interference when regulating the backlash,it could regulate the gap complete.
The researchs in this paper are shown in the following:
①Studied the establishment principle and characteristic of this new type involute beveloid gear,compared with the traditional involute beveloid gear,this reflect the advantage of the involute beveloid gear formed base on the movement of base circle. According to the basic principles of gear,studied the methods to manufacture this new type involute beveloid gear.
②According to the processing method by using the cutter of basic rack and the space Meshing Engagement Principles, the tooth surface equations of this new involute beveloid gear were derived by the cutter’s for the fist time.The complete and precise tooth surface of this new involute beveloid gear was generated by using Matlab.The precise solid model of this involute beveloid gear was estaldished in Pro/E by three-dimensional coordinates of points on the generated tooth surfaces.
③According to the tooth surface equations of this new involute beveloid gear and the principles of TCA,established the mathematical model of this new gear pair. Using Matlab decribe the contact points and lines of contact on the tooth surface,it achieved visualization of the contact analysis.
④Using ADAMS establish the dynamic model of this new gear pair.And then doing the dynamic emulation and analysis, acquired the curve about the force of engagement. Contrast with the force of engagement about standard spur gear which has backlash. This demonstrate the adjusting of this new type involute beveloid gear could effectively improve the meshing characteristic of spur gear.
本文的研究内容如下:
①研究了移动基圆变齿厚齿轮的成型原理、几何特点,将其与传统的变齿厚齿轮相比较,体现了移动基圆变齿厚齿轮的优点;根据齿轮的基本原理,提出移动基圆变齿厚直齿轮的插齿、滚齿加工方法以及用标准齿条刀具的加工方法。
②结合齿条刀具加工移动基圆变齿厚直齿轮的加工方法,根据齿轮啮合原理,由齿条刀具的齿面方程推导出移动基圆变齿厚直齿轮的齿面方程;并利用Matlab编程对移动基圆变齿厚直齿轮的齿面进行仿真,将得到的各点的坐标值导入Pro/E中,建立其精确的三维模型。
③利用前面推导出的齿面方程,根据齿面接触分析的基本原理,建立移动基圆变齿厚直齿轮传动副接触的数学模型,用Matlab编程对其求解,得到其齿面上的接触点和接触迹线,实现了接触分析的可视化。
④利用Adams软件,建立了该齿轮传动的动力学模型,对其进行动力学仿真分析,得到了其啮合力曲线,并将其与标准直齿轮传动产生齿侧间隙后的啮合力曲线相比较,体现了调隙的优越性。
Studied a new type of involute beveloid gear which was formed base on the movement of base circle.It has essential differences with the traditional involute beveloid gear in establishment principle.According to the basic principles of gear,when a gear with modification coefficient ,the tooth addendum, tooth dedendum, tooth thickness and space width of the gear will change.If it have a cluster of regular modification coefficients along the axialdirection of the gear,the thickness of tooth will change with regular,this constitute the traditional involute beveloid gear.However, with the changing of tooth thickness,the tooth addendum and tooth dedendum will change,then it lead to the tip diameter of involute beveloid gear will be stepup from the small end face to big end face,then the involute beveloid gear will be a conicity. So,it will have interference when regulating the backlash.But this new type of involute beveloid gear which was formed base on the movement of base circle could solve this problem.The basic establishment principle of this new type involute beveloid gear is that the base circle move ragularly along the axialdirection of the gear.So,the line formed by centers of base circles is misalign with axialdirection of the gear.Then the tooth thickness of involute beveloid gear is gradually getting thickening or thinning from the middle head face to another side.Because there is no modification coefficient, the tooth addendum and tooth dedendum will be same,then it will have interference when regulating the backlash,it could regulate the gap complete.
The researchs in this paper are shown in the following:
①Studied the establishment principle and characteristic of this new type involute beveloid gear,compared with the traditional involute beveloid gear,this reflect the advantage of the involute beveloid gear formed base on the movement of base circle. According to the basic principles of gear,studied the methods to manufacture this new type involute beveloid gear.
②According to the processing method by using the cutter of basic rack and the space Meshing Engagement Principles, the tooth surface equations of this new involute beveloid gear were derived by the cutter’s for the fist time.The complete and precise tooth surface of this new involute beveloid gear was generated by using Matlab.The precise solid model of this involute beveloid gear was estaldished in Pro/E by three-dimensional coordinates of points on the generated tooth surfaces.
③According to the tooth surface equations of this new involute beveloid gear and the principles of TCA,established the mathematical model of this new gear pair. Using Matlab decribe the contact points and lines of contact on the tooth surface,it achieved visualization of the contact analysis.
④Using ADAMS establish the dynamic model of this new gear pair.And then doing the dynamic emulation and analysis, acquired the curve about the force of engagement. Contrast with the force of engagement about standard spur gear which has backlash. This demonstrate the adjusting of this new type involute beveloid gear could effectively improve the meshing characteristic of spur gear.
引文
[1]濮良贵,纪名刚.机械设计(第七版)[M].北京:高等教育出版社,2001.
[2]萨本佶.高速齿轮传动设计[M].北京:机械工业出版社,1986.
[3]仙波正莊著,张范孚译.齿轮变位[M].上海:上海科学技术出版社,1984.
[4]沈一春.相交轴变厚齿轮计算机辅助设计及动态仿真[D].哈尔滨工业大学硕士学位论文,2002.
[5]刘宇.实现线接触的相交轴变厚齿轮的研究[D].哈尔滨工业大学硕士学位论文,2000.
[6]温建民.非渐开线空间变厚齿轮传动的研究[D].哈尔滨工业大学博士学位论文,2004.
[7]袁哲俊等.齿轮刀具设计上册[M].北京:新时代出版社,1983.
[8] J.W.Satherland,E.J.Sakusbury and F.W.Hoge. A model for the cutting force system in the gear breaching process. Machine Tool & Manufacture. 1997,37(9):1409-1411
[9] Beam A S, Beveloid Gearing Machine Design[J]. Machine Design, 1954, 12:220-238.
[10] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob( part1:Theoretical Analysis of Table Sliding Taper Hobbing)[J]. Transactions of the ASME, 1981, 103:446-451.
[11] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob. (Part2:Hobbing of Conical Involute gear)[J]. Transactions of the ASME, 1981, 103:542-455.
[12] Mitome K. Conical Involute Gear (Part 1. Design and production System) [J]. Bulletin of the JSME, 1983, 26(212):299-305.
[13] Mitome K. Conical Involute Gear (Part 2. Design and production System of Involute Pinion-type Involute Pinion-type Cutter) [J]. Bulletin of the JSME, 1983, 26(212):306-312.
[14] Mitome K. Conical Involute Gear (Part 3. Tooth Action of a Pair of Gear) [J].Bulletin of the JSME, 1985, 28(245):2757-2764.
[15] Mitome K. Development of over-ball Measurement of Straight Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(536):255-260.
[16] K. Mitome. Development of over-ball Measurement of Helical Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(538):348-353.
[17] Mitome K. Design of miter Conical Involute Gears Based on tooth Bearing[J]. JSME International journal, series C, 1995, 38(2):307-311.
[18] Mitome K. Yamazaki, T. Design of Conical Involute Gear Engaged with Profile Spur Gear on Intersecting Shafts[J]. Transactions of the Hapan Society of Mechanical Engineers, Part C, 1996, 62(598):2436-2441. (In Japanese)
[1]濮良贵,纪名刚.机械设计(第七版)[M].北京:高等教育出版社,2001.
[2]萨本佶.高速齿轮传动设计[M].北京:机械工业出版社,1986.
[3]仙波正莊著,张范孚译.齿轮变位[M].上海:上海科学技术出版社,1984.
[4]沈一春.相交轴变厚齿轮计算机辅助设计及动态仿真[D].哈尔滨工业大学硕士学位论文,2002.
[5]刘宇.实现线接触的相交轴变厚齿轮的研究[D].哈尔滨工业大学硕士学位论文,2000.
[6]温建民.非渐开线空间变厚齿轮传动的研究[D].哈尔滨工业大学博士学位论文,2004.
[7]袁哲俊等.齿轮刀具设计上册[M].北京:新时代出版社,1983.
[8] J.W.Satherland,E.J.Sakusbury and F.W.Hoge. A model for the cutting force system in the gear breaching process. Machine Tool & Manufacture. 1997,37(9):1409-1411
[9] Beam A S, Beveloid Gearing Machine Design[J]. Machine Design, 1954, 12:220-238.
[10] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob( part1:Theoretical Analysis of Table Sliding Taper Hobbing)[J]. Transactions of the ASME, 1981, 103:446-451.
[11] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob. (Part2:Hobbing of Conical Involute gear)[J]. Transactions of the ASME, 1981, 103:542-455.
[12] Mitome K. Conical Involute Gear (Part 1. Design and production System) [J]. Bulletin of the JSME, 1983, 26(212):299-305.
[13] Mitome K. Conical Involute Gear (Part 2. Design and production System of Involute Pinion-type Involute Pinion-type Cutter) [J]. Bulletin of the JSME, 1983, 26(212):306-312.
[14] Mitome K. Conical Involute Gear (Part 3. Tooth Action of a Pair of Gear) [J].Bulletin of the JSME, 1985, 28(245):2757-2764.
[15] Mitome K. Development of over-ball Measurement of Straight Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(536):255-260.
[16] K. Mitome. Development of over-ball Measurement of Helical Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(538):348-353.
[17] Mitome K. Design of miter Conical Involute Gears Based on tooth Bearing[J]. JSME International journal, series C, 1995, 38(2):307-311.
[18] Mitome K. Yamazaki, T. Design of Conical Involute Gear Engaged with Profile Spur Gear on Intersecting Shafts[J]. Transactions of the Hapan Society of Mechanical Engineers, Part C, 1996, 62(598):2436-2441. (In Japanese)
[41]魏沛堂.平行轴变齿厚斜齿轮传动齿面生成与啮合特性分析[D].重庆大学硕士学位论文,2010.
[42]陈小安,陈昶.可调侧隙变厚齿轮传动副[P].中国,ZL2006 1 0054346.5,2009-10-30
[43]李昌,韩兴等.基于Pro/E何ADAMS的齿轮啮合精确动力学仿真[J].机械与电子,2008(1):55-58.
[44]李三群,贾长治,武彩岗等.基于虚拟样机技术的齿轮啮合动力学仿真研究[J].系统仿真学报,2007,19(4):901-904.
[45]冯婧,霍睿,王孚懋.齿轮非线性动力学系统的振动功率流分析[J].振动与冲击,2010,29(5):203-206.
[46]王小群,孙萍,李威.非对称渐开线圆柱齿轮建模与扭转振动仿真[J].北京科技大学学报,2007,29(12):1264-1267.
[47]杨振,王三民,刘海霞等.负载与支承刚度对面齿轮传动系统动态特性的影响分析[J].燕山大学学报,2010,34(4):293-300.
[48]李华敏,李瑰贤等.齿轮机构设计与应用[M].北京:机械工业出版社,2007,294-308.
[49] Dooner DB. On the invariance of gear tooth curvature[J]. Mechanical Engineering Science,2006,208:1083-1096.
[50] Bunch.Jr, Earnest B. Gear with inset O-ring for setting backlash[P]. America, US5400672, 1995.3.
[51]申永胜.机械原理教程[M].北京:清华大学出版社,1999,160-164.
[52] Mitome K. Conical involute gear (part 2 :Design and production system of involute pinion - type cutter) [J]. Bulletin of the JSME ,1983 ,26 (212) :306 - 312.
[53]吴序堂.齿轮啮合原理[M].西安:西安交通大学出版社,1982.
[54]陈文华,贺青川等. ADAMS2007机构设计与分析范例[M].北京:机械工业出版社,2009.
[55]李增刚. ADAMS入门详解与实例[M].北京:国防工业出版社,2008,91-92 .
[56]吴宗泽.机械设计实用手册[M].北京:化学工业出版社,1999.
[2]萨本佶.高速齿轮传动设计[M].北京:机械工业出版社,1986.
[3]仙波正莊著,张范孚译.齿轮变位[M].上海:上海科学技术出版社,1984.
[4]沈一春.相交轴变厚齿轮计算机辅助设计及动态仿真[D].哈尔滨工业大学硕士学位论文,2002.
[5]刘宇.实现线接触的相交轴变厚齿轮的研究[D].哈尔滨工业大学硕士学位论文,2000.
[6]温建民.非渐开线空间变厚齿轮传动的研究[D].哈尔滨工业大学博士学位论文,2004.
[7]袁哲俊等.齿轮刀具设计上册[M].北京:新时代出版社,1983.
[8] J.W.Satherland,E.J.Sakusbury and F.W.Hoge. A model for the cutting force system in the gear breaching process. Machine Tool & Manufacture. 1997,37(9):1409-1411
[9] Beam A S, Beveloid Gearing Machine Design[J]. Machine Design, 1954, 12:220-238.
[10] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob( part1:Theoretical Analysis of Table Sliding Taper Hobbing)[J]. Transactions of the ASME, 1981, 103:446-451.
[11] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob. (Part2:Hobbing of Conical Involute gear)[J]. Transactions of the ASME, 1981, 103:542-455.
[12] Mitome K. Conical Involute Gear (Part 1. Design and production System) [J]. Bulletin of the JSME, 1983, 26(212):299-305.
[13] Mitome K. Conical Involute Gear (Part 2. Design and production System of Involute Pinion-type Involute Pinion-type Cutter) [J]. Bulletin of the JSME, 1983, 26(212):306-312.
[14] Mitome K. Conical Involute Gear (Part 3. Tooth Action of a Pair of Gear) [J].Bulletin of the JSME, 1985, 28(245):2757-2764.
[15] Mitome K. Development of over-ball Measurement of Straight Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(536):255-260.
[16] K. Mitome. Development of over-ball Measurement of Helical Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(538):348-353.
[17] Mitome K. Design of miter Conical Involute Gears Based on tooth Bearing[J]. JSME International journal, series C, 1995, 38(2):307-311.
[18] Mitome K. Yamazaki, T. Design of Conical Involute Gear Engaged with Profile Spur Gear on Intersecting Shafts[J]. Transactions of the Hapan Society of Mechanical Engineers, Part C, 1996, 62(598):2436-2441. (In Japanese)
[1]濮良贵,纪名刚.机械设计(第七版)[M].北京:高等教育出版社,2001.
[2]萨本佶.高速齿轮传动设计[M].北京:机械工业出版社,1986.
[3]仙波正莊著,张范孚译.齿轮变位[M].上海:上海科学技术出版社,1984.
[4]沈一春.相交轴变厚齿轮计算机辅助设计及动态仿真[D].哈尔滨工业大学硕士学位论文,2002.
[5]刘宇.实现线接触的相交轴变厚齿轮的研究[D].哈尔滨工业大学硕士学位论文,2000.
[6]温建民.非渐开线空间变厚齿轮传动的研究[D].哈尔滨工业大学博士学位论文,2004.
[7]袁哲俊等.齿轮刀具设计上册[M].北京:新时代出版社,1983.
[8] J.W.Satherland,E.J.Sakusbury and F.W.Hoge. A model for the cutting force system in the gear breaching process. Machine Tool & Manufacture. 1997,37(9):1409-1411
[9] Beam A S, Beveloid Gearing Machine Design[J]. Machine Design, 1954, 12:220-238.
[10] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob( part1:Theoretical Analysis of Table Sliding Taper Hobbing)[J]. Transactions of the ASME, 1981, 103:446-451.
[11] Mitome K. Table Sliding Taper Hobbing of Conical Gear Using Cylindrical Hob. (Part2:Hobbing of Conical Involute gear)[J]. Transactions of the ASME, 1981, 103:542-455.
[12] Mitome K. Conical Involute Gear (Part 1. Design and production System) [J]. Bulletin of the JSME, 1983, 26(212):299-305.
[13] Mitome K. Conical Involute Gear (Part 2. Design and production System of Involute Pinion-type Involute Pinion-type Cutter) [J]. Bulletin of the JSME, 1983, 26(212):306-312.
[14] Mitome K. Conical Involute Gear (Part 3. Tooth Action of a Pair of Gear) [J].Bulletin of the JSME, 1985, 28(245):2757-2764.
[15] Mitome K. Development of over-ball Measurement of Straight Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(536):255-260.
[16] K. Mitome. Development of over-ball Measurement of Helical Conical Involute Gear[J].日本机械学会论文集(C编), 1991, 57(538):348-353.
[17] Mitome K. Design of miter Conical Involute Gears Based on tooth Bearing[J]. JSME International journal, series C, 1995, 38(2):307-311.
[18] Mitome K. Yamazaki, T. Design of Conical Involute Gear Engaged with Profile Spur Gear on Intersecting Shafts[J]. Transactions of the Hapan Society of Mechanical Engineers, Part C, 1996, 62(598):2436-2441. (In Japanese)
[41]魏沛堂.平行轴变齿厚斜齿轮传动齿面生成与啮合特性分析[D].重庆大学硕士学位论文,2010.
[42]陈小安,陈昶.可调侧隙变厚齿轮传动副[P].中国,ZL2006 1 0054346.5,2009-10-30
[43]李昌,韩兴等.基于Pro/E何ADAMS的齿轮啮合精确动力学仿真[J].机械与电子,2008(1):55-58.
[44]李三群,贾长治,武彩岗等.基于虚拟样机技术的齿轮啮合动力学仿真研究[J].系统仿真学报,2007,19(4):901-904.
[45]冯婧,霍睿,王孚懋.齿轮非线性动力学系统的振动功率流分析[J].振动与冲击,2010,29(5):203-206.
[46]王小群,孙萍,李威.非对称渐开线圆柱齿轮建模与扭转振动仿真[J].北京科技大学学报,2007,29(12):1264-1267.
[47]杨振,王三民,刘海霞等.负载与支承刚度对面齿轮传动系统动态特性的影响分析[J].燕山大学学报,2010,34(4):293-300.
[48]李华敏,李瑰贤等.齿轮机构设计与应用[M].北京:机械工业出版社,2007,294-308.
[49] Dooner DB. On the invariance of gear tooth curvature[J]. Mechanical Engineering Science,2006,208:1083-1096.
[50] Bunch.Jr, Earnest B. Gear with inset O-ring for setting backlash[P]. America, US5400672, 1995.3.
[51]申永胜.机械原理教程[M].北京:清华大学出版社,1999,160-164.
[52] Mitome K. Conical involute gear (part 2 :Design and production system of involute pinion - type cutter) [J]. Bulletin of the JSME ,1983 ,26 (212) :306 - 312.
[53]吴序堂.齿轮啮合原理[M].西安:西安交通大学出版社,1982.
[54]陈文华,贺青川等. ADAMS2007机构设计与分析范例[M].北京:机械工业出版社,2009.
[55]李增刚. ADAMS入门详解与实例[M].北京:国防工业出版社,2008,91-92 .
[56]吴宗泽.机械设计实用手册[M].北京:化学工业出版社,1999.