﻿ 基于SolidWorks的一阶椭圆齿轮参数化建模研究
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 北京化工大学学报(自然科学版)  2017, Vol. 44 Issue (6): 95-100  DOI: 10.13543/j.bhxbzr.2017.06.015 0

### 引用本文

LIN JianBang, ZHAO Fu, DENG Kun. First-order elliptic gear parametric modeling based on solidworks[J]. Journal of Beijing University of Chemical Technology (Natural Science), 2017, 44(6): 95-100. DOI: 10.13543/j.bhxbzr.2017.06.015.

### 文章历史

First-order elliptic gear parametric modeling based on SolidWorks
LIN JianBang , ZHAO Fu , DENG Kun
School of Materials Science and Mechanical Engineering, Beijing Technology and Business University, Beijing 100048, China
Abstract: In view of the problems of complexity and low efficiency when designing elliptic gears, the parametric design and automatic modeling of elliptic gears have been studied. A mathematical model was established based on the basic theory of elliptic gear pitch curves and tooth profiles. On the basis of theoretical analysis, MATLAB programming language was used to solve the elliptic gear's pitch curve, tooth profile curve and tooth shape. Taking a first-order elliptic gear as an example, SolidWorks macros were used for parametric design, and a VBA interface was used to design an interface. Users thus only need to input parameters to the designed interface of the input box, and SolidWorks will then automatically generate an oval gear.
Key words: elliptic gear    MATLAB    parametric modeling    SolidWorks    secondary development

1 椭圆齿轮参数化设计数学条件 1.1 椭圆齿轮节曲线设计

 ${r_1}\left( 0 \right) = {r_1}\left( {2{\rm{ \mathsf{ π} }}} \right) = {r_1}\left( {2n{\rm{ \mathsf{ π} }}} \right)$ (1)

 $\frac{{2{\rm{ \mathsf{ π} }}}}{{{n_2}}} = \int_0^{\frac{{2{\rm{ \mathsf{ π} }}}}{{{n_1}}}} {\frac{1}{{f\left( {{\varphi _1}} \right)}}{\rm{d}}{\varphi _1}} = \int_0^{\frac{{2{\rm{ \mathsf{ π} }}}}{{{n_1}}}} {\frac{{{r_1}\left( {{\varphi _1}} \right)}}{{a - {r_1}\left( {{\varphi _1}} \right)}}{\rm{d}}{\varphi _1}}$ (2)
1.2 压力角校验

 $\tan {\mu _1} = \frac{{{r_1}}}{{{\rm{d}}{r_1}/{\rm{d}}{\varphi _1}}} = \frac{{1 - k}}{{k\sin \varphi }}$ (3)

P点为接触点，α0是工具齿条的齿形角(一般取20°)，α12P点的压力角。如果齿轮按顺时针方向回转，工作面是齿轮的右侧面，如图 1(a)所示，可以求出齿廓右侧的压力角α12

 ${\alpha _{12}} = {\mu _1} + {\alpha _0} - \frac{{\rm{ \mathsf{ π} }}}{2}$ (4)
 图 1 非圆齿轮传动压力角 Fig.1 Pressure angle of transmission with non-circular gears

 ${\alpha _{12}} = - {\mu _1} + {\alpha _0} - \frac{{\rm{ \mathsf{ π} }}}{2}$ (5)

2 基于MATLAB的椭圆轮齿计算 2.1 计算节曲线

 图 2 椭圆齿轮的节曲线 Fig.2 Pitch curve of elliptic gear

 ${r_1} = \frac{{A\left( {1 - k_1^2} \right)}}{{1 + {k_1}\cos {\varphi _1}}}$ (6)

 $L = 4A\int_0^{\frac{{\rm{ \mathsf{ π} }}}{2}} {\sqrt {1 - k_1^2{{\sin }^2}\varphi } {\rm{d}}\varphi }$ (7)

 $L = pz = {\rm{ \mathsf{ π} }}mz$ (8)

 图 3 主从动轮节曲线图 Fig.3 Pitch curves of driving gear and driven gear
 图 4 传动比函数的变化曲线 Fig.4 Transmission ratio function curve

2.2 轮齿位置的确定

 图 5 椭圆齿轮轮齿在节曲线的位置 Fig.5 Position of the elliptic gear tooth in the pitch curve

 图 6 MATLAB程序设计过程 Fig.6 MATLAB programming process
2.3 齿顶和齿根设计

 图 7 非圆齿轮的齿顶和齿根曲线图 Fig.7 Curves of addendum and tooth root of the noncircular gear
2.4 解析法求解椭圆齿轮齿廓

 图 8 单齿齿形图 Fig.8 Single tooth profile

 $\left\{ \begin{array}{l} {x_R} = r\cos \theta - S\cos {\alpha _n}\cos \left( {\theta + \tau + {\alpha _n}} \right)\\ {y_R} = r\sin \theta - S\cos {\alpha _n}\sin \left( {\theta + \tau + {\alpha _n}} \right) \end{array} \right.$ (9)
 图 9 齿廓计算图 Fig.9 Tooth profile calculation chart

 $S = \int_0^\theta {\sqrt {{r^2} + {{\left( {\frac{{{\rm{d}}r}}{{{\rm{d}}\theta }}} \right)}^2}} {\rm{d}}\theta }$ (10)

 $\left\{ \begin{array}{l} {r_R} = \sqrt {x_R^2 + y_R^2} \\ {\theta _R} = \arctan \frac{{{y_R}}}{{{x_R}}} \end{array} \right.$ (11)

 $\left\{ \begin{array}{l} {R_{\rm{a}}} = \sqrt {{r^2} + h_{\rm{a}}^2 + 2r{h_{\rm{a}}}\sin \tau } \\ {\theta _{\rm{a}}} = \theta - \arcsin \left( {\frac{{{h_{\rm{a}}}\cos \tau }}{{{R_{\rm{a}}}}}} \right)\\ \tau = \arctan \left( {r{\rm{d}}\theta /{\rm{d}}r} \right) \end{array} \right.$ (12)

 图 10 椭圆齿轮齿廓曲线齿形图 Fig.10 Tooth profile curve and tooth shape of the elliptic gear
3 椭圆齿轮参数化设计及自动建模 3.1 参数化设计

 图 11 参数化设计流程 Fig.11 Parametric design process
3.2 在SolidWorks中自动建模

SolidWorks的宏录制功能为用户提供了一种开发途径，本文在完成椭圆齿轮的设计之后，基于宏录制功能实现椭圆齿轮的自动参数化建模。

3.2.1 宏录制修改

 图 12 椭圆齿轮三维模型 Fig.12 Three dimensional model of the elliptic gear
3.2.2 窗体设计

3.2.3 应用程序嵌入SolidWorks

SolidWorks API中的每一个对象都有自己的属性、方法和事件，它们已经包括了SolidWorks所有的数据模型，用户可以根据自己的需求对对象属性进行设置以及对对象方法进行调用，使得开发的系统满足自己所需的特定功能。直接在SolidWorks工具栏中选择运行程序，根据界面里提示输入参数，实现自动建模。新建的DLL文件不能保存为中文名。

3.3 自动建模实例

 图 13 椭圆齿轮 Fig.13 Illustration of the elliptic gear
4 结束语

 [1] 梅丽文, 肖海兵, 赵家黎, 等. 基于Pro/E齿轮参数化设计及数控加工的研究[J]. 科学技术与工程, 2009, 9(19): 5656-5659. Mei L W, Xiao H B, Zhao J L, et al. Parameters of gear design and NC machining research based on Pro/E[J]. Science Technology and Engineering, 2009, 9(19): 5656-5659. DOI:10.3969/j.issn.1671-1815.2009.19.006 (in Chinese) [2] 贾松, 胡青春. 基于CAXA的非圆齿轮的三维造型与设计[J]. 机械传动, 2005, 29(1): 30-32/74. Jia S, Hu Q C, Three-dimensional modeling and design of noncircular gears based on CAXA[J]. Journal of Mechnaical Transmission, 2005, 29(1): 30-32/74. (in Chinese) [3] 高学强, 葛敬侠. SolidWorks中的非圆齿轮实体建模方法研究[J]. 工程图学学报, 2009, 30(4): 189-192. Gao X Q, Ge J X, Study on parametric solid modeling of non-circular gear in SolidWorks[J]. Journal of Engineering Graphics, 2009, 30(4): 189-192. (in Chinese) [4] 王淑杰. 非圆齿轮传动的快速优化设计[D]. 合肥: 合肥工业大学, 2005. Wang S J. Rapid optimal design of non-circular gear-drive[D]. Hefei:Hefei University of Technology, 2005. (in Chinese) [5] 卢杰, 米彩盈. 基于SolidWorks的联合参数化设计方法研究[J]. 图学学报, 2013, 34(6): 64-68. Lu J, Mi C Y, A new combined parametric design method based on SolidWorks[J]. Journal of Graphics, 2013, 34(6): 64-68. (in Chinese) [6] 范素香, 齐新华, 侯书林. 基于MATLAB及UG的偏心共轭非圆齿轮的设计[J]. 机械传动, 2011, 35(9): 70-72/76. Fan S X, Qi X H, Hou S L, Design of eccentric conjugated noncircular gear based on MATLAB and UG[J]. Journal of Mechanical Transmission, 2011, 35(9): 70-72/76. (in Chinese) [7] 胡赤兵, 苑明杰, 刘浩, 等. 基于MATLAB的椭圆类齿轮参数化设计[J]. 兰州理工大学学报, 2014, 40(2): 41-45. Hu C B, Yuan M J, Liu H, et al. Parametrization design of elliptic gears based on MATLAB[J]. Journal of Lanzhou University of Technology, 2014, 40(2): 41-45. (in Chinese) [8] 吴俊峰, 吕小波, 李传, 等. 非圆齿轮的三维设计与运动分析[J]. 湖北工业大学学报, 2014, 29(4): 69-72. Wu J F, Lv X B, Li C, et al. Solid modeling and simulation analysis of non-circular gear based on Solidworks and Maple[J]. Journal of Hubei University of Technology, 2014, 29(4): 69-72. (in Chinese) [9] 田芳勇, 姜衍仓, 胡赤兵, 等. 椭圆齿轮参数化设计与运动仿真系统的开发[J]. 兰州理工大学学报, 2011, 37(2): 30-33. Tian F Y, Jiang Y C, Hu C B, et al. Development of system of parametric design and motion simulation of elliptical gears[J]. Journal of Lanzhou University of Technology, 2011, 37(2): 30-33. (in Chinese) [10] Bair B W, Computer aided design of elliptical gears with circular-arcteeth[J]. Mechanism and Machine Theory, 2004, 39(2): 153-168. DOI:10.1016/S0094-114X(03)00111-3 (in Chinese) [11] Figliolini G, Angeles J. Geometric modeling of elliptical gears generated by shaper cutters[C]//Proceedings of the ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference. Montreal, Canada, 2002:661-670. [12] 张健, 于膑, 税静, 等. 基于MATLAB的非圆齿轮节曲线设计[J]. 机械与电子, 2016, 34(4): 17-20. Zhang J, Yu B, Shui J, et al. Design of the pitch curves of non-circular gears based on MATLAB[J]. Machinery & Electronics, 2016, 34(4): 17-20. (in Chinese)