Tooth contact includes two parts:tooth surface contact and edge contact. The conventional approach for tooth contact analysis needs to establish the different mathematical models for tooth surface contact and edge contact respectively. In addition, determination of each contact point entails the solution of a system of five nonlinear equations, which leads to instability of the algorithm. A new algorithm for tooth contact analysis is proposed-decomposition method. This new algorithm established the uniform mathematical model to analysis the tooth surface contact and edge contact, moreover, the number of solving nonlinear equations for searching contact point is reduced from 5 to 2. This novel algorithm of tooth contact analysis is simple, effective and could be used to various types of gear pairs. The effectiveness of this algorithm was demonstrated on a spiral bevel gear pair example. Contact pattern and transmission errors were calculated by the novel algorithm, Gleason software and the traditional algorithm respectively. Comparison in tooth surface contact analysis between the novel algorithm and the Gleason software shows that contact patterns are identical and the difference of the magnitude of transmission errors is about 0.29″. In comparing the novel algorithm with the traditional algorithm for edge contact analysis, there are relatively few differences for contact patterns. A pair of grinding spiral bevel gear were set on a gear meshing tester and the experimental tooth contact patterns verified the effectiveness of the proposed algorithm.
CAO Xuemei
,
YANG Bohui
,
DENG Xiaozhong
. Novel Decomposition Methodology for Tooth Contact Analysis and Experiment Tests[J]. Journal of Mechanical Engineering, 2018
, 54(5)
: 47
-52
.
DOI: 10.3901/JME.2018.05.047
[1] LITVIN F L. Local synthesis and tooth contact analysis of face-milled spiral bevel gears[R]. NASA,1991.
[2] 董学朱. 摆线齿锥齿轮及准双曲面齿轮设计和制造[M]. 北京:机械工业出版社,2003. DONG Xuezhu. Design and manufacturing of cycloid bevel gear and hypoid gear[M]. Beijing:China Machine Press,2003.
[3] FAN Q. Enhanced algorithms of contact simulation for hypoid gear drives produced by face-milling and face-hobbing processes[J]. ASME Journal of Mechanical Design,2007,129(1):31-37.
[4] FAN Q. Optimization of face cone element for spiral bevel and hypoid gears[J]. ASME Journal of Mechanical Design,2011,133(091002):1-7.
[5] SHEVELEVA G I,VOLKOV A E,MEDVEDEV V I. Algorithms for analysis of meshing and contact of spiral bevel gears[J]. Mechanism and Machine Theory,2007,42(2):198-215.
[6] 汪中厚,李刚,久保爱三. 基于数字化真实齿面的螺旋锥齿轮齿面接触分析[J]. 机械工程学报,2014,50(15):1-11 WANG Zhonghou,LI Gang,KUBO A. Tooth contact analysis of spiral bevel gears based on digital real tooth surfaces[J]. Journal of Mechanical Engineering,2014,50(15):1-11.
[7] KOLIVAND M,KAHRAMAN A. A load distribution model for hypoid gears using ease-off topography and shell theory[J]. Mechanism and Machine Theory,2009,44:1848-1865.
[8] KOLIVAND M,KAHRAMAN A. An ease-off based method for loaded tooth contact analysis of hypoid gears having local and global surface deviations[J]. ASME Journal of Mechanical Design,2010,132(6):071004-1-071004-8.
[9] 高建平,方宗德,杨宏斌. 螺旋锥齿轮边缘接触分析[J]. 航空动力学报,1998,13(3):289-292. GAO Jianping,FANG Zongde,YANG Hongbin. Analysis of edge contact for hypoid gear and spiral bevel gears[J]. Journal of Aerospace Power,1998,13(3):289-292.
[10] 方宗德,邓效忠,任东锋. 考虑边缘接触的弧齿锥齿轮承载接触分析[J]. 机械工程学报,2002,38(9):69-72. FANG Zongde,DENG Xiaozhong,REN Dongfeng. Loaded tooth contact analysis of spiral bevel gears considering edge contacts[J]. Chinese Journal of Mechanical Engineering,2002,38(9):69-72.
[11] 王延忠. 航空弧齿锥齿轮摩擦学设计和制造[M]. 北京:科学出版社,2014. WANG Yanzhong. Tribology design and manufacturing of aviation spiral bevel gears[M]. Beijing:Science Press,2014.
[12] 曹雪梅,邓效忠,聂少武. 基于共轭齿面修正的航空弧齿锥齿轮高阶传动误差齿面拓扑结构设计[J]. 航空动力学报,2015,30(1):195-200. CAO Xuemei,DENG Xiaozhong,NIE Shaowu. Ease-off flank topography design for aviation spiral bevel gears with higher-order transmission errors by modification of conjugate flank[J]. Journal of Aerospace Power,2015,30(1):195-200.
[13] 曹雪梅,邓效忠,耿龙龙. 弧齿锥齿轮齿面曲率干涉检验新方法与实验验证[J]. 航空动力学报,2015,30(2):491-497. CAO Xuemei,DENG Xiaozhong,GENG Longlong. An invariant approach for tooth surface curvature inference analysis of spiral bevel gears and experiment test[J]. Journal of Aerospace Power,2015,30(2):491-497.
[14] 曹雪梅,方宗德,张金良. 弧齿锥齿轮的齿面主动设计[J],机械工程学报,2007, 43(8):155-158. CAO Xuemei,FANG Zongde,ZHANG Jinliang. Function-oriented active tooth surface design of spiral bevel gears[J]. Chinese Journal of Mechanical Engineering,2007,43(8):155-158.
[15] 曹雪梅,方宗德,许浩. 弧齿锥齿轮的齿面主动设计及试验验证[J]. 机械工程学报,2008,44(7):209-214. CAO Xuemei,FANG Zongde,XU Hao. Function-oriented active tooth surface design of spiral bevel gears and experimental tests[J]. Chinese Journal of Mechanical Engineering,2008,44(7):209-214.
