Open Access
 Issue JNWPU Volume 38, Number 4, August 2020 897 - 903 https://doi.org/10.1051/jnwpu/20203840897 06 October 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 齿条产形与ease-off曲面构建

### 2 圆柱齿轮的齿条产成多项式曲面方程

(1) 式完整表达式为15项, 取其中的7项, 作为齿条拓扑面(u为纵向，v为齿廓方向), 则可以构建一个双峰抛物面

 图1齿条面坐标系
 图2齿面产成坐标系

### 3 差曲面ease-off的构建方法

 图3ease-off曲面映射关系
 图4差齿面ease-off

## 4 差齿面ease-off啮合仿真信息解析

### 5 等差线与修形梯度

(7) 式表示的为图4中的网格节点, 把其拟合为(1)式所示的二元四次多项式

 图5ease-off修形梯度图

### 6 差曲线与差程线

1) 差曲线瀑布图

2) 差程线与传动误差

(10) 式中抛物线的最低点代表了齿面啮合过程中的一个瞬时接触点, 一系列瞬时接触点构成了ease-off曲面上一条曲线——差程线

3) 瞬时接触椭圆参数

 图6差曲线瀑布图
 图7二阶抛物线传动误差
 图8瞬时接触椭圆参数

## 9 扭转抛物面拓扑

 图9对角修形ease-off
 图10对角修形传动误差

## 10 四阶抛物面拓扑

ease-off曲面结构如图11所示, 修形后齿面中部差曲率比二阶小, 靠近齿面边界陡峭, 类似于在抛物线修形基础上附加了修缘。接触区扩展呈长方形, 外部修形梯度急剧扩大。传动误差(见图12)呈平顶形状。四阶抛物线修形对于保持齿面接触刚度、低传动误差与低误差敏感性有利[17-18]。

 图11四阶抛物面ease-off
 图12四阶平顶传动误差

## 11 四阶双峰抛物面拓扑

 图13四阶双峰ease-off曲面
 图14双峰传动误差

## 12 考虑错位量的ease-off曲面分析

 图15轴线错位下ease-off曲面

## References

1. LITVIN F L, FUENTES A. Gear Geometry and Applied Theory[M]. New York: Cambridge University Press, 2004 [Google Scholar]
2. LITVIN F L. Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-Milled Formate Generated Spiral Bevel Gears[J]. Mechanism and Machine Theory, 2002, 37 (5): 441– 459 [Article] [CrossRef] [Google Scholar]
3. FANG Zongde, LIU Tao, DENG Xiaozhong. Tooth Contact Analysis of Spiral Bevel Gears Based on the Design of Transmission Error[J]. Acta Aeronautica et Astronautica Sinica, 2002, 23 (3): 226– 230 [Article] (in Chinese) [Google Scholar]
4. CAO Xuemei, ZHANG Hua, FANG Zongde. Design and Analysis of Laoded Transmission Errors for Aviation Spiral Bevel Gears[J]. Journal of Aerospace Power, 2009, 24 (11): 2618– 2624 [Article] (in Chinese) [Google Scholar]
5. 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 [Article] (in Chinese) [Google Scholar]
6. TANG Jinyuan, Lu Yanfeng, ZHOU Chao. Research on Improved Tooth Contact Analysis Algorithm of Spiral Bevel Gears[J]. Journal of Aerospace Power, 2009, 24 (1): 189– 195 [Article] (in Chinese) [Google Scholar]
7. 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 [Article] (in Chinese) [Google Scholar]
8. HERMANN J S. What "Ease-off" Shows about Bevel and Hypoid Gears[J]. Gear Technology, 2001, (9/10): 18– 23 [Article] [Google Scholar]
9. CHEN Shuhan, YAN Hongzhi, MING Xingzu, et al. Difference Surface Model Establishment and Simulation in Spiral Bevel Gear[J]. Journal of System Simulation, 2009, 21 (11): 3430– 3433 [Article] (in Chinese) [Google Scholar]
10. 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[J]. Journal of Aerospace Power, 2015, 30 (1): 195– 200 [Article] (in Chinese) [Google Scholar]
11. CAO Xuemei, SUN Ning, DENG Xiaozhong. Design for Straight Bevel Gear Based on Low Installation Error Sensitivity and Experiment Tests[J]. Journal of Aerospace Power, 2016, 31 (1): 227– 232 [Article] (in Chinese) [Google Scholar]
12. WEI Bingyang, DENG Xiaozhong, TONG Angxin, et al. Surface Synthesis Method on Generating Parameters Computation of Spiral Bevel-Gears[J]. Journal of Mechanical Engineering, 2016, 52 (1): 20– 25 [Article] (in Chinese) [Google Scholar]
13. WEI Bingyang, YANG Jianjun, TONG Angxin. Tooth Meshing Simulation and Analysis Based on Isometric Mapping Ease-Off Surface[J]. Journal of Aerospace Power, 2017, 32 (5): 1259– 1265 [Article] (in Chinese) [Google Scholar]
14. JIANG Jinke, FANG Zongde, SU Jinzhan. Design and Grinding for Modified Helical Gears with a Higher-Order Transmission Error[J]. Journal of Harbin Institute of Technology, 2014, 46 (9): 43– 49 [Article] (in Chinese) [Google Scholar]
15. ZHANG Yu, Yan Hongzhi, Zeng Tao, et al. Influence Regularity of Helical Movement and Cutter Parameters on the Generated Tooth Surface Characteristic of Duplex Helical Method[J]. Journal of Mechanical Engineering, 2018, 54 (5): 53– 61 [Article] (in Chinese) [CrossRef] [Google Scholar]
16. JIANG Jinke, FANG Zongde, JIA Haitao. Research on Design and CNC Grinding Machine for Diagonal Modified Helical Gearxy1 Journal of Mechanical Engineering, 2014, 50 (19): 158– 165 [Article] (in Chinese) [CrossRef] [Google Scholar]
17. Stadtfeld H J. The Ultimate Motion Graph[J]. ASM E J of Mechanical Design, 2000, 122 (3): 317– 322 [CrossRef] [Google Scholar]
18. WEI Bingyang, FANG Zongde, ZHOU Yanwei, et al. On Improving Design of Spiral Bevel Gear with Higher-Order Transmission Error Curvexy1 Journal of Northwestern Polytechnical University, 2003, 21 (6): 757– 760 [Article] (in Chinese) [Google Scholar]

## All Figures

 图1齿条面坐标系 In the text
 图2齿面产成坐标系 In the text
 图3ease-off曲面映射关系 In the text
 图4差齿面ease-off In the text
 图5ease-off修形梯度图 In the text
 图6差曲线瀑布图 In the text
 图7二阶抛物线传动误差 In the text
 图8瞬时接触椭圆参数 In the text
 图9对角修形ease-off In the text
 图10对角修形传动误差 In the text
 图11四阶抛物面ease-off In the text
 图12四阶平顶传动误差 In the text
 图13四阶双峰ease-off曲面 In the text
 图14双峰传动误差 In the text
 图15轴线错位下ease-off曲面 In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.