中心距偏差对微线段齿轮系统的动力学特性影响研究

徐锐; 黄康; 张靖; 汪久根

doi:10.13433/j.cnki.1003-8728.20200223

中心距偏差对微线段齿轮系统的动力学特性影响研究

doi: 10.13433/j.cnki.1003-8728.20200223

徐锐^{1, 3, 4,},
黄康²,
张靖^3, ,,
汪久根⁴

1.
安徽工程大学机械工程学院，安徽芜湖　241000
2.
合肥工业大学机械工程学院，合肥　230009
3.
浙江双环传动机械股份有限公司，浙江玉环　317600
4.
浙江大学机械工程学院，杭州　310027

基金项目: 国家自然科学基金项目（51775156）、安徽工程大学引进人才科研启动基金项目（2019YQQ005）、安徽高校协同创新项目（GXXT-2019-048）及安徽工程大学校级科研项目（Xjky2020008）

详细信息

作者简介:
徐锐（1985−），讲师，博士，研究方向为机械传动与齿轮动力学，xuruixr2006@163.com

通讯作者:
张靖，正高级工程师，博士，tony.zhang@foxmail.com

中图分类号: TH113
计量
- 文章访问数: 212
- HTML全文浏览量: 35
- PDF下载量: 6
- 被引次数: 0
出版历程
- 收稿日期: 2020-01-11
- 刊出日期: 2021-10-18

Influence of Center Distance Deviation on Dynamic Characteristics of Micro-segment Gear System

XU Rui^{1, 3, 4
,},
HUANG Kang²,
ZHANG Jin^{3
, ,},
WANG Jiugeng⁴

1.
School of Mechanical Engineering, Anhui Polytechnic University, Wuhu 241000, Anhui , China
2.
School of Mechanical Engineering, Hefei University of Technology, Hefei 230009, China
3.
Zhejiang Shuanghuan Driveline Co., Ltd., Yuhuan 317600, Zhejiang, China
4.
School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China

摘要

摘要: 为了提高微线段齿轮的应用性，从中心距偏差的角度对微线段齿轮的动力学特性进行了研究。依据微线段齿轮齿廓构型原理，基于齿轮啮合关系推导了其齿廓数学模型；采用离散化TCA（齿面接触分析）方法计算了微线段齿轮的传动误差，分析了不同中心距偏差对渐开线和微线段齿轮的传动误差和侧隙的影响；通过建立微线段齿轮动力学模型，分析了渐开线和微线段齿轮在不同载荷、转速下中心距偏差对动态响应的影响。结果表明：微线段齿轮比渐开线齿轮对中心距偏差更为敏感；在低速轻载工况下，渐开线齿轮的动力学特性更好，在载荷较大的工况下，尤其是在中高速重载工况下，当中心距偏差被控制在一定范围内时，微线段齿轮具有更好的动态特性。
- 微线段齿轮 /
- 中心距偏差 /
- TCA /
- 传动误差 /
- 非线性动力学
Abstract: According to the forming principle of micro-segment gear profile, the mathematical model of its tooth profile was established. The transmission error of the micro-segment gear was studied by the discrete TCA (tooth contact analysis) and the influence of different deviations on the transmission error and meshing backlash of the involute and micro-segment gear was analyzed comparatively. Through the establishment of micro-segment gear dynamics model, the influence of center distance deviation on dynamic response of involute and micro-segment gear under different loads and speeds was analyzed comparatively, and the result indicates that micro segment gear is more sensitive to center distance deviation than involute gear. Under the condition of low speed and light load, the dynamic characteristics of involute gear are better. But, under the condition of large load, especially under the condition of medium and high speed and heavy load, the micro segment gear has better dynamic characteristics when the center distance deviation is controlled within a certain range.
- micro-segment gear /
- center distance deviation /
- TCA(tooth contact analysis) /
- transmission error /
- non-linear dynamics

HTML全文

图 1 微线段齿轮与渐开线齿轮齿廓对比图

下载: 全尺寸图片幻灯片

图 2 微线段齿条齿廓构造原理

下载: 全尺寸图片幻灯片

图 3 微线段齿轮齿廓构造过程

下载: 全尺寸图片幻灯片

图 4 离散化TCA原理图

下载: 全尺寸图片幻灯片

图 5 传动误差计算示意图

下载: 全尺寸图片幻灯片

图 6 中心距偏差对渐开线齿轮传动误差的影响

下载: 全尺寸图片幻灯片

图 7 中心距偏差对微线段齿轮传动误差的影响

下载: 全尺寸图片幻灯片

图 8 微线段齿轮啮合线

下载: 全尺寸图片幻灯片

图 9 直齿轮副扭转振动模型

下载: 全尺寸图片幻灯片

图 10 微线段齿轮有限元模型

下载: 全尺寸图片幻灯片

图 11 微线段与渐开线齿轮时变啮合刚度

下载: 全尺寸图片幻灯片

图 12 $\varOmega\; {\rm{ = }}\;0.2,T = 100\;{\rm{N \cdot m}}$工况下的动态响应

下载: 全尺寸图片幻灯片

图 13 $\varOmega\; {\rm{ = }}\;0.5,T = 500\;{\rm{N \cdot m}}$工况下的动态响应

下载: 全尺寸图片幻灯片

图 14 $\varOmega \;{\rm{ = }}\;0.5,T = 1\;000\;{\rm{N \cdot m}}$工况下的动态响应

下载: 全尺寸图片幻灯片

图 15 $\varOmega\; {\rm{ = }}\;1,T = 1\;000\;{\rm{N \cdot m}}$工况下的动态响应

下载: 全尺寸图片幻灯片

表 1 渐开线齿轮参数

参数及单位	数值	参数及单位	数值
模数/mm	3	齿根圆/mm	82.5
齿数	30	齿宽/mm	30
压力角/（°）	20	中心距/mm	90
齿顶圆直径/mm	96

下载: 导出CSV

表 2 微线段齿轮参数

参数及单位	数值	参数及单位	数值
模数/mm	3	齿顶圆/mm	96
齿数	30	齿根圆/mm	82.5
初始压力角/（°）	20	齿宽/mm	30
初始压力角增量/（°）	0.00065	中心距/mm	90
初始基圆半径/mm	400000

下载: 导出CSV

表 3 传动误差拟合结果

中心距偏差/mm	拟合函数$e(\bar t)$
0.02	$\begin{array}{l} {\rm{0} }{\rm{.008\;682 - 2} }{\rm{.098} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(} }\omega { {\bar t) - 1} }{\rm{.268} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{sin(} }\omega { {\bar t)} }+ \\ {\rm{ 5} }{\rm{.838} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{cos(2} }\omega { {\bar t) + 2} }{\rm{.838} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 6} } } }{\rm{sin(2} }\omega { {\bar t)} }- \\ {\rm{ 1} }{\rm{.565} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(3} }\omega { {\bar t) + 3} }{\rm{.223} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{sin(3} }\omega { {\bar t)} } \end{array}$
0.04	$\begin{array}{l} {\rm{0} }{\rm{.010\;8 - 7} }{\rm{.231} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(} }\omega { {\bar t) - 2} }{\rm{.31} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{sin(} }\omega { {\bar t)} }+ \\ {\rm{ 9} }{\rm{.287} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{cos(2} }\omega { {\bar t) + 1} }{\rm{.999} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{sin(2} }\omega { {\bar t)} }- \\ {\rm{ 2} }{\rm{.424} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(3} }\omega { {\bar t) + 5} }{\rm{.257} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{sin(3} }\omega { {\bar t)} } \end{array}$
0.06	$\begin{array}{l} {\rm{0} }{\rm{.012\;73 - 4} }{\rm{.469} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(} }\omega { {\bar t) - 3} }{\rm{.094} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{sin(} }\omega { {\bar t)} }+ \\ {\rm{ 1} }{\rm{.197} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 3} } } }{\rm{cos(2} }\omega { {\bar t) - 8} }{\rm{.21} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{sin(2} }\omega { {\bar t)} }+ \\ {\rm{ 1} }{\rm{.031} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 5} } } }{\rm{cos(3} }\omega { {\bar t) + 6} }{\rm{.024} } \times {\rm{1} }{ {\rm{0} }^{ {\rm{ - 4} } } }{\rm{sin(3} }\omega { {\bar t)} } \end{array}$

下载: 导出CSV

表 4 两种方法得到的侧隙对比

中心距偏差$\Delta a$/mm	侧隙$b$/mm		侧隙变化值$\Delta b$/mm
中心距偏差$\Delta a$/mm	计算公式	离散化TCA	计算公式	离散化TCA
0	0.0470	0.0465	0	0
0.02	0.0607	0.0603	0.0137	0.0138
0.04	0.0744	0.0739	0.0274	0.0274
0.06	0.0881	0.0875	0.0411	0.0410

下载: 导出CSV

表 5 中心距偏差对微线段齿轮副侧隙的影响

中心距偏差$\Delta a$/mm	侧隙$b$/mm	侧隙变化值$\Delta b$/mm
0	0.0481	0
0.02	0.0509	0.0028
0.04	0.0531	0.0050
0.06	0.0546	0.0065

下载: 导出CSV

参考文献(30)

[1]	赵韩, 梁锦华, 刘红雨, 等. 微线段齿廓的形成原理及特性[J]. 机械工程学报, 1997, 33(5): 7-11 ZHAO H, LIANG J H, LIU H Y, et al. Constructing principle and features of tooth profiles with micro-segments[J]. Journal of Mechanical Engineering, 1997, 33(5): 7-11 (in Chinese)
[2]	李海翔, 李朝阳, 陈兵奎. 圆弧齿轮研究的进展[J]. 现代制造工程, 2005(3): 19-21 LI H X, LI Z Y, CHEN B K. Progress made in circular tooth gear[J]. Modern Manufacturing Engineering, 2005(3): 19-21 (in Chinese)
[3]	LIANG D, CHEN B K, PENG S, et al. Deviation calculation and analysis of tooth surfaces of conjugate-curve gear drive[J]. International Journal of Precision Engineering and Manufacturing, 2017, 18(5): 689-696 doi: 10.1007/s12541-017-0082-8
[4]	彭帅, 陈兵奎. 线面对构齿轮啮合原理[J]. 中国机械工程, 2020, 31(8): 937-943 PENG S, CHEN B K. Principle of geometric elements constructed tooth pairs with curve-surface mesh[J]. China Mechanical Engineering, 2020, 31(8): 937-943 (in Chinese)
[5]	赵宁, 郭辉, 方宗德, 等. 直齿面齿轮修形及承载接触分析[J]. 航空动力学报, 2008, 23(11): 2142-2146 ZHAO N, GUO H, FANG Z D, et al. Modification and loaded contact analysis of spur face gears[J]. Journal of Aerospace Power, 2008, 23(11): 2142-2146 (in Chinese)
[6]	KORTA J A, MUNDO D. Multi-objective micro-geometry optimization of gear tooth supported by response surface methodology[J]. Mechanism and Machine Theory, 2017, 109: 278-295 doi: 10.1016/j.mechmachtheory.2016.11.015
[7]	聂少武, 蒋闯, 邓效忠, 等. Ease-off拓扑修正的准双曲面齿轮齿面修形方法[J]. 中国机械工程, 2019, 30(22): 2709-2715, 2740 NIE S W, JIANG C, DENG X Z, et al. Flank modification method of hypoid gears with ease-off topology correction[J]. China Mechanical Engineering, 2019, 30(22): 2709-2715, 2740 (in Chinese)
[8]	唐进元, 周长江, 吴运新. 齿轮弯曲强度有限元分析精确建模的探讨[J]. 机械科学与技术, 2004, 23(10): 1146-1149, 1248 TANG J Y, ZHOU C J, WU Y X. A method for exact modeling of the bending of spur gear teeth by FEM[J]. Mechanical Science and Technology for Aerospace Engineering, 2004, 23(10): 1146-1149, 1248 (in Chinese)
[9]	SÁNCHEZ M B, PEDRERO J I, PLEGUEZUELOS M. Contact stress calculation of high transverse contact ratio spur and helical gear teeth[J]. Mechanism and Machine Theory, 2013, 64: 93-110 doi: 10.1016/j.mechmachtheory.2013.01.013
[10]	李大庆, 邓效忠, 魏冰阳. 蝶形砂轮安装误差对面齿轮齿面几何误差影响规律[J]. 机械设计与研究, 2019, 35(5): 59-62, 74 LI D Q, DENG X Z, WEI B Y. Research on the influence law of tooth surface errors of face gear by grinding disk installation errors[J]. Machine Design & Research, 2019, 35(5): 59-62, 74 (in Chinese)
[11]	蒋进科, 方宗德, 刘钊. 拓扑修形斜齿轮齿面插齿修正[J]. 华中科技大学学报, 2019, 47(7): 102-107 JIANG J K, FANG Z D, LIU Z. Modification of tooth surface shaping of topological modified helical gears[J]. Journal of Huazhong University of Science and Technology , 2019, 47(7): 102-107 (in Chinese)
[12]	黄康, 赵韩. 微线段齿轮与渐开线齿轮的弯曲强度比较分析[J]. 农业机械学报, 2001, 32(1): 115-117 HUANG K, ZHAO H. The comparative analysis of bending strength of micro-segment and involute gear[J]. Transactions of the Chinese Society of Agricultural Machinery, 2001, 32(1): 115-117 (in Chinese)
[13]	黄康, 田杰, 赵韩, 等. 斜齿微线段齿轮胶合承载能力的研究[J]. 合肥工业大学学报, 2005, 28(2): 118-120, 124 HUANG K, TIAN J, ZHAO H, et al. Study on the scuffing strength of micro-segment helical gear[J]. Journal of Hefei University of Technology, 2005, 28(2): 118-120, 124 (in Chinese)
[14]	黄康, 赵韩, 田杰. 微线段齿轮与渐开线齿轮温升对比实验研究[J]. 中国机械工程, 2006, 17(18): 1880-1883 HUANG K, ZHAO H, TIAN J. Experimental research on temperature rise comparison between micro-segment gear and involute gear[J]. China Mechanical Engineering, 2006, 17(18): 1880-1883 (in Chinese)
[15]	刘鹏, 赵韩, 黄康, 等. 基于势能法的微线段齿轮啮合刚度模型研究[J]. 应用力学学报, 2015, 32(6): 1069-1074 LIU P, ZHAO H, HUANG K, et al. Research on meshing stiffness calculation model for micro-segment gear based on potential energy method[J]. Chinese Journal of Applied Mechanics, 2015, 32(6): 1069-1074 (in Chinese)
[16]	KAHRAMAN A, SINGH R. Non-linear dynamics of a spur gear pair[J]. Journal of Sound and Vibration, 1990, 142(1): 49-75 doi: 10.1016/0022-460X(90)90582-K
[17]	陈思雨, 唐进元. 间隙对含摩擦和时变刚度的齿轮系统动力学响应的影响[J]. 机械工程学报, 2009, 45(8): 119-124 doi: 10.3901/JME.2009.08.119 CHEN S Y, TANG J Y. Effect of backlash on dynamics of spur gear pair system with friction and time-varying stiffness[J]. Journal of Mechanical Engineering, 2009, 45(8): 119-124 (in Chinese) doi: 10.3901/JME.2009.08.119
[18]	卢剑伟, 曾凡灵, 杨汉生, 等. 随机装配侧隙对齿轮系统动力学特性的影响分析[J]. 机械工程学报, 2010, 46(21): 82-86 doi: 10.3901/JME.2010.21.082 LU J W, ZENG F L, YANG H S. Influence of stochastic assembling backlash on nonlinear dynamic behavior of transmission gear pair[J]. Journal of Mechanical Engineering, 2010, 46(21): 82-86 (in Chinese) doi: 10.3901/JME.2010.21.082
[19]	MA H, PANG X, FENG R J, et al. Evaluation of optimum profile modification curves of profile shifted spur gears based on vibration responses[J]. Mechanical Systems and Signal Processing, 2016, 70-71: 1131-1149 doi: 10.1016/j.ymssp.2015.09.019
[20]	MUCCHI E, DALPIAZ G, RIVOLA A. Elastodynamic analysis of a gear pump. Part II: Meshing phenomena and simulation results[J]. Mechanical Systems and Signal Processing, 2010, 24(7): 2180-2197 doi: 10.1016/j.ymssp.2010.02.004
[21]	FERNÁNDEZ A, IGLESIAS M, DE-JUAN A, et al. Gear transmission dynamic: effects of tooth profile deviations and support flexibility[J]. Applied Acoustics, 2014, 77: 138-149 doi: 10.1016/j.apacoust.2013.05.014
[22]	MOHAMMED O D, RANTATALO M, AIDANPÄÄ J O. Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis[J]. Mechanical Systems and Signal Processing, 2015, 54-55: 293-305 doi: 10.1016/j.ymssp.2014.09.001
[23]	刘鹏, 赵韩, 黄康, 等. 线段齿轮法向接触刚度的改进分形模型研究[J]. 机械工程学报, 2018, 54(7): 114-122 doi: 10.3901/JME.2018.07.114 LIU P, ZHAO H, HUANG K, et al. Research on normal contact stiffness of micro-segments gear based on improved fractal model[J]. Journal of Mechanical Engineering, 2018, 54(7): 114-122 (in Chinese) doi: 10.3901/JME.2018.07.114
[24]	吴其林, 赵韩, 邱明明, 等. 微线段齿轮磨削加工方法及性能分析[J]. 机械工程学报, 2017, 53(13): 179-187 doi: 10.3901/JME.2017.13.179 WU Q L, ZHAO H, QIU M M, et al. Grinding method and performance analysis of micro-segment gears[J]. Journal of Mechanical Engineering, 2017, 53(13): 179-187 (in Chinese) doi: 10.3901/JME.2017.13.179
[25]	黄康, 汪涛. 微线段齿轮系统动力学特性分析[J]. 振动与冲击, 2018, 37(2): 248-253 HUANG K, WANG T. Dynamic features of a micro-segment Gear system[J]. Journal of vibration and shock, 2018, 37(2): 248-253 (in Chinese)
[26]	LITVIN F L, FUENTES A. Gear geometry and applied theory[M]. New York: Cambridge University Press, 2004: 375-403.
[27]	ZSCHIPPANG H A, WEIKERT S, KÜÇÜK K A, et al. Face-gear drive: geometry generation and tooth contact analysis[J]. Mechanism and Machine Theory, 2019, 142: 103576 doi: 10.1016/j.mechmachtheory.2019.103576
[28]	BATSCH M. Mathematical model and tooth contact analysis of convexo-concave helical bevel Novikov gear mesh[J]. Mechanism and Machine Theory, 2020, 149: 103842 doi: 10.1016/j.mechmachtheory.2020.103842
[29]	SCHLEICH B, WARTZACK S. A discrete geometry approach for tolerance analysis of mechanism[J]. Mechanism and Machine Theory, 2014, 77: 148-163 doi: 10.1016/j.mechmachtheory.2014.02.013
[30]	丁淳. 渐开线齿轮的侧隙公式[J]. 机械传动, 2004, 28(4): 28-32 DING C. A backlash formula for involute gears[J]. Journal of Mechanical Transmission, 2004, 28(4): 28-32 (in Chinese)