Modification design and load tooth contact analysis of a cylindrical gear with variable hyperbolic circular arc tooth trace

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (14) : 170-179.

MA Dengqiu1,2,LIU Yongping1,YE Zhenhuan2,LI Dawei1,WEI Yongqiao1

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Abstract

To improve the load-bearing capacity and dynamic characteristics of the variable hyperbolic circular arc tooth trace cylindrical gear (VHCATT cylindrical gear), the modification design method of the VHCATT cylindrical gear’s surface was put forward, that is, the cutter inclination method in the direction of tooth line and the parabola modification blade method in the direction of tooth profile. Firstly, according to the gear meshing principle and the modified tooth surface shaping principle of the VHCATT cylindrical gear, the modified tooth surface equation was derived, and the tooth surface reconstruction was realized by using MATLAB and UG. Secondly, the tooth contact analysis was to calculate the tooth surface clearance. At the same time, the contact point flexibility matrix was calculated by using the finite element method, and the load-bearing contact nonlinear mathematical programming model was established to obtain the load-bearing meshing characteristics further. Then, the influences of cutter inclination angle, parabolic coefficient and parabolic vertex position on load distribution and load transmission error of modified tooth surface were analyzed. The results show that: the reasonable cutter inclination angle and parabolic vertex position can effectively reduce the load of the tooth surface and improve the system load transmission error characteristics. The reasonable parabolic coefficient can improve the sudden change of load in the intermeshing of single tooth and double tooth. The further design and industrial applications of the VHCATT cylindrical gear can be accomplished based on the result.

Key words

variable hyperbolic circular arc tooth trace cylindrical gear / tooth surface modification design / load tooth contact analysis / tooth surface load distribution / load transmission error

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MA Dengqiu1,2,LIU Yongping1,YE Zhenhuan2,LI Dawei1,WEI Yongqiao1. Modification design and load tooth contact analysis of a cylindrical gear with variable hyperbolic circular arc tooth trace[J]. Journal of Vibration and Shock, 2023, 42(14): 170-179

References

[1] Ma D, Liu Y, Ye Z, et al. Analysis of the Tooth Surface Contact Area of a Circular Arc Tooth Trace Cylindrical Gear under Load [J]. Transactions of FAMENA, 2021, 45(1), 79-94.
[2] R. T. Tseng, C. B. Tsay. Mathematical Model and Surface Deviation of Cylindrical Gears with Curvilinear Shaped Teeth Cut by a Hob Cutter [J]. ASME Journal of Mechanical Design, 2005, 45: 982-987.
[3] 狄玉涛,洪晓晖,陈明.弧齿线圆柱齿轮齿面形成原理[J].哈尔滨轴承, 2006, 27(3): 58-61.
DI Yutao, HONG Xiaohui, CHEN Ming. Generation Principle of Actuate Tooth Trace Cylindrical Gear [J]. Journal of Harbin Bearing, 2006, 27(3): 58-61.
[4] 赵斐, 侯力, 段阳,等. 旋转刀盘圆弧齿轮成形理论分析及数字化建模研究[J]. 四川大学学报:工程科学版, 2016, 48(6):119-125.
ZHAO Fei, HOU Li, DUAN Yang, et al. Research on the Forming Theory Analysis and Digital Model of Circular Arc Gear Shaped by Rotary Cutter [J]. Journal of Sichuan University, 2016, 48(6): 119-125.
[5] 宋爱平, 吴伟伟, 高尚,等. 弧齿圆柱齿轮理想几何参数及其加工方法[J]. 上海交通大学学报, 2010. 44 (12). 1735- 1740.
SONG Aiping, WU Weiwei, GAO Shang, et al. The Ideal Geometry Parameters of Arch Cylindrical Gear and its Process Method [J]. Journal of Shanghai Jiao-tong University, 2010, 44(12):1735-1740.
[6] 常青林, 侯力, 孙志军,等. 弧齿圆柱齿轮两种加工方法的工艺分析[J]. 机械传动, 2014, 38(6): 96-100.
CHANG Qinlin, HOU Li, SUN Zhijun, et al. Process Analysis of two Kinds of Processing Method Cylindrical Gear with Curvilinear Shape Tooth[J]. Journal of Mechanical Transmission, 2014, 38(6): 96-100.
[7] Fuentes-Aznar A, Ruiz-Orzaez R, Gonzalez-Perez I. Comparison of Spur, Helical and Curvilinear Gear Drives by Means of Stress and Tooth Contact Analyses [J]. Meccanica, 2017, 52(7):1721-1738.
[8] Fuentes A, Ruiz-Orzaez R, Gonzalez-Perez I. Computerized Design, Simulation of Meshing, and Finite Element Analysis of two types of Geometry of Curvilinear Cylindrical Gears [J]. Computer Methods in Applied Mechanics Engineering, 2014, 272(2):321- 339.
[9] Zhang X, Xie Y. Design, Meshing Characteristics and Stress Analysis of Cylindrical Gears with Curvilinear Tooth Profile [J]. Transactions of Famena, 2016, 40(1):27-44.
[10] Chen Y C, Lo C C. Contact Stress and Transmission Errors under Load of a Modified Curvilinear Gear Set Based on Finite Element Analysis [J]. Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science 1989-1996 (vols 203-210), 2015, 229(2):191-204.
[11] 马登秋,魏永峭,叶振环,等. 圆弧齿线圆柱齿轮啮合接触冲击研究[J]. 振动与冲击, 2018,37(7):123-131.
MA Dengqiu, WEI Yongqiao, YE Zhenhuan, et al. Mesh Contact Impact of Circular Arc Tooth Trace Cylindrical Gears [J]. Journal of Vibration and Shock, 2018,37(7):123-131.
[12] Ma D , Liu Y , Ye Z , et al. Meshing Contact Impact Properties of Circular Arc Tooth Trace Cylindrical Gear Based on Rotating Knife Dish Milling Process[J]. Mathematical Problems in Engineering, 2021,2021:1-17.
[13] Wei Y , Guo R , Liu Y. Analytical Calculation of the Tooth Surface Contact Stress of Cylindrical Gear with Variable Hyperbolic Circular Arc Tooth Trace [J]. Symmetry, 2020, 12(8):1318.
[14] 林子光. 能连续泵油的曲线齿轮油泵[P]. 中国: ZL 94223886.9, 1995-12-03.
LIN Zi-guang. The Continuous Curve Gear Oil Pump [P]. China: ZL 94223886.9, 1995-12-03.
[15] 蒋进科,刘钊,刘红梅.Ease-off修形准双曲面齿轮齿面动态抗磨设计与分析[J].机械工程学报,2021,57(19):155-164.
JIANG Jinke, LIU Zhao, LIU Hongmei. Dynamic Anti-wear Design and Analysis for Hypoid Gears with Ease-off Flank Modification [J]. Journal of Mechanical Engineering,2021,57 (19): 155-164.
[16] 蒋进科,方宗德,刘钊.Ease-off拓扑修形准双曲面齿轮齿面多目标优化设计方法[J].西安交通大学学报,2019,53(06): 44-53.
JIANG Jinke, FANG Zongde, LIU Zhao. Design of Multi-Objective Tooth Optimization for Hypoid Gear with Ease-off Topological Modification [J]. Journal of Xi'an Jiaotong University,2019,53(06): 44-53.
[17] 贾超,方宗德.高速齿轮传递误差和啮入冲击的激励模拟及齿面优化修形[J].振动与冲击,2019,38(23):103-109+138.
JIA Chao, FANG Zongde. Simulation for Transmission Error and Mesh-in Impact Excitation of High Speed Gears and their Tooth Surface Optimal Modification [J]. Journal of Vibration and Shock,2019,38(23):103-109+138.
[18] 王峰,张健,徐兴,等.融合齿背接触机理的圆柱斜齿轮振动特性分析与双面修形优化研究[J].振动与冲击,2018,37(24): 53-60.
WANG Feng, ZHANG Jian, XU Xing, et al. A Study on Vibration Characteristics of a Cylindrical Spur Gear with the Contact Mechanism of Back Teeth and Optimization of Double Teeth Surfaces Modification [J]. Journal of Vibration and Shock,2018,37(24): 53-60.
[19] 魏冰阳，古德万，曹雪梅，等．采用曲面综合法的复杂齿面微分修形与拓扑结构设计[J/OL]．中国机械工程.https://kns.cnki.net/kcms/detail/42.1294.th.20220518.1105.014.html
WEI Bingyang, GU Dewan, CAO Xuemei, et al．Differential Modification and Topological Structure Design of Complex Tooth Surface by Surface Synthesis Method [J/OL]．China Mechanical Engineering. https://kns.cnki.net/kcms/detail/ 42.1294.th.20220518.1105.014.html
[20] 方宗德. 齿轮轮齿承载接触分析(LTCA)的模型和方法[J]. 机械传动, 1998, 22(2):1-3+16.
FANG Zongde. Model and Approach for Loaded Tooth Contact Analysis (LTCA) of Gear Drives [J]. Journal of Mechanical Transmission, 1998, 22(2):1-3+16.
[21] 常乐浩,刘更,吴立言.齿轮综合啮合误差计算方法及对系统振动的影响[J].机械工程学报,2015,51(01):123-130.
CHANG Lehao, LIU Geng, WU Liyan. Determination of Composite Meshing Errors and Its Influence on the Vibration of Gear System [J]. Journal of Mechanical Engineering,2015, 51 (01):123-130.
[22] 王笑乐,卢剑伟,杨士钦,等.载荷变化时准双曲面齿轮副啮合参数演变分析[J].振动与冲击,2021,40(20):143-149 +176.
WANG Xiaole, LU Jianwei, YANG Shiqin, et al. Analysis of Evolution of Meshing Parameters of Hypoid Gear Drive under Changing Loads [J]. Journal of Vibration and Shock, 2021, 40 (20): 143-149 +176.
[23] 牟彦铭,何雪明,方宗德.承载传动误差最小的高重合度弧齿锥齿轮波动齿面设计[J].航空动力学报,2021,36(10): 2080-2089.
MU Yanming, HE Xueming, FANG Zongde. Wave Tooth Surface Design of High Contact Ratio Spiral Bevel Gear with Minimum Loaded Transmission Error [J]. Journal of Aerospace Power, 2021,36(10):2080-2089.
[24] 李特文.齿轮几何学与应用理论[M].上海:上海科学技术出版社,2008.
FL Litvin. Gear Geometry and Applied Theory [M]. Shanghai：Shanghai Science and Technology Press, 2008.