Reverse Design and Kinematics Analysis of Reciprocating Linear Mechanisms  Based on Non-circular Differential Gear Trains

doi:10.3969/j.issn.1004-132X.2021.06.009

Abstract

Abstract: In order to achieve the desired reciprocating motions concisely and effectively, a new mechanism was proposed by combining non-circular differential gear trains with a rack to realize reciprocating linear motions. It was simple in forms and reliable in operations, through the reasonable pitch curve design, the ideal output motion curves might be obtained. The kinematics analysis of the mechanisms was carried out, and the influences of the pitch curve on the motion characteristics were analyzed. Taking the execution parts following the law of the cosine acceleration and sine acceleration as an example, the non-circular gear pitch curves were obtained in reverse. The influence laws and design criteria of different factors on pitch curve, such as swing angle of output gear, the transmission ratio of the differential gear train and the order of pitch curve, were researched. Besides, the influence laws of the above two motion laws on the transmission ratio, the pitch curve and the characteristics of quick return were compared. The principle prototype of non-circular differential gear trains with rack transmission system was built, and the feasibility and correctness of the new transmission system was verified.

Key words: non-circular gear, pitch curve, differential gear train, reciprocating mechanism, reverse design

摘要： 为了简洁有效地实现所需的往复运动，提出了一种非圆齿轮差动轮系组合并配以齿条来实现往复直线运动的新型机构，通过合理的节曲线设计，可得到理想的输出运动曲线，该机构形式简单、运行可靠。完成了机构运动学分析，并分析了节曲线对运动特性的影响机制。以执行部件遵循余弦加速度和正弦加速度运动规律输出为例，反求得到了该机构非圆齿轮的节曲线，研究了输出齿轮的摆动角度、差动轮系传动比以及节曲线阶数等参数对节曲线的影响规律和设计准则。比较了上述两种运动规律对节曲线、传动比以及急回特性的影响规律。搭建了非圆齿轮差动轮系传动系统原理样机，并验证了新型传动系统的可行性。

关键词: 非圆齿轮, 节曲线, 差动轮系, 往复运动机构, 反求设计

CLC Number:

TH132.41

WANG Feixue, LIU Ya, ZANG Xinliang . Reverse Design and Kinematics Analysis of Reciprocating Linear Mechanisms Based on Non-circular Differential Gear Trains[J]. China Mechanical Engineering, 2021, 32(06): 697-704.

汪飞雪, 刘亚, 臧新良 . 非圆齿轮差动轮系往复机构反求设计与运动学分析[J]. 中国机械工程, 2021, 32(06): 697-704.

References

［1］PONT A, LPEZ J, RIGOLA J, et al. Numerical Dynamic Analysis of Reciprocating Compressor Mechanism. Parametric Studies for Optimization Purposes［J］. Tribology International, 2017, 105:1-14.

［2］PRIKHODKO A A, SMELYAGIN A I. Dynamics of Rotationally Reciprocating Stirred Tank with Planetary Actuator［J］. Journal of Physics: Conf. Series, 2017, 858:012026.

［3］PRIKHODKO A A, SMELYAGIN A I. Kinematic Analysis of Mechanism for Converting Rotational Motion Intoreciprocating Rotational Motion［J］. Procedia Engineering, 2015, 129: 87-92.

［4］ZHANG Xin, FAN Shouwen. Synthesis of the Steepest Rotation Pitch Curve Design for Noncircular Gear［J］. Mechanism and Machine Theory, 2016, 102:16-35.

［5］ANDREI L, VASIE M. Noncircular Gears Designed by Geometric Hypothesis［J］. Applied Mechanics and Materials, 2014, 657: 684-688.

［6］KARPOV O, NOSKO P, FIL P, et al. Prevention of Resonance Oscillations in Gear Mechanisms Using Non-circular Gears［J］. Mechanism and Machine Theory, 2017, 114: 1-10.

［7］LYU Gang. Pitch Curve Design Defects Modification for Non-circular Bevel Gear［J］.Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2015, 229(12): 2231-2241.

［8］YUAN Yongliang, SONG Xuguan, SUN Wei, et al. Modeling and Dynamic Analysis of the Non-circular Gear System of a Bucket Wheel Stacker/Reclaimer［J］. AIP Advances, 2018, 8(6): 1-8.

［9］YU Yaxin, LIU Jikun, YE Bingliang, et al. Design and Experimental Research on Seedling Pick-up Mechanism of Planetary Gear Train with Combined Non-circular Gear Transmission［J］. Chinese Journal of Mechanical Engineering,2019,32:49.

［10］LIN Chao, XIA Xiguang, LI Peilu. Geometric Design and Kinematics Analysis of Coplanar Double Internal Meshing Non-circular Planetary Gear Train［J］. Advances in Mechanical Engineering, 2018, 10(12): 1-12.

［11］XU Gaohuan, CHEN Jianneng, ZHAO Huacheng. Numerical Calculation and Experiment of Coupled Dynamics of the Differential Velocity Vane Pump Driven by the Hybrid Higher-order Fourier Non-circular Gears［J］. Journal of Thermal Science, 2018, 27(3): 93-101.

［12］ZUO Yanjun, YU Xiaoxu, LI Wenge, et al. Kinematic Optimization of Transplanting Mechanism with B-spline Curve Gear for Rice Pot Seedling Based on MATLAB［J］. Applied Mechanics and Materials, 2014, 624:181-186.

［13］ZHENG Fangyan, HUA Lin, HAN Xinghui, et al. Synthesis of Indexing Mechanisms with Non-circular Gears［J］. Mechanism and Machine Theory, 2016, 105: 108-128.

［14］孙以涛,王生泽.单向驱动非圆齿轮差动轮系实现可调摆幅输出的研究［J］.机械传动, 2013, 37(7): 15-19.

SUN Yitao, WANG Shengze. Study on Realizing of Adjustable Swing Output with Unidirectional Drive Non-circular Differential Gear Train［J］. Journal of Mechanical Transmission 2013, 37(7): 15-19.

［15］陈建能,王英,任根勇,等. 非圆齿轮行星轮系引纬机构的反求设计与运动学分析［J］.中国机械工程, 2012, 23(20): 2405- 2409.

CHEN Jianneng, WANG Ying, REN Genyong, et al. Reverse Design and Kinematic Analysis of Non-circular Planetary Gear Trains Weft Insertion Mechanism［J］. China Mechanical Engineering, 2012, 23(20): 2405-2409.

［16］贵新成,詹隽青,赵重年,等.一种非圆齿轮差动无级变速传动设计［J］. 机械设计,2018, 35(9): 100-104.

GUI Xincheng, ZHAN Junqing, ZHAO Zhongnian, et al. Design of the Differential Infinitely-variable Transmission with Non-circular Gears［J］. Journal of Machine Design, 2018, 35(9): 100-104.

［17］刘大伟,任廷志.由补偿法构建封闭非圆齿轮节曲线［J］.机械工程学报,2011,47(13):147-152.

LIU Dawei, REN Tingzhi. Creating Pitch Curve of Closed Noncircular Gear by Compensation Method［J］. Journal of Mechanical Engineering, 2011,47(13):147-152.

[1]	HU Fuqing, SUN Jianghong, SUN Yingjie, SUN Yutong, MA Chao, ZHOU Fuqiang, . Design and Parameter Optimization of Slicing Machines Based on New Rotary-straight Line Reciprocating Mechanisms [J]. China Mechanical Engineering, 2024, 35(04): 614-623，635.
[2]	ZHANG Xiao, CHI Maoru, XIE Yuchen, WANG Huansheng, CAI Wubin, DAI Liangcheng. Optimization of Variable Gauge Train Wheel Treads Based on Reverse Design Method [J]. China Mechanical Engineering, 2023, 34(22): 2746-2757.
[3]	WANG Jian, MIAO Long, ZHANG Wenxiang, WANG Shukun. Active Control Method for Energy Conversion and Experimental Test of Hopping Robots [J]. China Mechanical Engineering, 2022, 33(24): 2961-2970.
[4]	LIN Chao1;XIA Xiguang1;XING Qingkun2;LIU Wensi1. Design and Kinematic Characteristics Analysis of an Intermittent Rotation Mechanism Based on Non-circular Gears [J]. China Mechanical Engineering, 2020, 31(10): 1142-1148.
[5]	HAN Jiang;GAO Ting;LI Dazhu;XIA Lian. Research and Implementation of Tooth Surface Machining Allowance Uniform Distribution Processing Technology of Non-circular Gears [J]. China Mechanical Engineering, 2018, 29(09): 1031-1038.
[6]	YE Jun1,2;CHEN Jianneng1,3;ZHAO Xiong1,3;SUN Xincheng2;XIA Xudong1,3;GAO Qifeng2. Design and Applications of Generalized Eccentric Noncircular Gears [J]. China Mechanical Engineering, 2018, 29(05): 565-571,578.
[7]	XU Lin;LIU Kai;CUI Yahui;MENG Peiyuan. Dynamic Tracking Performance Analysis of Differential Gear Trains [J]. China Mechanical Engineering, 2017, 28(23): 2868-2874,2879.
[8]	LIU Dawei1,2;LUO Linming2;WANG Guohui2;JIN Xin2. Integrated Design of Non-sinusoidal Generator of Continuous Casting Mold [J]. China Mechanical Engineering, 2017, 28(21): 2608-2613.
[9]	TAO Dehua1;WANG Ying1;CHEN Jianneng2;RONG Quansheng1;ZHOU Xian1;SHU Xuedao1. Design and Analysis of Non-circular Gear Slider-Crank Mechanisms Used as Driver for Pulsating Blood Flow Generators [J]. China Mechanical Engineering, 2017, 28(16): 1914-1920,1927.
[10]	Hu Ziyang, Yang Hui, Li Dazhu, Han Jiang. Optimization Design and Experimental Analyses of Non-circular Gears for Constant Flow Pumps [J]. China Mechanical Engineering, 2016, 27(22): 3082-3087.
[11]	Yu Gaohong, Yu Jiaping, Tong Junhua, Ye Bingliang, Zheng Shiyong, . Design of a Conjugate Concave-Convex Non-circular Gear Mechanism [J]. China Mechanical Engineering, 2016, 27(16): 2155-2159,2165.
[12]	Su Rui, Rui Xiaoming, Wu Xin. Conceptual Design and Simulation of a Novel Speed Self-stabilizing Mechanism [J]. China Mechanical Engineering, 2015, 26(8): 1058-1061.
[13]	Lü Gang, Fan Shouwen, Li Guanghui, Tong Shuiguang, Xiao Renyuan. Research on Design and Pitch Surface Shaping of New Type High-order Non-circular Gear [J]. China Mechanical Engineering, 2015, 26(22): 2989-2995.
[14]	Zheng Fangyan, Zhang Zhengyan, Chen Dingfang, Liu Youyuan. A New Type of Non-circular Gear Indexing Device [J]. China Mechanical Engineering, 2014, 25(22): 2997-3002.
[15]	Chen Ming, Liu Yanping. Study on Quasi-circular Curve and Its Properties [J]. China Mechanical Engineering, 2014, 25(10): 1324-1332.

Reverse Design and Kinematics Analysis of Reciprocating Linear Mechanisms Based on Non-circular Differential Gear Trains

非圆齿轮差动轮系往复机构反求设计与运动学分析

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics