Analysis on load sharing characteristic of two-stage star gear transmission based on function method
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摘要:
为获取定轴多分支功率分汇流齿轮传动的真实均载情况，提出一种基于函数法的静力学均载特性分析方法，综合考虑系统构成功率流闭环的特点以及误差随机性的影响，系统地分析了两级定轴三分支（星型）齿轮传动的均载特性，并定量分析了其误差敏感性，最后通过与现有算例的对比分析，对上述方法的准确性进行了验证。研究结果表明：制造和安装误差随机性对系统载荷分配的影响不可忽略，尤以误差值随机性为甚；函数法计算均载系数时可有效避免截断误差，又因计入了误差随机性的影响，故更接近真实情况。
Abstract:In order to obtain the actual load sharing performance of fixed-axis multi-branch power-split gear transmission, a method based on function method for static load sharing characteristic analysis was proposed. Considering the power closed-loop and error randomness, the load sharing characteristics of two-stage fixed-axis three-branch (star) gear transmission were systematically analyzed, and its error sensitivity was quantitatively analyzed. Finally, the above method was verified to be correct compared with the existing examples. The results showed that the manufacturing and installation error randomness on the system load distribution cannot be ignored, especially the randomness of error values. Function method can effectively avoid truncation error when calculating the load sharing coefficient, which was closer to the actual situation when considering error randomness.
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图 1 两级外啮合星型齿轮系统传动简图
Figure 1. Kinematic diagram of two-stage external meshing star gear system
图 2 两级外啮合星型齿轮系统等效计算模型
Figure 2. Equivalent calculation model of two-stage external meshing star gear system
图 4 各制造误差单独作用时各分支均载系数曲线
Figure 4. Load sharing coefficient curve of each branch when each manufacturing error occurs alone
图 5 各安装误差单独作用时各分支均载系数曲线
Figure 5. Load sharing coefficient curve of each branch when each installation error occurs alone
图 6 各制造误差单独变化时各分支均载系数变化
Figure 6. Load sharing coefficient variation of each branch when each manufacturing error changes alone
图 7 各安装误差单独变化时各分支均载系数变化
Figure 7. Load sharing coefficient variation of each branch when each installation error changes alone
图 9 考虑随机误差性时系统均载系数分布
Figure 9. Load sharing coefficient distribution when considering error randomness
图 10 单独考虑误差值和初始相位的随机性时系统均载系数分布
Figure 10. Load sharing coefficient distribution when considering the random effects of error value and initial phase separately
表 1 星型齿轮系统参数
Table 1. Parameters of star gear system
构件 齿数 模数 输入功率/
kW输入轴转速/
（r/min）第1级太阳轮 15 1.5 100 40000 第1级星轮 54 1.5 第2级太阳轮 15 1.5 第2级星轮 54 1.5 
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[1] 日高照晃,山本信行,石田武. 行星齿轮装置均载机构中的各种误和载荷分配的关系[C]//日本机械学会论文集. 东京: 日本机械学会,1986: 2200-2206. HIDAKA T,SUGIMOTO N,ISHIDA T. Effects of errors of elements on load distribution in planetary gears with various load equalizing mechanisms[C]// Japanese Mechanical Academic Society Collection. Tokyo: The Japanese Society of Mechanical Engineers,1986: 2200-2206. (in JapaneseHIDAKA T, SUGIMOTO N, ISHIDA T. Effects of errors of elements on load distribution in planetary gears with various load equalizing mechanisms[C]// Japanese Mechanical Academic Society Collection. Tokyo: The Japanese Society of Mechanical Engineers, 1986: 2200-2206. (in Japanese) [2] KAHRAMAN A. Load sharing characteristics of planetary transmissions[J]. Mechanism and Machine Theory,1994,29(8): 1151-1165. doi: 10.1016/0094-114X(94)90006-X [3] KAHRAMAN A. Static load sharing characteristics of transmission planetary gear sets: model and experiment: SAE Paper 1999-01-1050[R]. Detroit: Society of Automotive Engineers,1999. [4] BODAS A,KAHRAMAN A. Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets[J]. JSME International Journal Series C,2004,47(3): 908-915. doi: 10.1299/jsmec.47.908 [5] KRANTZ T. A method to analyze and optimize the load sharing of split path transmissions: NASA TM-107201 [R]. Cleveland: NASA Lewis Research Center,1996. [6] KRANTZ T,DELGADO I. Experimental study of split-path transmission load sharing NASA TM-107212 [R]. Cleveland: NASA Lewis Research Center,1996. [7] 肖铁英,袁盛治,陆卫杰. 行星齿轮机构均载系数的计算方法[J]. 东北重型机械学院学报,1992,16(4): 290-295. XIAO Tieying,YUAN Shengzhi,LU Weijie. Calculative method of load balance coefficient in planetary gear[J]. Journal of Northeast Heavy Machinery Institute,1992,16(4): 290-295. (in ChineseXIAO Tieying, YUAN Shengzhi, LU Weijie. Calculative method of load balance coefficient in planetary gear[J]. Journal of Northeast Heavy Machinery Institute, 1992, 16(4): 290-295. (in Chinese) [8] 陆俊华,李斌,朱如鹏. 行星齿轮传动静力学均载分析[J]. 机械科学与技术,2005,24(6): 702-704, 709. LU Junhua,LI Bin,ZHU Rupeng. Analysis of static load sharing in planetary gearing[J]. Mechanical Science and Technology,2005,24(6): 702-704, 709. (in Chinese doi: 10.3321/j.issn:1003-8728.2005.06.021LU Junhua, LI Bin, ZHU Rupeng. Analysis of static load sharing in planetary gearing[J]. Mechanical Science and Technology, 2005, 24(6): 702-704, 709. (in Chinese) doi: 10.3321/j.issn:1003-8728.2005.06.021 [9] 周惠琴,李素有,吴立言. 行星齿轮传动系统均载分析[J]. 机械科学与技术,2008,27(9): 1239-1242. ZHOU Huiqin,LI Suyou,WU Liyan. Analysis of static load sharing in a planetary gearing[J]. Mechanical Science and Technology for Aerospace Engineering,2008,27(9): 1239-1242. (in Chinese doi: 10.3321/j.issn:1003-8728.2008.09.029ZHOU Huiqin, LI Suyou, WU Liyan. Analysis of static load sharing in a planetary gearing[J]. Mechanical Science and Technology for Aerospace Engineering, 2008, 27(9): 1239-1242. (in Chinese) doi: 10.3321/j.issn:1003-8728.2008.09.029 [10] 邵晓荣. 齿轮制造及安装误差对行星齿轮均载系数的影响[J]. 东北重型机械学院学报,1994,18(4): 306-309. SHAO Xiaorong. Influence of gear manufacturing and installation errors on load sharing coefficient of planetary gears[J]. Journal of Northeast Heavy Machinery Institute,1994,18(4): 306-309. (in ChineseSHAO Xiaorong. Influence of gear manufacturing and installation errors on load sharing coefficient of planetary gears[J]. Journal of Northeast Heavy Machinery Institute, 1994, 18(4): 306-309. (in Chinese) [11] 袁擎宇,朱如鹏,朱自冰,等. 两级星型齿轮传动静力学均载分析[J]. 机械科学与技术,2004,23(7): 789-792. YUAN Qingyu,ZHU Rupeng,ZHU Zibing,et al. Analysis of static load sharing in a 2-stage star gearing system[J]. Mechanical Science and Technology for Aerospace Engineering,2004,23(7): 789-792. (in Chinese doi: 10.3321/j.issn:1003-8728.2004.07.011YUAN Qingyu, ZHU Rupeng, ZHU Zibing, et al. Analysis of static load sharing in a 2-stage star gearing system[J]. Mechanical Science and Technology for Aerospace Engineering, 2004, 23(7): 789-792. (in Chinese) doi: 10.3321/j.issn:1003-8728.2004.07.011 [12] 袁擎宇. 星型齿轮传动系统均载分析方法的研究[D]. 南京: 南京航空航天大学,2004. YUAN Qingyu. Research on the load sharing analysis method of star gear transmission system[D]. Nanjing: Nanjing University of Aeronautics and Astronautics,2004. (in ChineseYUAN Qingyu. Research on the load sharing analysis method of star gear transmission system[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2004. (in Chinese) [13] 杜进辅,方宗德,王宝宾,等. 基于变形协调的行星轮系均载特性研究[J]. 航空动力学报,2012,27(5): 1166-1171. DU Jinfu,FANG Zongde,WANG Baobin,et al. Study on load sharing behavior of planetary gear train based on deformation compatibility[J]. Journal of Aerospace Power,2012,27(5): 1166-1171. (in ChineseDU Jinfu, FANG Zongde, WANG Baobin, et al. Study on load sharing behavior of planetary gear train based on deformation compatibility[J]. Journal of Aerospace Power, 2012, 27(5): 1166-1171. (in Chinese) [14] DU Jinfu,MAO Jin,LIU Kai,et al. Load-sharing analysis of two-stage three-branch star gearing based on deformation compatibility[J]. Advances in Mechanical Engineering,2018,10(12): 168781401881954. [15] 孙振宇,冯金,杜进辅. 基于变形协调的恒星式减速器功率分流特性[J]. 机械传动,2016,40(4): 48-51, 57. SUN Zhenyu,FENG Jin,DU Jinfu. Power splitting characteristic of star gearing based on deformation compatibility[J]. Journal of Mechanical Transmission,2016,40(4): 48-51, 57. (in ChineseSUN Zhenyu, FENG Jin, DU Jinfu. Power splitting characteristic of star gearing based on deformation compatibility[J]. Journal of Mechanical Transmission, 2016, 40(4): 48-51, 57. (in Chinese) [16] 董皓,方宗德,王宝宾,等. 基于变形协调和间隙浮动的双路功率分流系统均载特性分析[J]. 航空动力学报,2013,28(4): 872-877. DONG Hao,FANG Zongde,WANG Baobin,et al. Load sharing characteristics analysis of power split system based on deflection compatibility and clearance floating[J]. Journal of Aerospace Power,2013,28(4): 872-877. (in ChineseDONG Hao, FANG Zongde, WANG Baobin, et al. Load sharing characteristics analysis of power split system based on deflection compatibility and clearance floating[J]. Journal of Aerospace Power, 2013, 28(4): 872-877. (in Chinese) [17] MO Shuai,MA Shuai,JIN Guoguang,et al. Research on multiple-split load sharing characteristics of 2-stage external meshing star gear system in consideration of displacement compatibility[J]. Mathematical Problems in Engineering,2017,2017(1): 1037479. [18] MO Shuai,ZHANG Yidu,WU Qiong. Research on multiple-split load sharing of two-stage star gearing system in consideration of displacement compatibility[J]. Mechanism and Machine Theory,2015,88: 1-15. doi: 10.1016/j.mechmachtheory.2015.01.005 [19] 莫帅,张以都,吴琼,等. 考虑齿轮位移协调的2级星形传动多分流均载研究[J]. 四川大学学报(工程科学版),2015,47(4): 175-180. MO Shuai,ZHANG Yidu,WU Qiong,et al. Study on multiple-split load sharing of 2-stage star gearing system based on gears displacement compatibility[J]. Journal of Sichuan University (Engineering Science Edition),2015,47(4): 175-180. (in ChineseMO Shuai, ZHANG Yidu, WU Qiong, et al. Study on multiple-split load sharing of 2-stage star gearing system based on gears displacement compatibility[J]. Journal of Sichuan University (Engineering Science Edition), 2015, 47(4): 175-180. (in Chinese) [20] 李志宾,王三民,李飞,等. 误差对同轴六分支分扭人字齿轮传动系统静均载性能影响[J]. 航空动力学报,2021,36(8): 1765-1775. LI Zhibin,WANG Sanmin,LI Fei,et al. Influence of error on static load-sharing performance of coaxial six-branch twist herringbone gear transmission system[J]. Journal of Aerospace Power,2021,36(8): 1765-1775. (in ChineseLI Zhibin, WANG Sanmin, LI Fei, et al. Influence of error on static load-sharing performance of coaxial six-branch twist herringbone gear transmission system[J]. Journal of Aerospace Power, 2021, 36(8): 1765-1775. (in Chinese) [21] 靳广虎,任薇,朱如鹏. 扭转刚度对功率分流传动系统均载特性的影响[J]. 航空动力学报,2019,34(11): 2478-2489. JIN Guanghu,REN Wei,ZHU Rupeng. Influence of torsional stiffness on load sharing characteristics of power split transmission system[J]. Journal of Aerospace Power,2019,34(11): 2478-2489. (in ChineseJIN Guanghu, REN Wei, ZHU Rupeng. Influence of torsional stiffness on load sharing characteristics of power split transmission system[J]. Journal of Aerospace Power, 2019, 34(11): 2478-2489. (in Chinese) [22] 靳广虎,高鹏,周镇宇,等. 两次载荷分流齿轮传动构型的静力学均载特性[J]. 航空动力学报,2020,35(10): 2104-2114. JIN Guanghu,GAO Peng,ZHOU Zhenyu,et al. Static load sharing characteristic of twice load split gear transmission configuration[J]. Journal of Aerospace Power,2020,35(10): 2104-2114. (in ChineseJIN Guanghu, GAO Peng, ZHOU Zhenyu, et al. Static load sharing characteristic of twice load split gear transmission configuration[J]. Journal of Aerospace Power, 2020, 35(10): 2104-2114. (in Chinese) [23] 王朝兵,陈小安,陈宏,等. 误差随机性对行星齿轮系传动精度的影响特性[J]. 重庆大学学报,2012,35(9): 41-47. WANG Chaobing,CHEN Xiaoan,CHEN Hong,et al. Influence of error’s randomness on transmission accuracy of planetary gear[J]. Journal of Chongqing University,2012,35(9): 41-47. (in Chinese doi: 10.11835/j.issn.1000-582X.2012.09.007WANG Chaobing, CHEN Xiaoan, CHEN Hong, et al. Influence of error’s randomness on transmission accuracy of planetary gear[J]. Journal of Chongqing University, 2012, 35(9): 41-47. (in Chinese) doi: 10.11835/j.issn.1000-582X.2012.09.007 [24] 范伶松,任爱华,孙章栋,等. 考虑随机制造误差的差减速器齿轮副振动特性分析[J]. 机械传动,2021,45(11): 134-138, 171. FAN Lingsong,REN Aihua,SUN Zhangdong,et al. Vibration characteristic analysis of differential reducer gear pair considering random manufacturing error[J]. Journal of Mechanical Transmission,2021,45(11): 134-138, 171. (in ChineseFAN Lingsong, REN Aihua, SUN Zhangdong, et al. Vibration characteristic analysis of differential reducer gear pair considering random manufacturing error[J]. Journal of Mechanical Transmission, 2021, 45(11): 134-138, 171. (in Chinese) [25] 朱陆陆. 蒙特卡洛方法及应用[D]. 武汉: 华中师范大学,2014. ZHU Lulu. The Monte Carlo method and application[D]. Wuhan: Central China Normal University,2014. (in ChineseZHU Lulu. The Monte Carlo method and application[D]. Wuhan: Central China Normal University, 2014. (in Chinese) -
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