齿面修形对人字齿轮啮合刚度影响分析与试验研究
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摘要
为了准确地计算考虑轴向窜动的人字齿轮时变啮合刚度,建立考虑轴向窜动的人字齿轮轮齿承载接触分析模型,在此基础上推导考虑安装误差的人字齿轮轮齿综合啮合刚度,分析不同载荷下的啮合刚度变化特性;采用遗传算法对人字齿轮齿面展开以轮齿啮合刚度波动幅值为目标的齿面三维修形优化设计。以某单级人字齿轮副为对象的实例计算表明,考虑轴向窜动的人字齿轮副啮合刚度随着外载的增加而增加,且增长幅度随着载荷增加而减缓,最后刚度均值及其波形幅值均趋于稳态。搭建人字齿轮封闭功率流式试验台,给出利用高精度圆光栅对人字齿轮啮合刚度的测量方法,结果表明,理论计算与试验测量的人字齿轮啮合刚度随啮合周期变化波形基本保持一致,在给定负载下,最大偏差小于8.8%,且修形前后啮合刚度波动幅值变化趋势亦保持一致。
In order to accurately calculating the time varying meshing stiffness of a herringbone gear pair,a herringbone gear teeth contact model was established considering the axial floating of driving gear. On this basis,the meshing stiffness were considering installation errors was deduced,and the variation characteristics of meshing stiffness under different loads were analyzed. A three dimensional tooth profile optimization design considering the fluctuating magnitude of meshing stiffness as a target was carried out by using a genetic algorithm. Taking a ship herringbone gear transmission system as an example,the results consistently indicate that the herringbone gear meshing stiffness experiences a process of first increasing and then gradually tending to be constant with the increase of external load. A herringbone gear transmission experiment testing system with closed power flow was set up to verify the theoretical analysis,and the meshing stiffness was measured through high precision Heidenhain angle encoders. The results of numerical simulations and the experimental data are in good agreement,the maximum deviation is 8. 8 %,and the amplitude variation trend of the meshing stiffnesses before and after teeth modification is also consistent.
In order to accurately calculating the time varying meshing stiffness of a herringbone gear pair,a herringbone gear teeth contact model was established considering the axial floating of driving gear. On this basis,the meshing stiffness were considering installation errors was deduced,and the variation characteristics of meshing stiffness under different loads were analyzed. A three dimensional tooth profile optimization design considering the fluctuating magnitude of meshing stiffness as a target was carried out by using a genetic algorithm. Taking a ship herringbone gear transmission system as an example,the results consistently indicate that the herringbone gear meshing stiffness experiences a process of first increasing and then gradually tending to be constant with the increase of external load. A herringbone gear transmission experiment testing system with closed power flow was set up to verify the theoretical analysis,and the meshing stiffness was measured through high precision Heidenhain angle encoders. The results of numerical simulations and the experimental data are in good agreement,the maximum deviation is 8. 8 %,and the amplitude variation trend of the meshing stiffnesses before and after teeth modification is also consistent.
引文
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[12]任万龙,郝宗睿,王越,等.改进粒子群算法在三维水翼设计中的应用[J].江苏大学学报(自然科学版),2017,38(2):168-172.REN Wanlong,HAO Zongrui,WANG Yue,et al.Application of improved particle swarm algorithm in 3 D design of hydrofoil[J].Journal of Jiangsu University(Natural Science Edition),2017,38(2):168-172.
[13]何仁,徐益强.并联混合动力汽车混合驱动模式的换挡规律[J].江苏大学学报(自然科学版),2016,37(6):657-662.HE Ren,XU Yiqiang.Shift schedule of parallel hybrid electric vehicles under hybrid driving mode[J].Journal of Jiangsu University(Natural Science Edition),2016,37(6):657-662.
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[15]TANAKA N,OHNO K,INNAMI T.GDN-6 Dynamic load on spiral bevel gears(gear dynamics and noise)[C]//The JSME international Conference on Motion and Power Transmissions.Fukuoka:The Japan Society of Mechanical Engineers,2001:27-32.
[16]杨洋,詹永照,王新宇.基于相对位置的2阶段低级动作分割方法[J].江苏大学学报(自然科学版),2017,38(2):186-191.YANG Yang,ZHAN Yongzhao,WANG Xinyu.A two-phase low-level motion data segmentation method based on relative position[J].Journal of Jiangsu University(Natural Science Edition),38(2):186-191.
[17]杨洋,詹永照,王新宇.基于加权置信度的运动捕捉数据低级时域分割算法[J].江苏大学学报(自然科学版),2015,36(3):310-318.YANG Yang,ZHAN Yongzhao,WANG Xinyu.Low-level temporal segmentation of motion capture data based on weighted confidence[J].Journal of Jiangsu University(Natural Science Edition),2015,36(3):310-318.
[2]王峰.人字齿轮传动系统振动特性分析与试验研究[D].西安:西北工业大学,2014.
[3]李茹贞,赵清慧.齿轮强度设计资料[M].北京:机械工业出版社,1984.
[4]ZHANG J J,ESAT I I,SHI Y H.Load analysis with varying mesh stiffness[J].Computers&Structures,1999,70(3):273-280.
[5]卜忠红,刘更,吴立言.斜齿轮啮合刚度变化规律研究[J].航空动力学报,2010,25(4):957-962.BU Zhonghong,LIU Geng,WU Liyan.Research on the variation rules of meshing stiffness of the helical gear[J].Hangkong Dongli Xuebao/journal of Aerospace Power,2010,25(4):957-962.
[6]吴新跃,朱石坚.人字齿轮传动的振动理论分析模型[J].海军工程大学学报,2001,13(5):13-19.WU Xinyue,ZHU Shijian.Theoretical vibration pattern of herringbone gearing[J].Journal of Naval University of Engineering,2001,13(5):13-19.
[7]吴文光.人字齿轮传动系统的建模及其动力学特性的有限元分析研究[D].南京:南京航空航天大学,2010.
[8]LITVIN F L,CHEN J S,LU J.Application of finite element analysis for determination of load share,real contact ratio,precision of motion,and stress analysis[J].Journal of Mechanical Design,1996,168(4):561-567.
[9]王峰,方宗德,李声晋.滚动轴承支撑人字齿轮传动系统动力传递过程分析研究[J].机械工程学报,2014,50(3):25-32.WANG Feng,FANG Zongde,LI Shengjin.Research and analysis on power transmission processing of herringbone gear trains system with rolling bearing support[J].Journal of Mechanical Engineering,2014,50(3):25-32.
[10]王峰,方宗德,李声晋.多载荷工况下人字齿轮传动系统振动特性分析[J].振动与冲击,2013,32(1):49-52.WANG Feng,FANG Zongde,LI Shengjin.Dynamic characteristics of a double helical gear under multi-load[J].Journal of Vibration and Shock,2013,32(1):49-52.
[11]王峰,方宗德,李声晋.重合度对人字齿轮非线性系统振动特性的影响分析[J].振动与冲击,2014,33(3):18-22.WANG Feng,FANG Zongde,LI Shengjin.Effect of contact ratio on dynamic behavior of a double-helical gear nonlinear system[J].Journal of Vibration and Shock,2014,33(3):18-22.
[12]任万龙,郝宗睿,王越,等.改进粒子群算法在三维水翼设计中的应用[J].江苏大学学报(自然科学版),2017,38(2):168-172.REN Wanlong,HAO Zongrui,WANG Yue,et al.Application of improved particle swarm algorithm in 3 D design of hydrofoil[J].Journal of Jiangsu University(Natural Science Edition),2017,38(2):168-172.
[13]何仁,徐益强.并联混合动力汽车混合驱动模式的换挡规律[J].江苏大学学报(自然科学版),2016,37(6):657-662.HE Ren,XU Yiqiang.Shift schedule of parallel hybrid electric vehicles under hybrid driving mode[J].Journal of Jiangsu University(Natural Science Edition),2016,37(6):657-662.
[14]范垂本.齿轮的强度和试验[M].北京:机械工业出版社,1979:129-132.
[15]TANAKA N,OHNO K,INNAMI T.GDN-6 Dynamic load on spiral bevel gears(gear dynamics and noise)[C]//The JSME international Conference on Motion and Power Transmissions.Fukuoka:The Japan Society of Mechanical Engineers,2001:27-32.
[16]杨洋,詹永照,王新宇.基于相对位置的2阶段低级动作分割方法[J].江苏大学学报(自然科学版),2017,38(2):186-191.YANG Yang,ZHAN Yongzhao,WANG Xinyu.A two-phase low-level motion data segmentation method based on relative position[J].Journal of Jiangsu University(Natural Science Edition),38(2):186-191.
[17]杨洋,詹永照,王新宇.基于加权置信度的运动捕捉数据低级时域分割算法[J].江苏大学学报(自然科学版),2015,36(3):310-318.YANG Yang,ZHAN Yongzhao,WANG Xinyu.Low-level temporal segmentation of motion capture data based on weighted confidence[J].Journal of Jiangsu University(Natural Science Edition),2015,36(3):310-318.