齿间动态载荷分配下的齿轮磨损分析
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摘要
为了寻求与实际更为符合的直齿圆柱齿轮磨损量计算方法,基于单双齿交替啮合和磨损后轮廓形状改变对齿间载荷的影响,推导了相邻2对轮齿在共同承担载荷时的动态载荷分配公式,得到了啮合轮齿的齿间动态载荷;基于Winkler弹性模型和轮齿啮合原理,获得了磨损量计算所需要的压力分布及啮合速度;基于Archard磨损模型,推导了齿轮的磨损量计算模型。算例显示:随着磨损次数的增加,磨损量逐渐增大;齿根处磨损最为剧烈,单双齿转换处的磨损有缓慢微幅波动;磨损与载荷耦合增加;在考虑载荷分配后,最大磨损量大幅减小。研究表明,计算齿轮磨损需考虑齿轮间动态载荷的分配问题。
To put forward a more practical calculation method of wear in spur gears,based on the influence of alternative gear meshing and profile deviation on teeth load,the formula of load distribution among gear teeth is deduced.And then the distributed pressure and velocity of meshing point are calculated on the basis of the Winkler's elastic model and principle of gear meshing.The wear model of spur gear is obtained based on the Archard's wear model.Numerical example shows that the wear of each meshing point on tooth profile accumulates as wearing cycles increase,the wear at the conversion position from single to double teeth-meshing area fluctuates slightly and slowly,the wear changes sharply near the root of the gear,the gear's dynamic load and wear are coupled to grow,and the maximum wear decreases greatly after considering load distribution.This study shows that the load distribution among gear teeth should be considered for wear calculation.
To put forward a more practical calculation method of wear in spur gears,based on the influence of alternative gear meshing and profile deviation on teeth load,the formula of load distribution among gear teeth is deduced.And then the distributed pressure and velocity of meshing point are calculated on the basis of the Winkler's elastic model and principle of gear meshing.The wear model of spur gear is obtained based on the Archard's wear model.Numerical example shows that the wear of each meshing point on tooth profile accumulates as wearing cycles increase,the wear at the conversion position from single to double teeth-meshing area fluctuates slightly and slowly,the wear changes sharply near the root of the gear,the gear's dynamic load and wear are coupled to grow,and the maximum wear decreases greatly after considering load distribution.This study shows that the load distribution among gear teeth should be considered for wear calculation.
引文
[1]ANDERSSON S.Partial EHD theory and initial wear of gears[D].Stockholm,Sweden:Royal Institute of Technology,1975.
[2]FLODIN A,ANDERSSON S.Simulation of mild wear in spur gears[J].Wear,1997,207:16-23.
[3]FLODIN A.Wear of spur and helical gears[D].Stockholm,Sweden:Royal Institute of Technology,2000.
[4]WU S,CHENG H S.Sliding wear calculation in spur gears[J].Journal of Tribology,1993,115:493-500.
[5]王晓笋,巫世晶,周旭辉,等.含磨损故障的齿轮传动系统非线性动力学特性[J].振动与冲击,2013,32(16):37-43,69.WANG Xiao-sun,WU Shi-jing,ZHOU Xu-hui,et al.Nonlinear dynamics analysis of gear transmission system with wear fault[J].Journal of Vibration and Shock,2013,32(16):37-43,69.
[6]KUANG J H,LIN A D.The effect of tooth wear on the vibration spectrum of a spur gear pair[J].Journal of Vibration and Acoustics,2001,123:311-317.
[7]LIU X,YANG Y,ZHANG J.Investigation on coupling effects between surface wear and dynamics in a spur gear system[J].Tribology International,2016,101:383-394.
[8]JOHNSON K L.Contact mechanics[M].Cambridge,UK:Cambridge University Press,1985:104-106.
[9]张奎晓,胡鹏,张义民.基于渐开线齿轮精确建模的啮合刚度的数值计算[J].机械设计与制造,2013(2):66-73.ZHANG Kui-xiao,HU Peng,ZHANG Yi-min.Numerical calculation of meshing stiffness based on precise modeling of involute gear[J].Machinery Design&Manufacture,2013(2):66-73.
[10]冯松,毛军红,谢友柏.齿面磨损对齿轮啮合刚度影响的计算与分析[J].机械工程学报,2015,51(15):27-32.FENG Song,MAO Junhong,XIE Youbai.Analysis and calculation of gear mesh stiffness with tooth wear[J].Journal of Mechanical Engineering,2015,51(15):27-32.
[11]王淑仁,闫玉涛,丁津原.渐开线直齿圆柱齿轮啮合磨损试验研究[J].东北大学学报(自然科学版),2004,25(2):146-149.WANG Shu-ren,YAN Yu-tao,DING Jin-yuan.Experimental study on mesh-wear of involute spur gears[J].Journal of Northeastern University(Natural Science),2004,25(2):146-149.
[12]FLODIN A.Wear investigation of spur gear teeth[J].Tribotest Journal,2000(7):45-60.
[2]FLODIN A,ANDERSSON S.Simulation of mild wear in spur gears[J].Wear,1997,207:16-23.
[3]FLODIN A.Wear of spur and helical gears[D].Stockholm,Sweden:Royal Institute of Technology,2000.
[4]WU S,CHENG H S.Sliding wear calculation in spur gears[J].Journal of Tribology,1993,115:493-500.
[5]王晓笋,巫世晶,周旭辉,等.含磨损故障的齿轮传动系统非线性动力学特性[J].振动与冲击,2013,32(16):37-43,69.WANG Xiao-sun,WU Shi-jing,ZHOU Xu-hui,et al.Nonlinear dynamics analysis of gear transmission system with wear fault[J].Journal of Vibration and Shock,2013,32(16):37-43,69.
[6]KUANG J H,LIN A D.The effect of tooth wear on the vibration spectrum of a spur gear pair[J].Journal of Vibration and Acoustics,2001,123:311-317.
[7]LIU X,YANG Y,ZHANG J.Investigation on coupling effects between surface wear and dynamics in a spur gear system[J].Tribology International,2016,101:383-394.
[8]JOHNSON K L.Contact mechanics[M].Cambridge,UK:Cambridge University Press,1985:104-106.
[9]张奎晓,胡鹏,张义民.基于渐开线齿轮精确建模的啮合刚度的数值计算[J].机械设计与制造,2013(2):66-73.ZHANG Kui-xiao,HU Peng,ZHANG Yi-min.Numerical calculation of meshing stiffness based on precise modeling of involute gear[J].Machinery Design&Manufacture,2013(2):66-73.
[10]冯松,毛军红,谢友柏.齿面磨损对齿轮啮合刚度影响的计算与分析[J].机械工程学报,2015,51(15):27-32.FENG Song,MAO Junhong,XIE Youbai.Analysis and calculation of gear mesh stiffness with tooth wear[J].Journal of Mechanical Engineering,2015,51(15):27-32.
[11]王淑仁,闫玉涛,丁津原.渐开线直齿圆柱齿轮啮合磨损试验研究[J].东北大学学报(自然科学版),2004,25(2):146-149.WANG Shu-ren,YAN Yu-tao,DING Jin-yuan.Experimental study on mesh-wear of involute spur gears[J].Journal of Northeastern University(Natural Science),2004,25(2):146-149.
[12]FLODIN A.Wear investigation of spur gear teeth[J].Tribotest Journal,2000(7):45-60.