Influence of Installation Position of Gear Pair Machined with Duplex Helical Method on Meshing Performance with Advancing or Retreating Conditions
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摘要: 螺旋锥齿轮副轴心偏置距、安装距、轴交角对其啮合性能有重要影响,本文针对准双曲面齿轮副正、反驱啮合性能,考虑不同相对安装位置调整量,在建立双重螺旋法加工的齿面基础上,采用齿面接触分析(TCA)和动力学分析方法,分别对齿轮副接触轨迹、传动误差和动态特性进行了研究。结果表明:极限VH值对大轮反驱面角加速度影响较正驱面显著;正极限V值有利于大轮正驱面动态性能改善;负极限V值易使大轮正驱面在齿根处产生边缘接触;正极限H值易使大轮正反驱面在齿根处产生边缘接触;通过齿轮副滚检实验验证了TCA仿真结果的正确性。同时,建立了安装位置调整量与接触迹位移量之间的映射关系,为预控齿面接触迹线位置提供参考。Abstract: The offset, pinion axis distance and shaft angle of hypoid gear have significant influence on its meshing performance. In view of meshing characteristics of hypoid gear pair with the conditions of advancing or retreating, considering adjustment of different relative installation positions, on the basis of the tooth flank machined with duplex helical method, via tooth contact analysis (TCA) and dynamic analysis, the contact trace, transmission error and dynamic characteristics of concave or convex are studied respectively. The results show that value of limit VH has a noticeable effect on the fluctuation of angular acceleration of concave comparing with convex, and the positive limit V is beneficial to the improvement of the dynamic performance of convex, and the negative limit V is easy to cause edge contact of convex, and the positive limit H is easy to cause edge contact of concave and convex. And the correctness of the TCA is verified by the rolling test. Also, the mapping function between the adjustment of installation position and the displacement of contact trace is established, which providesthe reference for the pre-control of the position of contact trace of tooth flank.
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Key words:
- duplex helical method /
- installation positions /
- meshing performance /
- concave /
- pre-control
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表 1 大小轮加工参数
参数名称 小轮 大轮 齿数 8 43 模数/mm 6.861 6.861 齿面宽/mm 44.691 41 偏置距/mm 25.4 0 轴交角/(°) 90 90 旋向 左旋 右旋 加工方法 双重螺旋法 成形法 螺旋运动系数 0.7661 0 螺旋角/(°) 45 33.788 齿顶高/mm 9.03 1.6 齿根高/mm 3.18 10.48 径向刀位/mm 117.385 116.573 角向刀位/mm 65.626 0 轴向轮位/mm −0.1467 3.1416 垂直轮位/mm 28.568 0 安装角/(°) −3.631 68.73 表 2 安装位置调整量
参数名称 范围 小轮偏置距调整量/mm −0.2~0.2 小轮安装距调整量/mm −0.2~0.2 轴交角调整量/(°) −0.03~0.03 表 3 接触参数
名称 数值 接触类型 体对体 刚度系数 3.16×109 N·s/m 阻尼系数 50 000 N·s/m 力指数 1.5 渗透深度 1.0×10−4 m 静摩擦系数 0.1 静摩擦系数 0.05 静滑移速度 1.0×10−4 m/s 动滑移速度 0.01 m/s 表 4 极限VH值对大轮正、反驱时角加速度
驱动情况 VH调整量/mm 均方根值/(rad·s−2) 波动幅值/% 正驱 ΔV=0,ΔH=0 608.31 – ΔV=0.2,ΔH=0 578.512 −4.9 ΔV=−0.2,ΔH=0 626.57 +3 ΔV=0,ΔH=0.2 655.137 +7.7 ΔV=0,ΔH=−0.2 603.31 −1 反驱 ΔV=0,ΔH=0 565.04 – ΔV=0.2,ΔH=0 598.67 +5.8 ΔV=−0.2,ΔH=0 633.514 +12.12 ΔV=0,ΔH=0.2 612.28 +8.36 ΔV=0,ΔH=−0.2 604.8 +7.04 -
[1] 苏进展, 方宗德. 弧齿锥齿轮印痕稳定性优化设计与试验[J]. 航空动力学报, 2012, 27(11): 2622-2628Su J Z, Fang Z D. Optimization design and test of stability of contact patterns of spiral bevel gears[J]. Journal of Aerospace Power, 2012, 27(11): 2622-2628 (in Chinese) [2] Liu G L, Zhang R T, Zhao N. Quantitative analysis of the influence of installation errors on the contact pattern of spiral bevel gears[J]. Applied Mechanics and Materials, 2011, 86: 278-282 [3] 唐进元, 杜晋. 考虑安装误差敏感性的螺旋锥齿轮主动设计方法[J]. 中国机械工程, 2009, 20(10): 1197-1202 doi: 10.3321/j.issn:1004-132X.2009.10.014Tang J Y, Du J. Active design method of spiral bevel gears considering mounting error sensitivity[J]. China Mechanical Engineering, 2009, 20(10): 1197-1202 (in Chinese) doi: 10.3321/j.issn:1004-132X.2009.10.014 [4] 汪中厚, 余剑, 张兴林. 安装误差对弧齿锥齿轮齿面接触轨迹影响的分析研究[J]. 机械传动, 2014, 38(2): 21-24Wang Z H, Yu J, Zhang X L. Analysis and study on the influence of installation error on spiral bevel gear tooth surface contact trajectory[J]. Journal of Mechanical Transmission, 2014, 38(2): 21-24 (in Chinese) [5] Ding H, Zhou Y S, Tang J Y, et al. A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears[J]. Mechanism and Machine Theory, 2017, 109: 155-170 [6] Ding H, Tang J Y, Zhou Y S, et al. A multi-objective correction of machine settings considering loaded tooth contact performance in spiral bevel gears by nonlinear interval number optimization[J]. Mechanism and Machine Theory, 2017, 113: 85-108 [7] 张碧玉, 孙月海, 邱杰. 螺旋变性展成法加工锥齿轮副的建模与仿真分析[J]. 机械科学与技术, 2017, 36(7): 1055-1062Zhang B Y, Sun Y H, Qiu J. Modeling and simulation analysis of spiral bevel gear processing using spread-out helix modified roll[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36(7): 1055-1062 (in Chinese) [8] Zhang Y, Yan H Z, Zeng T, et al. Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade[J]. Journal of Central South University, 2016, 23(3): 544-554 [9] Velex P, Maatar M. A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behaviour[J]. Journal of Sound and Vibration, 1996, 191(5): 629-660 [10] 严宏志, 刘明, 王祎维. 摆线齿准双曲面齿轮的动态啮合性能[J]. 中南大学学报, 2013, 44(10): 4026-4032Yan H Z, Liu M, Wang Y W. Dynamic meshing performance of cycloid hypoid gear[J]. Journal of Central South University , 2013, 44(10): 4026-4032 (in Chinese) [11] 戴瑜, 曾韬, 丁志文. 偏心机构磨削螺旋锥齿轮成型法大轮的研究[J]. 机械工程师, 2005,(11): 72-74 doi: 10.3969/j.issn.1002-2333.2005.11.039Dai Y, Zeng T, Ding Z W. Research on grinding the formate gear of spiral bevel gear by means of the eccentric mechanism[J]. Mechanical Engineer, 2005,(11): 72-74 (in Chinese) doi: 10.3969/j.issn.1002-2333.2005.11.039 [12] 喻子豪, 刘祚时, 张平. 基于Pro/E和Abaqus的弧齿锥齿轮建模与动态接触分析[J]. 机械传动, 2018, 42(10): 83-90Yu Z H, Liu Z S, Zhang P. Modeling and dynamic contact analysis of spiral bevel gear based on Pro/E and Abaqus[J]. Journal of Mechanical Transmission, 2018, 42(10): 83-90 (in Chinese) [13] 刘光磊, 张瑞庭, 赵宁, 等. 一种弧齿锥齿轮安装误差变动范围的确定方法[J]. 机械工程学报, 2012, 48(3): 34-40Liu G L, Zhang R T, Zhao N, et al. An approach to determine installation errors of spiral bevel gears[J]. Journal of Mechanical Engineering, 2012, 48(3): 34-40 (in Chinese) [14] 杜进辅, 方宗德, 徐敏, 等. 克林根贝格制准双曲面齿轮边缘承载接触分析[J]. 机械科学与技术, 2015, 34(7): 1002-1005Du J F, Fang Z D, Xu M, et al. Contact analysis of edge loaded tooth for Klingelnberg hypoid gears[J]. Mechanical Science and Technology for Aerospace Engineering, 2015, 34(7): 1002-1005 (in Chinese) [15] 黄丰云, 周子寒, 朱建国, 等. 基于ADAMS的主动齿轮轴承安装距的振动性能研究[J]. 机械传动, 2016, 40(6): 42-46Huang F Y, Zhou Z H, Zhu J G, et al. Research of the vibration performance of driving gear bearing mounting distance based on ADAMS[J]. Journal of Mechanical Transmission, 2016, 40(6): 42-46 (in Chinese)