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摘要:
为了进一步提高金属蜗杆与塑料斜齿轮传动中塑料齿轮的承载能力,研究了传统等齿距蜗杆与斜齿轮啮合传动时受力的特点,提出了蜗杆与斜齿轮不等齿距啮合方法。基于梁弯曲理论和轮齿变形理论,得到了齿面载荷、变形及接触刚度的关系,并以轮齿齿根弯曲变形率相等为前提,推导了不等齿距啮合的设计方法,得到了不等齿距啮合时蜗杆的齿距调整量,通过静态强度实验进行了验证。实验结果表明:不等齿距设计可以使塑料斜齿轮的承载能力提高13.69%。
Abstract:In order to further improve the bearing capacity of plastic gears in the transmission of metal worm and plastic helical gears, the force characteristics of the traditional equal-pitch worm helical gear meshing transmission were studied in depth, and the unequal pitch meshing of the worm and the helical gear was innovatively proposed. Based on beam bending theory and gear tooth deformation theory, the relationship between tooth surface load, deformation and contact stiffness is obtained.On the premise that the bending deformation rate of the gear tooth root is equal, the theoretical design method of unequal meshing is deduced, and the pitch adjustment of the worm in the case of unequal pitch meshing is obtained, which is verified by static strength experiments.The experimental results show that the unequal pitch design can increase the load-bearing capacity of the plastic helical gear by 13.69%.
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Key words:
- unequal tooth pitch /
- metal worm /
- plastic helical gear /
- meshing theory /
- tooth root bending stress
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表 1 式(7)~式(10)中符号及意义
Table 1. Symbols and meanings in formula (7)-(10)
参数 含义 B/mm 齿宽 E/Pa 弹性模量 Fi/N 每齿法向载荷 Sk/mm 齿顶厚 w/mm 悬臂梁长度 Sm/mm 载荷作用线与齿根圆之间的距离 SF/mm 危险截面宽度 z/mm 危险截面与齿根圆之间的距离 n/mm 全齿高 α/(°) 加载角 δB/mm 轮齿接触点弹性弯曲挠度 δS/mm 轮齿剪切变形 δg/mm 轮齿基体偏移量 δp/mm 赫兹接触压力产生的变形 δ/mm 轮齿总挠度 ν 泊松比 ρ1, ρ2/mm 蜗杆斜齿轮的曲率半径 表 2 实验样板参数
Table 2. Experimental model parameters
参数 等齿距蜗杆 不等齿距蜗杆 塑料斜齿轮 法向模数 1 0.985 1 法向压力角/(°) 12 12 12 螺旋角/旋向 9°9′44″(左) 9°9′44″(左) 9°9′44″(左) 齿数 1 1 63 轴向齿距/mm 3.182 2 3.134 5 3.182 2 齿顶圆直径/mm 7.9 7.9 65.35 齿根圆直径/mm 4.36 4.36 61.9 -
[1] 云永琥, 胡泓, 塔静宁. 塑料斜齿轮与钢制蜗杆啮合力变化规律的研究[J]. 机械传动, 2018, 42(11): 27-32. https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201811005.htmYUN Y H, HU H, TA J N. Research of the variation of meshing force of the plastic helical gear and steel worm[J]. Journal of Mechanical Transmission, 2018, 42(11): 27-32(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201811005.htm [2] 欧阳志喜, 石照耀. 塑料齿轮设计与制造[M]. 北京: 化学工业出版社, 2011: 343-350.OUYANG Z X, SHI Z Y. Design and manufacturing of plastic gears[M]. Beijing: Chemical Industry Press, 2011: 343-350(in Chinese). [3] LETZELTER E, VAUJANY J P. Quasi static load sharing model in the case of nylon 6/6 cylindrical gears[J]. Materials & Design, 2009, 30(10): 4360-4368. [4] 姜碧琼, 任重义, 段建中. 双圆弧齿轮啮合点载荷分配研究[J]. 机械传动, 2017, 41(4): 58-61. https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201704013.htmJIANG B Q, REN Z Y, DUAN J Z. Research of the load distribution at the meshing point of double circular arc gear[J]. Journal of Mechanical Transmission, 2017, 41(4): 58-61(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201704013.htm [5] 符双学, 周长江, 韩旭. 典型工况下啮合齿间有效载荷分布及齿轮强度分析[J]. 机械传动, 2016, 40(8): 102-106. https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201608023.htmFU S X, ZHOU C J, HAN X. Payload distribution and gear strength analysis of gear meshing process under the typical contact condition[J]. Journal of Mechanical Transmission, 2016, 40(8): 102-106(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201608023.htm [6] 王博. 塑料斜齿轮钢制蜗杆传动强度与传动性能研究[D]. 长春: 吉林大学, 2016: 56-58.WANG B. Transmission strength and performance study of plastic helical gear and steel worm drive[D]. Changchun: Jilin University, 2016: 56-58(in Chinese). [7] 孙训方. 材料力学[M]. 5版. 北京: 科学出版社, 2009: 205-210.SUN X F. Mechanics of materials[M]. 5th ed. Beijing: Science Press, 2009: 205-210(in Chinese). [8] 刘鸿文. 材料力学[M]. 5版. 北京: 高等教育出版社, 2011: 286-290.LIU H W. Mechanics of materials[M]. 5th ed. Beijing: Higher Education Press, 2011: 286-290(in Chinese). [9] ELKHOLY A H. Tooth load sharing in high-contact ratio spur gears[J]. ASME Journal of Mechanisms, Transmissions, and Automation in Design, 1985, 107(1): 11-16. doi: 10.1115/1.3258674 [10] FALAH A H, ELKHOLY A H. Load and stress analysis of cylindrical worm gearing using tooth slicing method[J]. Transactions of the Canadian Society for Mechanical Engineering, 2006, 30(1): 97-112. doi: 10.1139/tcsme-2006-0007 [11] LITVIN F L, FUENTES A. Gear geometry and applied theory[M]. Cambridge: Cambridge University Press, 2004: 441-475. [12] SHIGLEY J A, MISCHKE C R, BUDYNAS R G. Mechanical engineering design[M]. 9th ed. New York: McGraw-Hill Inc, 2010: 721-780. [13] 郝一舒, 李磊. 基于COSMOS/Works的塑料斜齿轮与钢制蜗杆啮合特性研究[J]. 机械设计, 2007, 24(2): 56-59. https://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ200702018.htmHAO Y S, LI L. Research on the characteristics of engagement between plastic helical gear and steel worm based on COSMOS/Works[J]. Journal of Machine Design, 2007, 24(2): 56-59(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ200702018.htm [14] 刘舸. 圆柱蜗杆斜齿轮传动的理论分析及试验研究[D]. 重庆: 重庆大学, 2004: 78.LIU G. Theoretical analysis and experimental investigation of an involute cylindrical worm-helical gear drive[D]. Chongqing: Chongqing University, 2004: 78(in Chinese). [15] 张生明. 论斜齿轮与蜗杆配合方法和工艺探析[J]. 中国医疗设备, 2009, 24(12): 24-26. doi: 10.3969/j.issn.1674-1633.2009.12.008ZHANG S M. Discussion on coordinated methods and technique of bevel wheel and worm[J]. Information of Medical Equipment, 2009, 24(12): 24-26(in Chinese). doi: 10.3969/j.issn.1674-1633.2009.12.008 [16] 李磊. 塑料蜗轮与钢制蜗杆的啮合性能研究[D]. 上海: 同济大学, 2007: 83.LI L. Research of the gearing characteristics between plastic worm wheel and steel worm[D]. Shanghai: Tongji University, 2007: 83(in Chinese). [17] 魏敏, 魏勇. 汽车微电机中蜗杆斜齿轮啮合传动设计[J]. 装备制造技术, 2012(9): 49-51. doi: 10.3969/j.issn.1672-545X.2012.09.018WEI M, WEI Y. The design of worm and spiral gear meshing transmission in the automobile micro motors[J]. Manufacturing Technology, 2012(9): 49-51(in Chinese). doi: 10.3969/j.issn.1672-545X.2012.09.018 [18] 鲍洪, 安琦. 渐开线直齿轮轮齿载荷及应力计算方法[J]. 华东理工大学学报(自然科学版), 2012, 38(1): 116-122. https://www.cnki.com.cn/Article/CJFDTOTAL-HLDX201201019.htmBAO H, AN Q. A method of calculating load and stress of involute spur gear[J]. Journal of East China University of Science and Technology(Natural Science Edition), 2012, 38(1): 116-122(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HLDX201201019.htm [19] HEINZ P B. Understanding right-angle gear backlash[J]. Hydrocarbon Processing, 2017, 1: 54. [20] 罗光汉. 基于Pro/E的斜齿齿轮副变位系数与侧隙的优化设计[J]. 制造业自动化, 2016, 38(2): 115-116. https://www.cnki.com.cn/Article/CJFDTOTAL-JXGY201602029.htmLUO G H. The optimization of modification coefficient and backlash of helical gear pairs based on Pro/E[J]. Manufacturing Automation, 2016, 38(2): 115-116(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXGY201602029.htm [21] 郝一舒, 岳滨楠. 塑料斜齿轮与钢制蜗杆的啮合理论分析[J]. 机械传动, 2009, 33(5): 9-11.HAO Y S, YUE B N. Analysis of the mesh theory between plastic helical gear and steel worm[J]. Journal of Mechanical Transmission, 2009, 33(5): 9-11(in Chinese). [22] 郝一舒, 马士涛. 塑料斜齿轮与钢制蜗杆传动的非线性边界分析[J]. 机械设计, 2008, 25(7): 45-48. https://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ200807016.htmHAO Y S, MA S T. Nonlinear boundary analysis of plastic helical gear and steel worm transmission[J]. Journal of Machine Design, 2008, 25(7): 45-48(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JXSJ200807016.htm