基于有限元法的TI蜗杆副传动强度及热分析
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摘要
基于齿轮啮合、轮齿接触分析及传热学理论,利用有限元分析研究方法,对TI蜗杆副及ZC_1蜗杆副的传动强度及轮齿温度分布进行了系统分析。
通过探讨一般实体的三维造型技术,提出了基于虚拟制造技术及齿轮加工范成法实现ZC_1蜗杆副有限元建模的构建方法;以pro/e造型软件和ansys分析软件为技术平台,根据蜗杆副的数学模型及构造特点,获得了有益于有限元分析的蜗杆副有限元模型,为TI型与ZC_1型蜗杆传动强度的比较分析建立了基础。
基于三维弹性接触有限元法,探讨了一定载荷条件下,选用传统材料副时,TI蜗杆传动的啮合接触特点及应力分布状态;分析了相同设计参数下不同材料副TI蜗杆传动接触性能的差异;对不同载荷作用下的硬齿面副TI蜗杆传动齿间载荷分配进行了研究;并对基本相同条件下ZC_1型与TI型蜗杆传动的承载能力进行了比较分析。研究结果表明,与ZC_1型圆柱蜗杆传动相比,TI型环面蜗杆传动的瞬时接触齿对多,齿间载荷分配相对均匀,轮齿最大接触应力小。
运用传热学的基本知识,借鉴一般热系统的分析方法,建立了蜗杆减速器热系统模型;借助热电比拟原理,应用热网络方法模拟减速器热态网络,并建立了蜗杆传动系统的热网络图;数值计算得到给定中心距条件下蜗杆减速器的温度场分布,探讨了利用蜗杆减速器表面温度预测减速器效率的方法;基于热网络法获得的边界条件,通过有限元法分析了蜗杆副轮齿的温度场分布,验证了热网络分析方法的可靠性及有效性。
According to the theories of differential geometry and gearing meshing, tooth contact analysis and thermal transmission, the transmission strength of TI and ZC_1 worm gearing and tooth temperature are studied systematically by finite element method.
Based on the study of three-dimensional building for general solid, the FE model construction approach for ZC_1 worm drive is obtained through the combination of virtual manufacture technique and generating cutting method. Considering the mathematic pattern and structure feature, the ZC_1 model for finite element analysis is established by molding software and analysis software, which is made a base for further comparison and analysis of the transmission strength of the TI and ZC_1 worm gearing.
Under a certain load condition, the meshing contact characteristics and stress distribution state of the TI worm gearing with traditional material pair is studied by means of elastic contact analysis. The deference of transmission performance with deferent material pairs is analyzed and the load distribution between gear teeth on harden tooth pairs are discussed in the condition of different loads. The load-bearing capability of ZC_1 and TI worm gearing with the same design parameters is carried out for comparison, and the results suggest that, compared to ZC_1 cylinder worm gearing, the instantaneous contact tooth of the TI hourglass worm drive is more, the load distribution between engaging gear tooth is relatively uniform, and the maximum contact stress is smaller.
Using the analysis method of general thermal system for reference, the heat system model of worm speed reducer is obtained by thermal transfer theory. Meanwhile, on the base of thermal-electricity analogy principle, the thermal network method is applied on the establishment of the speed reducer thermal state chart. Then the temperature field of the speed reducer under certain center distance is calculated, and the method for predicting the transmission efficiency by temperature is discussed. Finally, the finite element method is utilized for analyzing the tooth temperature with the boundary condition obtained from the thermal network results.
通过探讨一般实体的三维造型技术,提出了基于虚拟制造技术及齿轮加工范成法实现ZC_1蜗杆副有限元建模的构建方法;以pro/e造型软件和ansys分析软件为技术平台,根据蜗杆副的数学模型及构造特点,获得了有益于有限元分析的蜗杆副有限元模型,为TI型与ZC_1型蜗杆传动强度的比较分析建立了基础。
基于三维弹性接触有限元法,探讨了一定载荷条件下,选用传统材料副时,TI蜗杆传动的啮合接触特点及应力分布状态;分析了相同设计参数下不同材料副TI蜗杆传动接触性能的差异;对不同载荷作用下的硬齿面副TI蜗杆传动齿间载荷分配进行了研究;并对基本相同条件下ZC_1型与TI型蜗杆传动的承载能力进行了比较分析。研究结果表明,与ZC_1型圆柱蜗杆传动相比,TI型环面蜗杆传动的瞬时接触齿对多,齿间载荷分配相对均匀,轮齿最大接触应力小。
运用传热学的基本知识,借鉴一般热系统的分析方法,建立了蜗杆减速器热系统模型;借助热电比拟原理,应用热网络方法模拟减速器热态网络,并建立了蜗杆传动系统的热网络图;数值计算得到给定中心距条件下蜗杆减速器的温度场分布,探讨了利用蜗杆减速器表面温度预测减速器效率的方法;基于热网络法获得的边界条件,通过有限元法分析了蜗杆副轮齿的温度场分布,验证了热网络分析方法的可靠性及有效性。
According to the theories of differential geometry and gearing meshing, tooth contact analysis and thermal transmission, the transmission strength of TI and ZC_1 worm gearing and tooth temperature are studied systematically by finite element method.
Based on the study of three-dimensional building for general solid, the FE model construction approach for ZC_1 worm drive is obtained through the combination of virtual manufacture technique and generating cutting method. Considering the mathematic pattern and structure feature, the ZC_1 model for finite element analysis is established by molding software and analysis software, which is made a base for further comparison and analysis of the transmission strength of the TI and ZC_1 worm gearing.
Under a certain load condition, the meshing contact characteristics and stress distribution state of the TI worm gearing with traditional material pair is studied by means of elastic contact analysis. The deference of transmission performance with deferent material pairs is analyzed and the load distribution between gear teeth on harden tooth pairs are discussed in the condition of different loads. The load-bearing capability of ZC_1 and TI worm gearing with the same design parameters is carried out for comparison, and the results suggest that, compared to ZC_1 cylinder worm gearing, the instantaneous contact tooth of the TI hourglass worm drive is more, the load distribution between engaging gear tooth is relatively uniform, and the maximum contact stress is smaller.
Using the analysis method of general thermal system for reference, the heat system model of worm speed reducer is obtained by thermal transfer theory. Meanwhile, on the base of thermal-electricity analogy principle, the thermal network method is applied on the establishment of the speed reducer thermal state chart. Then the temperature field of the speed reducer under certain center distance is calculated, and the method for predicting the transmission efficiency by temperature is discussed. Finally, the finite element method is utilized for analyzing the tooth temperature with the boundary condition obtained from the thermal network results.
引文
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3. 詹东安,交错轴渐开线型共轭副的啮合理论及应用研究[博士学位论文],西安:西安交通大学,1998
4. 刘洪斌,基于渐开线齿轮形修磨轮包络蜗杆传动理论研究及精加工 TI 蜗杆的新方法[博士学位论文],天津:天津大学,2001
5. 段路茜,TI 蜗杆传动啮合理论研究及优化设计[博士学位论文],天津:天津大学,2004
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8. Band R V, Peterson R E, Load and stress cycle in gear teeth, Mechanical Engineering, 1929, 51(9):635～662
9. Terauchi Y, Nagamua K, Study on deflection of spur gear teeth, Bull JSME, 1981, 23(188):447～452
10. Huseyin Filiz I, Eyercioqlu O, Evaluation of gear tooth stresses by finite element method, AMSE Journal of Engineering for Industry, 1995,117(2): 232～239
11. 吴鸿业,华崇志,用有限元法研究蜗杆副轮齿承载状况,机械工程学报,1991,27(4):30~36
12. 秦东兴,秦大同,石万凯,包络环面蜗杆传动的实体建模和几何分析,重庆大学学报,1998,21(4):86～88
13. Q Datong, Q Dongxing, Tooth contact analysis of hourglass worm gearing on the condition that errors mixed with deformation, International Journal of Gearing and Transmissions, 2000
14. 秦东兴,秦大同,杨洪成,包络环面蜗杆传动的承载接触研究,重庆大学学报(自然科学版),2001,24(2):1～4
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18. 徐步青,佟景伟,移动载荷下齿根应力的时间历程,机械传动,2001,25(3),21～24
19. Kawalec A, Wiktor J, Ceglarek D, Comparative analysis of tooth root strength using ISO and AGMA standards in spur and helical gears with FEM-based verification, Journal of Mechanical Design, 2006, 128 (5): 1141～1158
20. Tsai SJ, Wu SH, Experimental and numerical root stress analysis of conical gears, International conference on gears, VDI Berichte, VolsⅠ&Ⅱ, 2005:1127～1144
21. 胡如夫,张东速,中等功率条件下提高齿轮减速器的热效率研究,中国工程科学,2004,6(4):72～76
22. Lord AA, Gethin DT, Roylance BJ, Thermal analysis of gear transmission systems using experimental and finite element modeling techniques, Proceeding of the International Conference on Gearing, Transmissions, Mechanical Systems, 2000, 223～231
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24. Block H, The Thermal network method for predicting bulk temperature in gear transmission[M], Mew York: Wiley, 1969
25. 吴昌林,余联庆,方晓初,汽车变速箱的热网络分析,华中理工大学学报,1998,26(4):63～66
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34. 李绍彬,李润方,林腾蛟,行星齿轮传动装置内齿轮齿热有限元分析,机械传动,2003,27(1):1～2
35. 屈文涛,沈允文,徐建宁,双圆弧齿轮齿轮传动的温度场和热变形分析,石油机械,2006,34(3):13～19
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2. F.Jarchow, W.Predki, Tragfahigkeitsoptimierte Schneckentriebe, VDI~Berichtes, 1983, Nr.88:11～22
3. 詹东安,交错轴渐开线型共轭副的啮合理论及应用研究[博士学位论文],西安:西安交通大学,1998
4. 刘洪斌,基于渐开线齿轮形修磨轮包络蜗杆传动理论研究及精加工 TI 蜗杆的新方法[博士学位论文],天津:天津大学,2001
5. 段路茜,TI 蜗杆传动啮合理论研究及优化设计[博士学位论文],天津:天津大学,2004
6. 齐麟,张亚雄等,蜗杆传动设计(下册),北京:机械工业出版社,1987
7. 徐灏,机械设计手册(第一卷),北京:机械工业出版社,2004
8. Band R V, Peterson R E, Load and stress cycle in gear teeth, Mechanical Engineering, 1929, 51(9):635～662
9. Terauchi Y, Nagamua K, Study on deflection of spur gear teeth, Bull JSME, 1981, 23(188):447～452
10. Huseyin Filiz I, Eyercioqlu O, Evaluation of gear tooth stresses by finite element method, AMSE Journal of Engineering for Industry, 1995,117(2): 232～239
11. 吴鸿业,华崇志,用有限元法研究蜗杆副轮齿承载状况,机械工程学报,1991,27(4):30~36
12. 秦东兴,秦大同,石万凯,包络环面蜗杆传动的实体建模和几何分析,重庆大学学报,1998,21(4):86～88
13. Q Datong, Q Dongxing, Tooth contact analysis of hourglass worm gearing on the condition that errors mixed with deformation, International Journal of Gearing and Transmissions, 2000
14. 秦东兴,秦大同,杨洪成,包络环面蜗杆传动的承载接触研究,重庆大学学报(自然科学版),2001,24(2):1～4
15. 李秀珍,鲁宝香,李贵涛等,ZC1 蜗杆传动变形的有限元分析,机械设计与研究,1999,2,52～54
16. [日]仙庄正波,齿轮强度计算[M],姜勇译,北京:机械工业出版社,1984
17. V. Simon, Stress analysis in double enveloping worm gears by finite element method, Transactions of the ASME Journal of Mechanical Design, 1993, 115:179～185
18. 徐步青,佟景伟,移动载荷下齿根应力的时间历程,机械传动,2001,25(3),21～24
19. Kawalec A, Wiktor J, Ceglarek D, Comparative analysis of tooth root strength using ISO and AGMA standards in spur and helical gears with FEM-based verification, Journal of Mechanical Design, 2006, 128 (5): 1141～1158
20. Tsai SJ, Wu SH, Experimental and numerical root stress analysis of conical gears, International conference on gears, VDI Berichte, VolsⅠ&Ⅱ, 2005:1127～1144
21. 胡如夫,张东速,中等功率条件下提高齿轮减速器的热效率研究,中国工程科学,2004,6(4):72～76
22. Lord AA, Gethin DT, Roylance BJ, Thermal analysis of gear transmission systems using experimental and finite element modeling techniques, Proceeding of the International Conference on Gearing, Transmissions, Mechanical Systems, 2000, 223～231
23. Yshio Terauch, On the heat balance of gear equipment, ASME Int. J, vol.34, No.1, P97～105, 1991
24. Block H, The Thermal network method for predicting bulk temperature in gear transmission[M], Mew York: Wiley, 1969
25. 吴昌林,余联庆,方晓初,汽车变速箱的热网络分析,华中理工大学学报,1998,26(4):63～66
26. Block H, The flash temperature concept [J], Wear, 1963,6:483～493
27. T. Tobe, M. Kato, A study on flash temperatures on the spur gear teeth, Transactions of the ASME, Journal of Engineering for Industry ,1974
28. Y. Terauchi, H. Mori, Comparison of theories and experimental results for surface temperature of spur gear teeth, Transactions of the ASME, Journal of Engineering for Industry, 1974
29. Y. Herauchi, K. Hagamura, C. L Wu, On the heat balance of gear meshing (experimental and analytical heat transfer coefficicent on tooth faces), JSME International Journal, series |||, vol. 32, No. 3, 1989
30. G. Deng, M. Kato, N. Maruyama, K. Morikawa and N. Hitomi, Initial temperature evaluation for flash temperature index of gear tooth, Transactions of the ASME, Journal of Tribology, vol. 117, 1995
31. 孙月海,王树人、程福安,临近蜗轮齿面处温度的实验研究,机械传动,1997,21(4):30～33
32. Lord AA, Gethin DT, Roylance BJ, Thermal analysis of gear transmission systems experimental and finite element modeling techniques, Proceeding of the International Conference on Gearing, Transmission, Mechanical System, 2000, 223～331
33. 李润方,黎豫生,耦合热弹性接触有限元法及其在齿轮传动中的应用,重庆大学学报,1993,16(1):96～101
34. 李绍彬,李润方,林腾蛟,行星齿轮传动装置内齿轮齿热有限元分析,机械传动,2003,27(1):1～2
35. 屈文涛,沈允文,徐建宁,双圆弧齿轮齿轮传动的温度场和热变形分析,石油机械,2006,34(3):13～19
36. D. P. Townsend and L. S. Akin, Analytical and experimental spur gear tooth temperature as affected by operating variables, Transaction of ASME, Journal of Mechanical Design, vol. 103, 1981
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