齿轮疲劳寿命及齿根裂纹仿真分析
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摘要
齿轮传动具有效率高、结构紧凑、工作可靠和传动比稳定等特点,广泛应用于机械传动领域。在齿轮所有失效形式中,疲劳断齿所占比例最大,其次是表面接触疲劳,因此疲劳破坏是齿轮失效的最主要形式之一。开展齿轮疲劳寿命及齿根裂纹仿真方法研究,对提高齿轮的可靠性和使用寿命具有重要的理论意义和工程应用价值。
本课题来源于国家科技支撑计划项目。综合运用机械疲劳分析理论、断裂力学理论以及有限元法和边界元法,对齿轮的疲劳寿命问题进行数值仿真分析。本文的主要研究工作如下:
①对风电机组各工况实测输入转矩的随机载荷历程进行雨流循环计数,得到载荷循环数、均值与幅值的关系,并将其合成为转矩总载荷谱。
②在ANSYS中建立增速箱输出级斜齿轮副的三维接触有限元模型,计算静载荷下斜齿轮副的应力应变;在FE-SAFE软件中,考虑材料的S-N曲线和应变-寿命曲线,采用名义应力法和局部应力应变法计算了斜齿轮副的疲劳寿命,并研究了载荷、表面粗糙度、残余应力以及轮齿修形对斜齿轮副疲劳寿命的影响规律。
③采用三维断裂分析软件FRANC3D,对含半椭圆形初始裂纹的直齿轮模型进行边界元分析,计算齿根裂纹前缘的应力强度因子,并研究了载荷、裂纹大小和裂纹形状对齿根初始裂纹应力强度因子的影响规律。
④利用FRANC3D的边界元裂纹自动扩展功能,模拟了齿根和齿面裂纹的扩展轨迹,分析了齿根裂纹扩展过程中的裂纹张开位移和应力强度因子,并对齿根裂纹扩展寿命进行估算。
As the characteristic of high efficiency, compact structure, reliable operation and stable transmission ratio etc, gear transmission is widely used in mechanical transmission field. Of all gear fatigue failure forms, fatigue broken of teeth takes up a largest proportion, followed by surface contact fatigue. Therefore fatigue damage is one of the main forms of gear failure. The research on gear fatigue life and tooth root crack simulation method has important theoretical significance and great engineering application value to improve the reliability and service life of gear.
The project is supported by National Key Technology R&D Program of China. With mechanical fatigue analysis theory, fracture mechanics theory, finite element method and boundary element method, a comprehensive numerical simulation analysis of gear fatigue life has been carried out. The main research work in this paper can be summarized as follows:
1) After carrying out rain-flow counting for random load histories of wind turbine input torque in every working condition, the relation of load cycles, mean value and amplitude of the torque is obtained. Meanwhile, the total load spectrum of torque is combined.
2) In ANSYS, 3D contact finite element model of output gear pair of speed-increase gearbox is built to calculate the stress-strain of helical gear pair under static load. Considering S-N curves and strain-life curves of materials, fatigue life of the helical gear pair is calculated by nominal stress method and local stress strain method respectively in FE-SAFE. Furthermore, the influence of load magnitude, residual stress, tooth surface roughness and profile modification on fatigue life of helical gear pair is researched.
3) Boundary element analysis of spur gear model with a semioval initial crack is carried out with 3D fracture analysis software FRANC3D to calculate stress intensity factors of tooth root crack front, and then the influence of load magnitude, crack size and crack shape to stress intensity factors on tooth root initial crack is researched.
4) Using the boundary element based crack automatic propagation function of FRANC3D, growth trajectories of cracks in tooth root and tooth surface are simulated. The crack opening displacement and stress intensity factors are analyzed in the process of crack growth in tooth root, and then the tooth root crack growth life is predicted.
本课题来源于国家科技支撑计划项目。综合运用机械疲劳分析理论、断裂力学理论以及有限元法和边界元法,对齿轮的疲劳寿命问题进行数值仿真分析。本文的主要研究工作如下:
①对风电机组各工况实测输入转矩的随机载荷历程进行雨流循环计数,得到载荷循环数、均值与幅值的关系,并将其合成为转矩总载荷谱。
②在ANSYS中建立增速箱输出级斜齿轮副的三维接触有限元模型,计算静载荷下斜齿轮副的应力应变;在FE-SAFE软件中,考虑材料的S-N曲线和应变-寿命曲线,采用名义应力法和局部应力应变法计算了斜齿轮副的疲劳寿命,并研究了载荷、表面粗糙度、残余应力以及轮齿修形对斜齿轮副疲劳寿命的影响规律。
③采用三维断裂分析软件FRANC3D,对含半椭圆形初始裂纹的直齿轮模型进行边界元分析,计算齿根裂纹前缘的应力强度因子,并研究了载荷、裂纹大小和裂纹形状对齿根初始裂纹应力强度因子的影响规律。
④利用FRANC3D的边界元裂纹自动扩展功能,模拟了齿根和齿面裂纹的扩展轨迹,分析了齿根裂纹扩展过程中的裂纹张开位移和应力强度因子,并对齿根裂纹扩展寿命进行估算。
As the characteristic of high efficiency, compact structure, reliable operation and stable transmission ratio etc, gear transmission is widely used in mechanical transmission field. Of all gear fatigue failure forms, fatigue broken of teeth takes up a largest proportion, followed by surface contact fatigue. Therefore fatigue damage is one of the main forms of gear failure. The research on gear fatigue life and tooth root crack simulation method has important theoretical significance and great engineering application value to improve the reliability and service life of gear.
The project is supported by National Key Technology R&D Program of China. With mechanical fatigue analysis theory, fracture mechanics theory, finite element method and boundary element method, a comprehensive numerical simulation analysis of gear fatigue life has been carried out. The main research work in this paper can be summarized as follows:
1) After carrying out rain-flow counting for random load histories of wind turbine input torque in every working condition, the relation of load cycles, mean value and amplitude of the torque is obtained. Meanwhile, the total load spectrum of torque is combined.
2) In ANSYS, 3D contact finite element model of output gear pair of speed-increase gearbox is built to calculate the stress-strain of helical gear pair under static load. Considering S-N curves and strain-life curves of materials, fatigue life of the helical gear pair is calculated by nominal stress method and local stress strain method respectively in FE-SAFE. Furthermore, the influence of load magnitude, residual stress, tooth surface roughness and profile modification on fatigue life of helical gear pair is researched.
3) Boundary element analysis of spur gear model with a semioval initial crack is carried out with 3D fracture analysis software FRANC3D to calculate stress intensity factors of tooth root crack front, and then the influence of load magnitude, crack size and crack shape to stress intensity factors on tooth root initial crack is researched.
4) Using the boundary element based crack automatic propagation function of FRANC3D, growth trajectories of cracks in tooth root and tooth surface are simulated. The crack opening displacement and stress intensity factors are analyzed in the process of crack growth in tooth root, and then the tooth root crack growth life is predicted.
引文
[1] Pariente I F, Guagliano M. Contact fatigue damage analysis of shot peened gears by means of X-ray measurements[J]. Engineering Failure Analysis, 2009, 16(3): 964-971.
[2] Sekercioglu T, Kovan V. Pitting failure of truck spiral bevel gear[J]. Engineering Failure Analysis, 2007, 14(4): 614-619.
[3] Pandey R K. Failure analysis of coal pulveriser gear box[J]. Engineering Failure Analysis, 2007, 14(4): 541-547.
[4] Asi O. Fatigue failure of a helical gear in a gearbox[J]. Engineering Failure Analysis, 2006, 13(7): 1116-1125.
[5]李国云,秦大同.风力发电机齿轮箱加速疲劳试验技术分析[J].重庆大学学报,2009,32(11):1252-1256.
[6]陈举华,徐楠,安艳秋.42CrMo材料硬齿面齿轮全寿命试验及数据分析[J].机械传动,2005,29(5):63-65.
[7]王威强,徐楠,贺庆强.42CrMo硬齿面齿轮虚拟全寿命的试验与分析[J].农业机械学报,2006,37(3):126-129.
[8]赵宁,李虎.应用修正的P-S-N曲线计算齿轮疲劳寿命[J].现代制造工程,2007,(5):105-108.
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[11]王国军,闫清东.齿轮弯曲疲劳寿命有限元计算方法研究[J].农业装备与车辆工程,2006,(1):40-42.
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[13]陈赛克,王毅.基于精确模型的齿轮接触疲劳寿命有限元分析[J].机械传动,2007,31(2):81-82.
[14]章文强,盛云,于莉等.燃料电池轿车变速器齿轮接触应力分析及疲劳寿命计算[J].计算机辅助设计,2007,16(4):36-39.
[15]陈德民.圆柱斜齿轮动态强度与疲劳损伤仿真[J].计算机辅助工程,2006,(15):294-296.
[16]袁菲,徐颖强.考虑齿间载荷分布的齿轮弯曲疲劳寿命估算[J].机械设计,2006,23(4):35-37.
[17]夏延秋,丁津原,马先贵等.摩擦系数对齿轮接触疲劳寿命的影响[J].机械传动,2002,26(1):48-49.
[18] Guagliano M, Riva E, Guidetti M. Contact fatigue failure analysis of shot-peened gears[J].Engineering Failure Analysis, 2002, 9(2): 147–158.
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[21] Glodez S, Sraml M, Kramberger J. A computational model for determination of service life of gears[J]. International Journal of Fatigue, 2002, 24(10): 1013–1020.
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[23] Abersek B, Flasker J, Glodez S. Review of mathematical and experimental models for determination of service life of gears[J]. Engineering Fracture Mechanics, 2004, 71 (4-6): 439-453.
[24] Kramberger J, Sraml M, Potrc I, et al. Numerical calculation of bending fatigue life of thin-rim spur gears[J]. Engineering Fracture Mechanics, 2004, 71 (4-6): 647–656.
[25] Glodez S, Abersek B, Flasker J, et al. Evaluation of the service life of gears in regard to surface pitting[J]. Engineering Fracture Mechanics, 2004, 71 (4-6): 429–438.
[26] Glodez S, Ren Z, Flasker J. Surface fatigue of gear teeth flanks[J]. Computers and Structures,1999, 73(1-5): 475-483.
[27]周赵风,徐梓斌.齿轮轮齿裂缝的产生及其应力分析[J].机械强度,2004,26(2):231-234.
[28] Guagliano M, Vergani L. Mode I stress intensity factors for curved cracks in gears by a weight functions method[J]. Fatigue and Fracture of Engineering Materials and Stmctures, 2001, 24(1): 41-52.
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[30]顾浩.渐开线齿轮齿根断裂力学分析[D].南京航空航天大学,2007.
[31]张洪才,黄克正,陈举华.基于断裂力学理论的表面淬火齿轮疲劳寿命的数值计算[J].应用力学学报,2004,21(1):17-21.
[32]邵忍平,黄欣娜,李宗斌.裂纹对齿轮轮齿结构振动的影响[J].机械强度,2004,26(6):629-635.
[33]张延超,邵忍平,刘宏昱.裂纹故障对齿轮传动系统动力特性的影响[J].机械设计与制造,2006,10:12-14.
[34]邵忍平,徐志锋,曹精明.裂纹故障齿轮结构声振特性与模拟研究[J].航空动力学报,2010,25(6):1327-1334.
[35] Belsak A, Flasker J. Detecting cracks in the tooth root of gears[J]. Engineering Failure Analysis,2007, 14(8): 1466-1475.
[36] Belsak A, Flasker J. Method for detecting fatigue crack in gears[J]. Theoretical and Applied Fracture Mechanics, 2006, 46(2): 105-113.
[37] Ciavarella M, Demelio G. Numerical methods for optimization of specific sliding, stress concentration and fatigue life of gears[J]. International journal of fatigue, 1999, 21(5): 456-474
[38] Blarasin A, Guangliano M, Vergani L. Fatigue crack growth prediction in specimens similar to spur gear teeth[J]. Fatigue Fract Engng Mater Struct, 1997, 20(8): 1171-1182.
[39] Lewicki D G. Gear crack propagation path studies-guidelines for ultra-safe design[J]. Journal of the American Helicopter Society, 2002, 47, (1), 64-72.
[40]郭辉,赵宁,曹蕾蕾等.渐开线直齿轮齿根裂纹扩展模拟[J].系统仿真学报,2007,19(13):2899-2902.
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[2] Sekercioglu T, Kovan V. Pitting failure of truck spiral bevel gear[J]. Engineering Failure Analysis, 2007, 14(4): 614-619.
[3] Pandey R K. Failure analysis of coal pulveriser gear box[J]. Engineering Failure Analysis, 2007, 14(4): 541-547.
[4] Asi O. Fatigue failure of a helical gear in a gearbox[J]. Engineering Failure Analysis, 2006, 13(7): 1116-1125.
[5]李国云,秦大同.风力发电机齿轮箱加速疲劳试验技术分析[J].重庆大学学报,2009,32(11):1252-1256.
[6]陈举华,徐楠,安艳秋.42CrMo材料硬齿面齿轮全寿命试验及数据分析[J].机械传动,2005,29(5):63-65.
[7]王威强,徐楠,贺庆强.42CrMo硬齿面齿轮虚拟全寿命的试验与分析[J].农业机械学报,2006,37(3):126-129.
[8]赵宁,李虎.应用修正的P-S-N曲线计算齿轮疲劳寿命[J].现代制造工程,2007,(5):105-108.
[9]袁菲.某火炮传动系统随机载荷下齿轮疲劳寿命预测方法研究[D].西北工业大学,2006.
[10]李德建.59坦克传动装置齿轮的疲劳分析[D].大连理工大学,2007.
[11]王国军,闫清东.齿轮弯曲疲劳寿命有限元计算方法研究[J].农业装备与车辆工程,2006,(1):40-42.
[12]邓小雷,周兆忠,汪建平等.工程塑料齿轮疲劳寿命有限元分析[J].轻工机械,2008,26(6):44-47.
[13]陈赛克,王毅.基于精确模型的齿轮接触疲劳寿命有限元分析[J].机械传动,2007,31(2):81-82.
[14]章文强,盛云,于莉等.燃料电池轿车变速器齿轮接触应力分析及疲劳寿命计算[J].计算机辅助设计,2007,16(4):36-39.
[15]陈德民.圆柱斜齿轮动态强度与疲劳损伤仿真[J].计算机辅助工程,2006,(15):294-296.
[16]袁菲,徐颖强.考虑齿间载荷分布的齿轮弯曲疲劳寿命估算[J].机械设计,2006,23(4):35-37.
[17]夏延秋,丁津原,马先贵等.摩擦系数对齿轮接触疲劳寿命的影响[J].机械传动,2002,26(1):48-49.
[18] Guagliano M, Riva E, Guidetti M. Contact fatigue failure analysis of shot-peened gears[J].Engineering Failure Analysis, 2002, 9(2): 147–158.
[19] Cavallaro G P, Wilks T P, Subramanian C, et al. Bending fatigue and contact fatigue characteristics of carburized gears[J]. Surface and Coatings Technology, 1995, 71(2): 182-192
[20] Aslantas K, Tasgetiren S. A study of spur gear pitting formation and life prediction[J]. Wear, 2004, 257 (11): 1167–1175.
[21] Glodez S, Sraml M, Kramberger J. A computational model for determination of service life of gears[J]. International Journal of Fatigue, 2002, 24(10): 1013–1020.
[22] Kramberger J, Sraml M, Glodez S, et al. Computational model for the analysis of bending fatigue in gears[J]. Computers and Structures, 2004, 82(23-26): 2261-2269.
[23] Abersek B, Flasker J, Glodez S. Review of mathematical and experimental models for determination of service life of gears[J]. Engineering Fracture Mechanics, 2004, 71 (4-6): 439-453.
[24] Kramberger J, Sraml M, Potrc I, et al. Numerical calculation of bending fatigue life of thin-rim spur gears[J]. Engineering Fracture Mechanics, 2004, 71 (4-6): 647–656.
[25] Glodez S, Abersek B, Flasker J, et al. Evaluation of the service life of gears in regard to surface pitting[J]. Engineering Fracture Mechanics, 2004, 71 (4-6): 429–438.
[26] Glodez S, Ren Z, Flasker J. Surface fatigue of gear teeth flanks[J]. Computers and Structures,1999, 73(1-5): 475-483.
[27]周赵风,徐梓斌.齿轮轮齿裂缝的产生及其应力分析[J].机械强度,2004,26(2):231-234.
[28] Guagliano M, Vergani L. Mode I stress intensity factors for curved cracks in gears by a weight functions method[J]. Fatigue and Fracture of Engineering Materials and Stmctures, 2001, 24(1): 41-52.
[29] Nicoletto G. Gear tooth stress analysis by the complex potentials method[J]. Meccanica, 1992, 27(2): 105-110.
[30]顾浩.渐开线齿轮齿根断裂力学分析[D].南京航空航天大学,2007.
[31]张洪才,黄克正,陈举华.基于断裂力学理论的表面淬火齿轮疲劳寿命的数值计算[J].应用力学学报,2004,21(1):17-21.
[32]邵忍平,黄欣娜,李宗斌.裂纹对齿轮轮齿结构振动的影响[J].机械强度,2004,26(6):629-635.
[33]张延超,邵忍平,刘宏昱.裂纹故障对齿轮传动系统动力特性的影响[J].机械设计与制造,2006,10:12-14.
[34]邵忍平,徐志锋,曹精明.裂纹故障齿轮结构声振特性与模拟研究[J].航空动力学报,2010,25(6):1327-1334.
[35] Belsak A, Flasker J. Detecting cracks in the tooth root of gears[J]. Engineering Failure Analysis,2007, 14(8): 1466-1475.
[36] Belsak A, Flasker J. Method for detecting fatigue crack in gears[J]. Theoretical and Applied Fracture Mechanics, 2006, 46(2): 105-113.
[37] Ciavarella M, Demelio G. Numerical methods for optimization of specific sliding, stress concentration and fatigue life of gears[J]. International journal of fatigue, 1999, 21(5): 456-474
[38] Blarasin A, Guangliano M, Vergani L. Fatigue crack growth prediction in specimens similar to spur gear teeth[J]. Fatigue Fract Engng Mater Struct, 1997, 20(8): 1171-1182.
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