基于分形理论的双渐开线齿轮接触应力研究
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摘要
综合考虑接触面粗糙度、材料特性等因素对齿轮接触应力的影响,基于分形理论和经典Hertz接触理论建立双渐开线齿轮分形接触模型.该模型中,影响载荷和实际接触面积的主要因素包括分形维数、粗糙度幅值和材料特性参数.理论分析表明:分形维数一定时,真实接触面积随着载荷的增大而增大;载荷一定时,接触面积随着粗糙度幅值的增大而减小;随着材料特性参数值的增加,在一定程度上加强了软材料轮齿承载能力,同时会使得微凸体由弹性变形到塑性变形的临界面积减小.对比分形接触模型和有限元模型两种计算双渐开线齿轮轮齿接触应力方法,结果证明了分形接触模型计算双渐开线齿轮接触应力的有效性.
Considering the influence of contact surface roughness, material characteristics and other factors on the contact stress of gears, the fractal contact model of double-involute gear was established which based on the fractal theory and the classical Hertz contact theory. In this model, the main factors influencing the load and the actual contact area consisted of fractal dimension, roughness amplitude and material characteristic parameters. Theoretical calculation showed that when the fractal dimension was constant, the real contact area increased with the increase of load. When the load was constant, the contact area decreasesd with the increase of roughness amplitude. With the increase of the material characteristic parameter value, the bearing capacity of the soft material wheel tooth was enhanced to some extent, while the critical area of the micro-convex body from elastic deformation to plastic deformation was reduced.Through the comparison of two methods including fractal contact model and finite element model for calculating tooth contact stress of double involute gear teeth, the results demonstrate the effectiveness of using fractal contact model to calculate contact stress of double involute gear.
Considering the influence of contact surface roughness, material characteristics and other factors on the contact stress of gears, the fractal contact model of double-involute gear was established which based on the fractal theory and the classical Hertz contact theory. In this model, the main factors influencing the load and the actual contact area consisted of fractal dimension, roughness amplitude and material characteristic parameters. Theoretical calculation showed that when the fractal dimension was constant, the real contact area increased with the increase of load. When the load was constant, the contact area decreasesd with the increase of roughness amplitude. With the increase of the material characteristic parameter value, the bearing capacity of the soft material wheel tooth was enhanced to some extent, while the critical area of the micro-convex body from elastic deformation to plastic deformation was reduced.Through the comparison of two methods including fractal contact model and finite element model for calculating tooth contact stress of double involute gear teeth, the results demonstrate the effectiveness of using fractal contact model to calculate contact stress of double involute gear.
引文
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[14]Xu Hongbin,Zhang Guanghui,Jiateng Zhengming.Study on bending strength of fractional double involute gear[J].China Mechanical Engineering,1999,10(11):1267-1269(in Chinese)[许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮弯曲强度的研究[J].中国机械工程,1999,10(11):1267-1269].doi:10.3321/j.issn:1004-132X.1999.11.020.
[15]Tang Zhonglian.Influence of tooth face roughness on gearing contact fatigue stress[D].Taiyuan:Taiyuan University of Technology,2011(in Chinese)[汤中连.齿面粗糙度对齿轮传动接触疲劳应力的影响[D].太原:太原理工大学,2011].
[16]Gao Chuangkuan,Zhou Mou,Qi Xiumei.Effect of gear tooth friction force on gear contact stress[J].Mechanical Strength,2003,25(6):642-645(in Chinese)[高创宽,周谋,亓秀梅.齿面摩擦力对齿轮接触应力的影响[J].机械强度,2003,25(6):642-645].doi:10.3321/j.issn:1001-9669.2003.06.011.
[17]Fan Zhimin,Zhang Guanghui.Analysis of meshing characteristics of double involute gear with fractional order[J].Chinese Journal of Mechanical Engineering,2002,38(9):73-76(in Chinese)[樊智敏,张光辉.分阶式双渐开线齿轮啮合特性分析[J].机械工程学报,2002,38(9):73-76].doi:10.3321/j.issn:0577-6686.2002.09.016.
[18]Pu Lianggui,Ji Minggang.Mechanical design[M].Beijing:Higher Education Press,2001(in Chinese)[濮良贵,纪名刚.机械设计[M].北京:高等教育出版社,2001].
[19]Chen Qi.Research on gear contact strength analysis of automobile gearbox by fractal theory[D].Hefei:Hefei University of Technology,2010(in Chinese)[陈奇.基于分形理论的汽车变速箱齿轮接触强度研究[D].合肥:合肥工业大学,2010].
[20]Ge Shirong.The fractal behavior and fractal characterization of rough surfaces[J].Tribology,1997,17(1):73-80(in Chinese)[葛世荣.粗糙表面的分形特征与分形表达研究[J].摩擦学学报,1997,17(1):73-80].doi:10.3321/j.issn:1004-0595.1997.01.011.
[2]Bhushan B.Introduction to Tribology[M].New York:John Wiley&sons,2002.
[3]Majumdar A,Bhushan B.Fractal model of elastic-plastic contact between rough surfaces[J].Transactions of ASME,Journal of Tribology,1991,113(1):1-11.doi:10.1115/1.2920588.
[4]Wang S,Komvopoulos K.A fractal theory of the interfacial temperature distribution in the slow sliding regime:part l-elastic contact and heat transfer analysis[J].Transactions of ASME,Journal of Tribology,1994,116(4):812-823.doi:10.1115/1.2927338.
[5]Huang Kang,Zhao Han,Chen Qi.Research of fractal contact model on contact carrying capacity of two cylinders’surface[J].Tribology,2008,28(6):529-533(in Chinese)[黄康,赵韩,陈奇.两圆柱体表面接触承载能力的分形模型研究[J].摩擦学学报,2008,28(6):529-533].doi:10.3321/j.issn:1004-0595.2008.06.009.
[6]Zhao Han,Chen Qi,Huang Kang.Fractal model of normal contact stiffness between two cylinders’joint interfaces[J].Journal of Mechanical Engineering,2011,44(47):53-58(in Chinese)[赵韩,陈奇,黄康.两圆柱体结合面的法向接触刚度分形模型[J].机械工程学报,2011,44(47):53-58].
[7]Liu Peng,Zhao Han,Huang Kang,et al.Research on normal contact stiffness of micro-segments gear based on improved fractal model[J].Journal of Mechanical Engineering,2018,54(7):114-122(in Chinese)[刘鹏,赵韩,黄康,等.线段齿轮法向接触刚度的改进分形模型研究[J].机械工程学报,2018,54(7):114-122].
[8]Chen Qi,Huang Kang,Zhang Yan,et al.Analysis of influence on gear’s contact strength based on fractal contact model[J].China Mechanical Engineering,2013,24(16):2208-2211(in Chinese)[陈奇,黄康,张彦,等.基于分形接触模型的齿轮接触强度影响参数分析[J].中国机械工程,2013,24(16):2208-2211].doi:10.3969/j.issn.1004-132X.2013.16.015.
[9]Ge Shirong,Zhu Hua.Fractal tribology[M].Beijing:China Machine Press,2005(in Chinese)[葛世荣,朱华.摩擦学的分形[M].北京:机械工业出版社,2005].
[10]Chen Guoan,Ge Shirong.Prediction model of sliding wear during running-in process based on fractal theory[J].Chinese Journal of Mechanical Engineering,2000,36(2):29-33(in Chinese)[陈国安,葛世荣.基于分形理论的磨合磨损预测模型[J].机械工程学报,2000,36(2):29-33].doi:10.3321/j.issn:0577-6686.2000.02.009.
[11]Xu Fan,Chen Qi,Ma Yunbo,et al.Research on fractal contact model for contact carrying capacity of two cylinders,surfaces considering lubrication factors[J].Journal of Hefei University of Technology,2017,40(2):169-174(in Chinese)[徐帆,陈奇,马运波,等.考虑润滑因素的两圆柱体接触承载能力的分形模型研究[J].合肥工业大学学报(自然科学版),2017,40(2):169-174].doi:10.3969/j.issn.1003-5060.2017.02.006.
[12]Zhang Guanghui,Xu Hongbin,Long Hui.Fractional double involute gear[J].Chinese Journal of Mechanical Engineering,1995,31(6):47-52(in Chinese)[张光辉,许洪斌,龙慧.分阶式双渐开线齿轮[J].机械工程学报,1995,31(6):47-52].doi:10.3321/j.issn:0577-6686.1995.06.016.
[13]Xu Hongbin,Zhang Guanghui,Jiateng Zhengming.Study on photoelastic test and bending strength test of fractional double involute gear[J].Chinese Journal of Mechanical Engineering,2000,36(8):39-42(in Chinese)[许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮的光弹试验与弯曲强度试验研究[J].机械工程学报,2000,36(8):39-42].doi:10.3321/j.issn:0577-6686.2000.08.009.
[14]Xu Hongbin,Zhang Guanghui,Jiateng Zhengming.Study on bending strength of fractional double involute gear[J].China Mechanical Engineering,1999,10(11):1267-1269(in Chinese)[许洪斌,张光辉,加藤正名.分阶式双渐开线齿轮弯曲强度的研究[J].中国机械工程,1999,10(11):1267-1269].doi:10.3321/j.issn:1004-132X.1999.11.020.
[15]Tang Zhonglian.Influence of tooth face roughness on gearing contact fatigue stress[D].Taiyuan:Taiyuan University of Technology,2011(in Chinese)[汤中连.齿面粗糙度对齿轮传动接触疲劳应力的影响[D].太原:太原理工大学,2011].
[16]Gao Chuangkuan,Zhou Mou,Qi Xiumei.Effect of gear tooth friction force on gear contact stress[J].Mechanical Strength,2003,25(6):642-645(in Chinese)[高创宽,周谋,亓秀梅.齿面摩擦力对齿轮接触应力的影响[J].机械强度,2003,25(6):642-645].doi:10.3321/j.issn:1001-9669.2003.06.011.
[17]Fan Zhimin,Zhang Guanghui.Analysis of meshing characteristics of double involute gear with fractional order[J].Chinese Journal of Mechanical Engineering,2002,38(9):73-76(in Chinese)[樊智敏,张光辉.分阶式双渐开线齿轮啮合特性分析[J].机械工程学报,2002,38(9):73-76].doi:10.3321/j.issn:0577-6686.2002.09.016.
[18]Pu Lianggui,Ji Minggang.Mechanical design[M].Beijing:Higher Education Press,2001(in Chinese)[濮良贵,纪名刚.机械设计[M].北京:高等教育出版社,2001].
[19]Chen Qi.Research on gear contact strength analysis of automobile gearbox by fractal theory[D].Hefei:Hefei University of Technology,2010(in Chinese)[陈奇.基于分形理论的汽车变速箱齿轮接触强度研究[D].合肥:合肥工业大学,2010].
[20]Ge Shirong.The fractal behavior and fractal characterization of rough surfaces[J].Tribology,1997,17(1):73-80(in Chinese)[葛世荣.粗糙表面的分形特征与分形表达研究[J].摩擦学学报,1997,17(1):73-80].doi:10.3321/j.issn:1004-0595.1997.01.011.