双压力角非对称渐开线直齿轮的应力分析及齿廓曲线的优化
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摘要
本文利用ANSYS分析了双压力角非对称渐开线直齿轮的齿根弯曲应力和齿面接触应力,并应用一阶方法对齿廓曲线进行了优化,针对不同的设计参数,得到了不同的优化结果。
首先,基于渐开线齿轮的啮合原理,利用渐开线方程和过渡曲线方程,建立了双压力角非对称渐开线直齿轮的通用齿廓方程,并对主要参数进行了计算,利用ANSYS提供的APDL语言,建立了双压力角非对称渐开线齿轮的参数化模型。
其次,利用ANSYS对双压力角非对称渐开线直齿轮齿面接触应力和齿根弯曲应力进行了有限元分析,分析了两侧压力角变化对齿面接触应力和齿根弯曲应力的影响,得出了齿面接触应力和齿根弯曲应力随压力角变化的规律,并与相应的对称齿轮进行了比较,分析结果显示:在一侧压力角不变的情况下,增大另一侧压力角,齿轮的受压侧齿根弯曲应力明显减小;在非工作侧压力角不变的情况下,增大工作侧的压力角,齿轮的齿面接触强度也有一定程度的提高。
最后,根据分析计算的结果,利用ANSYS中提供的一阶优化设计方法,对双压力角非对称渐开线齿轮的各个参数进行了优化。针对不同的设计参数,得到了不同的优化结果,概括起来:设计变量,约束条件的多少直接影响了最终的优化结果,设计变量越多优化的结果越理想,约束条件越多越容易得到局部最优值,而不利于得到全局最优值。因此,在优化过程中,应增加设计变量,减少约束条件,这样才能得到全局最优结果。
双压力角非对称齿轮在做单向传动时,具有明显的优势,而这些优势是对称齿轮所不具备的。因此,进行非对称齿轮设计具有十分重要的理论意义和现实意义。
This article mainly analyzed the bending stress and contact stress of the asymmetric involute gear with two pressure angles by using ANSYS. The first-order method has been used to optimize the tooth profile curve and different design parameters obtained different optimized results.
Firstly, based on the involute gear meshing theories and the involute gear characteristics, and used involute equation and the transition curve equation, the general equation of the asymmetric involute gear with two pressure angles have been established, and the main parameters have been calculated. Using APDL language, the parameterized model of the asymmetric involute gear with two pressure angles have been established.
Secondly, the bending stress and contact stress of the asymmetric involute gear with two pressure angles have been analyzed by using ANSYS. This article studied how the pressure angles influence the bending stress and the contact stress and obtained the change rule with the pressure angles and compared the bending stress and the contact stress of asymmetric gear with symmetric gears.The results showed: one side pressure angle unchanged, the other side pressure angle increased, the gear tooth root bending stress significantly reduced, and the non-working side pressure angle unchanged, the work side pressure angle increased, the gear tooth contact intensity increased certainly.
Finally, based on analysis results, using the first-order optimization method, all parameters of the asymmetric involute gear with two pressure angles were optimized. The different design parameters have been obtained different optimization results. The number of design variables and constraint variables directly affected the optimization result. More design variables are used, more ideal results are got. More constrained variables are used, more easily accessed to the local excellent value. Therefore, in the optimization process, the design variables should be increased and the constrained variables should be reduced, in order to get globally optimal results.
Asymmetric gear with two pressure angles has distinct advantages which the symmetric gear does not have when he doing one-way drive. Therefore, asymmetric gear design has great theoretical and practical significance.
首先,基于渐开线齿轮的啮合原理,利用渐开线方程和过渡曲线方程,建立了双压力角非对称渐开线直齿轮的通用齿廓方程,并对主要参数进行了计算,利用ANSYS提供的APDL语言,建立了双压力角非对称渐开线齿轮的参数化模型。
其次,利用ANSYS对双压力角非对称渐开线直齿轮齿面接触应力和齿根弯曲应力进行了有限元分析,分析了两侧压力角变化对齿面接触应力和齿根弯曲应力的影响,得出了齿面接触应力和齿根弯曲应力随压力角变化的规律,并与相应的对称齿轮进行了比较,分析结果显示:在一侧压力角不变的情况下,增大另一侧压力角,齿轮的受压侧齿根弯曲应力明显减小;在非工作侧压力角不变的情况下,增大工作侧的压力角,齿轮的齿面接触强度也有一定程度的提高。
最后,根据分析计算的结果,利用ANSYS中提供的一阶优化设计方法,对双压力角非对称渐开线齿轮的各个参数进行了优化。针对不同的设计参数,得到了不同的优化结果,概括起来:设计变量,约束条件的多少直接影响了最终的优化结果,设计变量越多优化的结果越理想,约束条件越多越容易得到局部最优值,而不利于得到全局最优值。因此,在优化过程中,应增加设计变量,减少约束条件,这样才能得到全局最优结果。
双压力角非对称齿轮在做单向传动时,具有明显的优势,而这些优势是对称齿轮所不具备的。因此,进行非对称齿轮设计具有十分重要的理论意义和现实意义。
This article mainly analyzed the bending stress and contact stress of the asymmetric involute gear with two pressure angles by using ANSYS. The first-order method has been used to optimize the tooth profile curve and different design parameters obtained different optimized results.
Firstly, based on the involute gear meshing theories and the involute gear characteristics, and used involute equation and the transition curve equation, the general equation of the asymmetric involute gear with two pressure angles have been established, and the main parameters have been calculated. Using APDL language, the parameterized model of the asymmetric involute gear with two pressure angles have been established.
Secondly, the bending stress and contact stress of the asymmetric involute gear with two pressure angles have been analyzed by using ANSYS. This article studied how the pressure angles influence the bending stress and the contact stress and obtained the change rule with the pressure angles and compared the bending stress and the contact stress of asymmetric gear with symmetric gears.The results showed: one side pressure angle unchanged, the other side pressure angle increased, the gear tooth root bending stress significantly reduced, and the non-working side pressure angle unchanged, the work side pressure angle increased, the gear tooth contact intensity increased certainly.
Finally, based on analysis results, using the first-order optimization method, all parameters of the asymmetric involute gear with two pressure angles were optimized. The different design parameters have been obtained different optimization results. The number of design variables and constraint variables directly affected the optimization result. More design variables are used, more ideal results are got. More constrained variables are used, more easily accessed to the local excellent value. Therefore, in the optimization process, the design variables should be increased and the constrained variables should be reduced, in order to get globally optimal results.
Asymmetric gear with two pressure angles has distinct advantages which the symmetric gear does not have when he doing one-way drive. Therefore, asymmetric gear design has great theoretical and practical significance.
引文
[1]吴忠,非对称齿廓渐开线齿轮齿形的仿真设计分析,包头钢铁学院学报,2004年6月,第23卷第2期,155-158
[2]张玉梅,朱如鹏,双压力角非对称齿轮啮合特性及应力分析研究,[学位论文],太原理工大学,2005年
[3]Faydor L.Litvin,Qiming Lian,Alexander L.Kapelevich,Asymmetric modified spur gear drives:reduction of noise,localization of contact,simulation of meshing and stress analysis,Comput.Methods Appl.Mech.Engrg.188(2000)363-390
[4]Alexander Kapelevich,Geometry and design of involute spur gears with asymmetric teeth,Mechanism and Machine Theory 35(2000)117-130
[5]谭伟明,安军,陈就等,非对称齿形渐开线非圆齿轮的齿廓曲线数学模型,佛山科学技术学院学报,2002年6月,第20卷第20期,22-26
[6]FaydorL.Litvin,Alfonso Fuentes,Matt Howkins,Design,generation and TCA of new type of asymmetric face-gear drive with modified geometry,Comput.Methods Appl.Mech.Engrg.190(2001)5837-5865
[7]Faydor L.Litvin,Alfonso Fuentes,Ignacio Gonzalez-Perez,Luca Carvenali,Kazumasa Kawasaki,Robert F.Handschuh,Modified involute helical gears:computerized design,simulation of meshing and stress analysis,Comput.Methods Appl.Mech.Engrg.192(2003)3619-3655
[8]F.L.LITVIN,Topology of Modified Surfaces of Involute Helical Gears with Line Contact Developed for Improvement of Bearing Contact,Reduction of Transmission Errors,and Stress Analysis,Mathematical and Computer Modelling 42(2005)1063-1078
[9]肖望强,李威,李梅,双压力角非对称齿廓齿轮齿根弯曲应力的有限元分析,北京科技大学学报,2006年6月,第28卷第6期,570-575
[10]蒋立冬,常山,石玉权等,非对称渐开线直齿轮齿廓设计与有限元分析,热能动力工程,2003年8月,第18卷第5期,478-541
[11]张玉梅,朱如鹏,非对称齿轮弯曲应力的解析法及有限元分析,机械工程师,2004 年,第12期,36-38
[12]娄依志,王小群,李威,非对称渐开线圆柱齿轮的动力学特性,北京科技大学学报,2005年6月,第27卷第3期,334-337
[13]肖望强,李威,李梅,双压力角非对称齿廓齿轮齿根弯曲应力的有限元分析,北京科技大学学报,2006年6月,第28卷第6期,570-575
[14]肖望强,李威,韩建友等,双压力角非对称齿轮传动接触分析,北京科技大学学报,2006年12月,第28卷第12期,1167-1173
[15]Shyue-Cheng Yang,Study on an internal gear with asymmetric involute teeth,Mechanism and Machine Theory 151(2006)353-361
[16]吴忠,非对称渐开线齿轮齿根弯曲应力的计算分析,包头钢铁学院学报,2004年3月,第23卷第1期,61-64
[17]孙桓,陈作模,机械原理,第五版,北京,高等教育出版社,1996年
[18]吴继泽,王统,齿根过渡曲线与齿根应力,北京,国防工业出版社,1989年
[19]杨汾爱,张志强,龙小乐等,基于精确模型的斜齿轮接触应力有限元分析.机械科学与技术,2003,第22卷第2期,206-208
[20]徐克圣,非对称齿轮齿根过渡曲线与齿根应力,大连铁道学院学报,2002年3月,第23卷第1期,31-33
[21]刘元伟,徐克圣,赵亮等,非对称齿齿轮泵研究,大连铁道学院学报,1999年9月,第20卷第3期,52-55
[22]陈赛克,基于ANSYS的直齿圆柱齿轮齿根应力的有限元分析,仲恺农业技术学院学报,2005年,第18卷第3期,10-14
[23]祝磊,马赢,ANSYS7.0入门与提高,北京,清华大学出版社,2004年7月
[24]雷镭,武宝林,谢新兵,基于ANSYS软件的直齿轮接触应力分析,机械传动,2006年,第30卷第2期,50-59
[25]K.Mao,Gear tooth contact analysis and its application in the reduction of fatigue wear,Wear 262(2007)1281-1288
[26]Yilmaz Can,Cenk Misirli,Analysis of spur gear forms with tapered tooth profile,Materials and Design(2007),doi:10.1016/j.matdes.2007.03.015
[27]Chien-Fa Chen,Chung-Biau Tsay,Computerized tooth profile generation and analysis of characteristics of elliptical gears with circular-arc teeth,Journal of Materials Processing Technology 148(2004)226-234
[28]邱宣怀,机械设计,第四版,北京,高等教育出版社,2000年6月
[29]陈秀宁,机械优化设计,浙江大学出版社,1991年
[30]朱传敏,田志仁,宋孔杰,齿轮修形曲线的优化设计,山东工业大学学报,1998年6月,第28卷第2期,122-126
[31]Huseyin Imrek,Hayrettin Duzcukoglu,Relation between wear and tooth width modification in spur gears,Wear 262(2007)390-394
[2]张玉梅,朱如鹏,双压力角非对称齿轮啮合特性及应力分析研究,[学位论文],太原理工大学,2005年
[3]Faydor L.Litvin,Qiming Lian,Alexander L.Kapelevich,Asymmetric modified spur gear drives:reduction of noise,localization of contact,simulation of meshing and stress analysis,Comput.Methods Appl.Mech.Engrg.188(2000)363-390
[4]Alexander Kapelevich,Geometry and design of involute spur gears with asymmetric teeth,Mechanism and Machine Theory 35(2000)117-130
[5]谭伟明,安军,陈就等,非对称齿形渐开线非圆齿轮的齿廓曲线数学模型,佛山科学技术学院学报,2002年6月,第20卷第20期,22-26
[6]FaydorL.Litvin,Alfonso Fuentes,Matt Howkins,Design,generation and TCA of new type of asymmetric face-gear drive with modified geometry,Comput.Methods Appl.Mech.Engrg.190(2001)5837-5865
[7]Faydor L.Litvin,Alfonso Fuentes,Ignacio Gonzalez-Perez,Luca Carvenali,Kazumasa Kawasaki,Robert F.Handschuh,Modified involute helical gears:computerized design,simulation of meshing and stress analysis,Comput.Methods Appl.Mech.Engrg.192(2003)3619-3655
[8]F.L.LITVIN,Topology of Modified Surfaces of Involute Helical Gears with Line Contact Developed for Improvement of Bearing Contact,Reduction of Transmission Errors,and Stress Analysis,Mathematical and Computer Modelling 42(2005)1063-1078
[9]肖望强,李威,李梅,双压力角非对称齿廓齿轮齿根弯曲应力的有限元分析,北京科技大学学报,2006年6月,第28卷第6期,570-575
[10]蒋立冬,常山,石玉权等,非对称渐开线直齿轮齿廓设计与有限元分析,热能动力工程,2003年8月,第18卷第5期,478-541
[11]张玉梅,朱如鹏,非对称齿轮弯曲应力的解析法及有限元分析,机械工程师,2004 年,第12期,36-38
[12]娄依志,王小群,李威,非对称渐开线圆柱齿轮的动力学特性,北京科技大学学报,2005年6月,第27卷第3期,334-337
[13]肖望强,李威,李梅,双压力角非对称齿廓齿轮齿根弯曲应力的有限元分析,北京科技大学学报,2006年6月,第28卷第6期,570-575
[14]肖望强,李威,韩建友等,双压力角非对称齿轮传动接触分析,北京科技大学学报,2006年12月,第28卷第12期,1167-1173
[15]Shyue-Cheng Yang,Study on an internal gear with asymmetric involute teeth,Mechanism and Machine Theory 151(2006)353-361
[16]吴忠,非对称渐开线齿轮齿根弯曲应力的计算分析,包头钢铁学院学报,2004年3月,第23卷第1期,61-64
[17]孙桓,陈作模,机械原理,第五版,北京,高等教育出版社,1996年
[18]吴继泽,王统,齿根过渡曲线与齿根应力,北京,国防工业出版社,1989年
[19]杨汾爱,张志强,龙小乐等,基于精确模型的斜齿轮接触应力有限元分析.机械科学与技术,2003,第22卷第2期,206-208
[20]徐克圣,非对称齿轮齿根过渡曲线与齿根应力,大连铁道学院学报,2002年3月,第23卷第1期,31-33
[21]刘元伟,徐克圣,赵亮等,非对称齿齿轮泵研究,大连铁道学院学报,1999年9月,第20卷第3期,52-55
[22]陈赛克,基于ANSYS的直齿圆柱齿轮齿根应力的有限元分析,仲恺农业技术学院学报,2005年,第18卷第3期,10-14
[23]祝磊,马赢,ANSYS7.0入门与提高,北京,清华大学出版社,2004年7月
[24]雷镭,武宝林,谢新兵,基于ANSYS软件的直齿轮接触应力分析,机械传动,2006年,第30卷第2期,50-59
[25]K.Mao,Gear tooth contact analysis and its application in the reduction of fatigue wear,Wear 262(2007)1281-1288
[26]Yilmaz Can,Cenk Misirli,Analysis of spur gear forms with tapered tooth profile,Materials and Design(2007),doi:10.1016/j.matdes.2007.03.015
[27]Chien-Fa Chen,Chung-Biau Tsay,Computerized tooth profile generation and analysis of characteristics of elliptical gears with circular-arc teeth,Journal of Materials Processing Technology 148(2004)226-234
[28]邱宣怀,机械设计,第四版,北京,高等教育出版社,2000年6月
[29]陈秀宁,机械优化设计,浙江大学出版社,1991年
[30]朱传敏,田志仁,宋孔杰,齿轮修形曲线的优化设计,山东工业大学学报,1998年6月,第28卷第2期,122-126
[31]Huseyin Imrek,Hayrettin Duzcukoglu,Relation between wear and tooth width modification in spur gears,Wear 262(2007)390-394