非对称直齿圆锥齿轮的啮合特性与应力分析研究
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摘要
标准渐开线齿轮的左右两侧齿廓形状是对称的,可以用来实现双向传动。但在实际使用中有相当数量的齿轮只传递单向动力或运动,这类齿轮的工作齿廓与非工作齿廓的应力状态和啮合状态不同,若能根据这一特殊性重新设计轮齿的两侧齿廓,齿轮的传动性能将得到进一步提高,进而发挥出更高的工作性能。因此设计具有不对称齿廓形状的齿轮,开展非对称齿轮的研究具有重要的理论意义和实际意义。
本文首次将非对称齿廓的设计思想应用于直齿圆锥齿轮的研究中,分析比较了不同压力角对齿根弯曲应力和齿面接触应力的影响。
首先,基于平面齿轮的切齿原理,推导了应用广泛的“8”字啮合直齿圆锥齿轮的齿面方程;利用ANSYS软件提供的APDL语言,建立了以压力角为参数的非对称直齿圆锥齿轮参数化模型;讨论了非对称直齿圆锥齿轮的啮合特性。
其次,利用ANSYS软件对非对称直齿圆锥齿轮齿根弯曲应力进行了分析计算,分析比较了不同的非工作侧压力角对受拉侧齿廓和受压侧齿廓齿根弯曲应力的影响,得到了一些具有工程应用价值的结论。
再次,运用ANSYS软件对非对称直齿圆锥齿轮的一对轮齿在节线处啮合的接触应力进行了计算,分析比较了不同的工作侧压力角对齿面接触应力的影响。
最后,对本文所做工作进行了总结,探讨了本文可能存在的一些问题,并对下一步的研究工作进行了展望。
Standard involute gear tooth profile of the right and left sides are symmetrical shape, which can be used to achieve two-way transmission. However, in actual use, a considerable number of gear only transfer directed movement or dynamical force, so the state of stress and meshing of working tooth profile and non-working tooth profile is different. If according to this particularity to re-design the two sides of the tooth profile, the gear transmission performance will be further improved, then play a better performance. Therefore, designing asymmetric shape of tooth profile of gear, and developing asymmetric gear studying will have the vital theoretical and practical significance.
For the first time, this article applies the asymmetrical tooth profile design concept in the straight tooth bevel gear research, and analyses how the pressure angles influence the bending stress of the tooth root and the contact stress of the tooth surface.
Firstly, based on face gear cutting tooth principle, the tooth face equation of Octoid straight tooth bevel gear which were widely used has been established; using APDL language, the parameterized model of the asymmetrical straight tooth bevel gear has been established by taking the pressure angle as the parameter; the meshing characteristic of the asymmetrical straight tooth bevel gear has been discussed.
Secondly, the bending stress of the asymmetrical straight tooth bevel gear has been analyzed by using ANSYS, and analyses how the pressure angles on the non-working side influence the bending stress of pulled side and pressed side. Some valuable conclusions are educed.
Thirdly, using the software ANSYS of finite elements analysis, the contact stress of only one pair of the asymmetrical straight tooth bevel gear teeth has been computed which were meshing along the pitch line, analyses how the pressure angles on the working side influence the contact stress.
At last, there is a summary of this dissertation and prospect of this research.
本文首次将非对称齿廓的设计思想应用于直齿圆锥齿轮的研究中,分析比较了不同压力角对齿根弯曲应力和齿面接触应力的影响。
首先,基于平面齿轮的切齿原理,推导了应用广泛的“8”字啮合直齿圆锥齿轮的齿面方程;利用ANSYS软件提供的APDL语言,建立了以压力角为参数的非对称直齿圆锥齿轮参数化模型;讨论了非对称直齿圆锥齿轮的啮合特性。
其次,利用ANSYS软件对非对称直齿圆锥齿轮齿根弯曲应力进行了分析计算,分析比较了不同的非工作侧压力角对受拉侧齿廓和受压侧齿廓齿根弯曲应力的影响,得到了一些具有工程应用价值的结论。
再次,运用ANSYS软件对非对称直齿圆锥齿轮的一对轮齿在节线处啮合的接触应力进行了计算,分析比较了不同的工作侧压力角对齿面接触应力的影响。
最后,对本文所做工作进行了总结,探讨了本文可能存在的一些问题,并对下一步的研究工作进行了展望。
Standard involute gear tooth profile of the right and left sides are symmetrical shape, which can be used to achieve two-way transmission. However, in actual use, a considerable number of gear only transfer directed movement or dynamical force, so the state of stress and meshing of working tooth profile and non-working tooth profile is different. If according to this particularity to re-design the two sides of the tooth profile, the gear transmission performance will be further improved, then play a better performance. Therefore, designing asymmetric shape of tooth profile of gear, and developing asymmetric gear studying will have the vital theoretical and practical significance.
For the first time, this article applies the asymmetrical tooth profile design concept in the straight tooth bevel gear research, and analyses how the pressure angles influence the bending stress of the tooth root and the contact stress of the tooth surface.
Firstly, based on face gear cutting tooth principle, the tooth face equation of Octoid straight tooth bevel gear which were widely used has been established; using APDL language, the parameterized model of the asymmetrical straight tooth bevel gear has been established by taking the pressure angle as the parameter; the meshing characteristic of the asymmetrical straight tooth bevel gear has been discussed.
Secondly, the bending stress of the asymmetrical straight tooth bevel gear has been analyzed by using ANSYS, and analyses how the pressure angles on the non-working side influence the bending stress of pulled side and pressed side. Some valuable conclusions are educed.
Thirdly, using the software ANSYS of finite elements analysis, the contact stress of only one pair of the asymmetrical straight tooth bevel gear teeth has been computed which were meshing along the pitch line, analyses how the pressure angles on the working side influence the contact stress.
At last, there is a summary of this dissertation and prospect of this research.
引文
[1]张玉梅,双压力角非对称齿轮啮合特性及应力分析研究,[学位论文],南京,南京航空航天大学,2005
[2]徐晓东,非对称渐开线齿轮的啮合特性及应力分析研究,[学位论文],南京,南京航空航天大学,2005
[3]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,2004,23(1),61-64
[4]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,2005,27(3),334-337
[5]刘元伟,徐克圣,赵亮等,非对称齿齿轮泵设计研究,大连铁道学院学报,1999,20(3),52-55
[6]徐克圣,刘元伟,李丽,非对称齿形加工的计算机仿真,大连铁道学院学报,2000,21(4),13-17
[7]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,2002,23(1),31-33
[8]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(自然科学版),2002,20(2),22-25
[9]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,1989,106-110
[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,2003,18(5),478-481
[11]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,2006,28(6),570-575
[12]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,2006,28(12),1167-1173
[13]肖望强,李威,韩建友等,双压力角非对称齿廓渐开线齿轮的振动分析,中国机械工程,2006,17(6),645-648
[14]肖望强,李威,韩建友,非对称齿廓渐开线齿轮传动的热分析,农业机械学报,2006,37(6),164-167
[15]赵德金,直齿圆锥齿轮的建模和运动仿真,延边大学农学学报,2005,27(4),292-294
[16]陈霞,夏巨谌,胡国安等,直齿圆锥齿轮啮合过程数值模拟,机械设计,2006,32(4):21-23
[17]杨生华,齿轮接触有限元分析,计算力学学报,2003,20(2)189-194
[18]吴忠鸣,王新云,夏巨谌等,基于ANSYS的直齿圆锥齿轮建模及动态接触有限元分析,机械传动,2005,29(5),49-52
[19]褚世华,一种新型非对称齿形的齿轮泵,化工矿山技术,1994,23(6),37-39
[20]夏立中,非对称渐开线多齿轮泵的理论分析,东北煤炭技术,1997,1(1),22-26
[21]陈天旗,高鹏,刘元伟,非对称齿齿轮泵非对称齿轮公法线的测量,大连铁道学院学报,2000,21(2),25-27
[22]Alexander Kapelevich,Geometry and design of involute spur gears with asymmetric teeth,Mechanism and Machine Theory,2000,117-130
[23]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,Computer methods in applied mechanics and engineering,188(2000)363-390
[24]Alexander L,Kapelevich,Roderick E,Kleiss,Direct Gear Design for Spur and Helical Involute Gears,GEAR TECHNOLOGY,2002,SEPTEMBER/OCTOBER,29-35
[25]Alexander L,Kapelevich,Yuriy V,Shekhtman,Direct Gear Design:Bending Stress Minimization,GEAR TECHNOLOGY,2003,SEPTEMBER/OCTOBER,44-47
[26]Alex Kapelevich,Thomas McNamara,Direct Gear Design-for Optimal Gear Performance,www,akgears,com
[27]Alexander L,Kapelevich,Thomas M,McNamara,Direct Gear Design for Automotive Applications,www,akgears,com
[28]Alexander L,Kapelevich,Thomas M,McNamara,Introduction to Direct Gear Design
[29]Shyue-Cheng Yang,Study on an internal gear with asymmetric involute teeth,Mechanism and Machine Theory,2006
[30]XIE Wen-bo,IIJIMA Kiichiroh,LU Hao,Numerical Analysis of Plastic Gear Stiffness,Journal of Shanghai Jiaotong University(Science),2005,10(3):303-306
[31]F,L,Litvin,Jian Lu,D,P,Townsend,etc,Computerized simulation of meshing of conventional helical involute gears and modification of geometry,Mechanism and Machine Theory,1999,34:123-147,
[32]孙桓,陈作模,机械原理(第五版),北京,高等教育出版社,1996
[33]国营渭阳柴油机厂,直齿圆锥齿轮,北京,国防工业出版社,1978
[34]刘惟信,圆锥齿轮与双曲面齿轮传动,北京,民交通出版社,1980
[35]周延泽,吴继泽,直齿圆锥齿轮齿面和齿根过渡曲面方程,北京航空航天大学学,1993,112-120
[36]蒋法国,差速器行星齿轮的有限元法强度分析,[学位论文],长春,吉林大学,2006
[37]宁少惠,齿面摩擦力对齿根弯曲应力的影响,[学位论文],太原,太原理工大学,2005
[38]常江,齿轮副的静、动态数值计算与动态弹性实验研究,[学位论文],天津,天津大学,2004
[39]李金澎,大模数直齿轮轮齿弯曲强度与齿面接触研究,[学位论文],大连,大连理工大学,2005
[40]刘晖,基于参数化的齿轮传动接触有限元分析,[学位论文],大连,大连交通大学,2003
[41]徐戊矫,制造误差与承载变形耦合条件下平面二次包络环面蜗杆的啮合分析与啮合控制研究,[学位论文],重庆,重庆大学,2005
[42]东方人华,ANSYS7.0入门与提高,北京,清华大学出版社,2004
[43]盛云,双圆弧弧齿锥齿轮的实体建模及其弯曲应力的有限元分析,[学位论文],天津,天津工业大学,2005
[44]李剑锋,王钧效,王寿佑等,直齿圆锥齿轮齿向载荷分布及齿间载荷分配,山东工业大学学报,1996,26(4),445-450
[45]王云成,差速器行星齿轮的有限元法强度分析,[学位论文],长春,吉林大学,2005
[46]穆立茂,利用UG实现直齿圆锥齿轮的三维造型,机械,2004,31(10),24-26
[47]夏巨谌,陈霞,直齿圆锥齿轮的精确建模及其接触应力的有限元分析,轻工机械,2007,25(1),69-71
[48]钱学毅,郭波,邹丽梅,基于ANSYS和Pro/E的直齿圆锥齿轮齿根应力有限元分析,机械传动,2006,30(5),66-67
[49]刘大利,郭覃,周哲波,利用Pro/E Wildfire和CAXA进行渐开线直齿圆锥齿轮精确建模,煤矿机械,2007,28(3),74-75
[50]李震,李强,基于SolidWorks直齿圆锥齿轮参数化设计及有限元分析,设计与研究,2007,10,46-47
[2]徐晓东,非对称渐开线齿轮的啮合特性及应力分析研究,[学位论文],南京,南京航空航天大学,2005
[3]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,2004,23(1),61-64
[4]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,2005,27(3),334-337
[5]刘元伟,徐克圣,赵亮等,非对称齿齿轮泵设计研究,大连铁道学院学报,1999,20(3),52-55
[6]徐克圣,刘元伟,李丽,非对称齿形加工的计算机仿真,大连铁道学院学报,2000,21(4),13-17
[7]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,2002,23(1),31-33
[8]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(自然科学版),2002,20(2),22-25
[9]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,1989,106-110
[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,2003,18(5),478-481
[11]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,2006,28(6),570-575
[12]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,2006,28(12),1167-1173
[13]肖望强,李威,韩建友等,双压力角非对称齿廓渐开线齿轮的振动分析,中国机械工程,2006,17(6),645-648
[14]肖望强,李威,韩建友,非对称齿廓渐开线齿轮传动的热分析,农业机械学报,2006,37(6),164-167
[15]赵德金,直齿圆锥齿轮的建模和运动仿真,延边大学农学学报,2005,27(4),292-294
[16]陈霞,夏巨谌,胡国安等,直齿圆锥齿轮啮合过程数值模拟,机械设计,2006,32(4):21-23
[17]杨生华,齿轮接触有限元分析,计算力学学报,2003,20(2)189-194
[18]吴忠鸣,王新云,夏巨谌等,基于ANSYS的直齿圆锥齿轮建模及动态接触有限元分析,机械传动,2005,29(5),49-52
[19]褚世华,一种新型非对称齿形的齿轮泵,化工矿山技术,1994,23(6),37-39
[20]夏立中,非对称渐开线多齿轮泵的理论分析,东北煤炭技术,1997,1(1),22-26
[21]陈天旗,高鹏,刘元伟,非对称齿齿轮泵非对称齿轮公法线的测量,大连铁道学院学报,2000,21(2),25-27
[22]Alexander Kapelevich,Geometry and design of involute spur gears with asymmetric teeth,Mechanism and Machine Theory,2000,117-130
[23]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,Computer methods in applied mechanics and engineering,188(2000)363-390
[24]Alexander L,Kapelevich,Roderick E,Kleiss,Direct Gear Design for Spur and Helical Involute Gears,GEAR TECHNOLOGY,2002,SEPTEMBER/OCTOBER,29-35
[25]Alexander L,Kapelevich,Yuriy V,Shekhtman,Direct Gear Design:Bending Stress Minimization,GEAR TECHNOLOGY,2003,SEPTEMBER/OCTOBER,44-47
[26]Alex Kapelevich,Thomas McNamara,Direct Gear Design-for Optimal Gear Performance,www,akgears,com
[27]Alexander L,Kapelevich,Thomas M,McNamara,Direct Gear Design for Automotive Applications,www,akgears,com
[28]Alexander L,Kapelevich,Thomas M,McNamara,Introduction to Direct Gear Design
[29]Shyue-Cheng Yang,Study on an internal gear with asymmetric involute teeth,Mechanism and Machine Theory,2006
[30]XIE Wen-bo,IIJIMA Kiichiroh,LU Hao,Numerical Analysis of Plastic Gear Stiffness,Journal of Shanghai Jiaotong University(Science),2005,10(3):303-306
[31]F,L,Litvin,Jian Lu,D,P,Townsend,etc,Computerized simulation of meshing of conventional helical involute gears and modification of geometry,Mechanism and Machine Theory,1999,34:123-147,
[32]孙桓,陈作模,机械原理(第五版),北京,高等教育出版社,1996
[33]国营渭阳柴油机厂,直齿圆锥齿轮,北京,国防工业出版社,1978
[34]刘惟信,圆锥齿轮与双曲面齿轮传动,北京,民交通出版社,1980
[35]周延泽,吴继泽,直齿圆锥齿轮齿面和齿根过渡曲面方程,北京航空航天大学学,1993,112-120
[36]蒋法国,差速器行星齿轮的有限元法强度分析,[学位论文],长春,吉林大学,2006
[37]宁少惠,齿面摩擦力对齿根弯曲应力的影响,[学位论文],太原,太原理工大学,2005
[38]常江,齿轮副的静、动态数值计算与动态弹性实验研究,[学位论文],天津,天津大学,2004
[39]李金澎,大模数直齿轮轮齿弯曲强度与齿面接触研究,[学位论文],大连,大连理工大学,2005
[40]刘晖,基于参数化的齿轮传动接触有限元分析,[学位论文],大连,大连交通大学,2003
[41]徐戊矫,制造误差与承载变形耦合条件下平面二次包络环面蜗杆的啮合分析与啮合控制研究,[学位论文],重庆,重庆大学,2005
[42]东方人华,ANSYS7.0入门与提高,北京,清华大学出版社,2004
[43]盛云,双圆弧弧齿锥齿轮的实体建模及其弯曲应力的有限元分析,[学位论文],天津,天津工业大学,2005
[44]李剑锋,王钧效,王寿佑等,直齿圆锥齿轮齿向载荷分布及齿间载荷分配,山东工业大学学报,1996,26(4),445-450
[45]王云成,差速器行星齿轮的有限元法强度分析,[学位论文],长春,吉林大学,2005
[46]穆立茂,利用UG实现直齿圆锥齿轮的三维造型,机械,2004,31(10),24-26
[47]夏巨谌,陈霞,直齿圆锥齿轮的精确建模及其接触应力的有限元分析,轻工机械,2007,25(1),69-71
[48]钱学毅,郭波,邹丽梅,基于ANSYS和Pro/E的直齿圆锥齿轮齿根应力有限元分析,机械传动,2006,30(5),66-67
[49]刘大利,郭覃,周哲波,利用Pro/E Wildfire和CAXA进行渐开线直齿圆锥齿轮精确建模,煤矿机械,2007,28(3),74-75
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