装载机差速器齿轮的非线性接触与疲劳寿命分析
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摘要
装载机驱动桥差速器齿轮的寿命预测对驱动桥的结构设计具有重要意义,但因装载机结构和受力情况复杂,预测结果与实际寿命的差距都很大。论文以ZL50轮式装载机差速器齿轮为研究对象,应用概率统计法、非线性接触有限元理论与疲劳分析理论,深入、系统地研究了差速器齿轮非线性接触有限元计算和疲劳分析与寿命预测的方法,分析了载荷谱、齿轮实体模型和材料力学特性参数的不确定性对疲劳寿命预测的影响。
通过分析轮式装载机的实际工况,依据发动机与液力变矩器共同作用的匹配特性曲线,确定了装载机最大工作载荷。在此基础上,以装载机载荷的正态分布函数为依据,运用“3σ”法则和概率统计法,并根据程序载荷谱的分级原则,编制了装载机差速器齿轮的程序转矩载荷谱。
依据差速器齿轮的齿廓曲线与齿根过渡曲线方程,利用Pro/E参数化建模功能创建了精确的差速器齿轮三维实体模型,为其有限元分析与疲劳寿命分析打下了基础。
采用非线性接触有限元法对差速器齿轮进行齿轮接触全过程的数值模拟,探讨了单元类型与网格质量、约束方式和接触实常数的设置对非线性计算的收敛性和结果精度的影响,并建立了疲劳寿命分析相应的应力谱。
对基于差速器齿轮有限元实际应力谱的疲劳寿命分析,以材料的S-N疲劳特性曲线为基础,分别讨论了应力集中、尺寸效应和表面状况对零件疲劳寿命的影响,建立了零件的S-N曲线方程;探讨了钢材料临界疲劳损伤DC R的取值范围;运用Elementary Miner法则和Haibach法则修正后的Miner理论,分别对差速器半轴齿轮进行弯曲疲劳寿命预测,得到了半轴齿轮的中位使用寿命区间,并探讨了载荷数据统计对疲劳寿命分析的影响。
研究结果表明:利用准确的齿面方程建立的齿轮三维模型,在有限元三维虚拟环境下进行力学分析,精度是足够的。当装载机的载荷服从正态分布,差速器齿轮的载荷谱为对称循环载荷时,在一对轮齿从接触到分离的啮合周期内,可以得到齿轮薄弱环节的应力谱,利用疲劳累积损伤理论,即可预测出齿轮的疲劳寿命。装载机在实际工作环境的试验表明:寿命预测结果与实际情况相符,验证了研究方法的可信性。同时,为其它齿轮寿命预测提供了新的方法和理论。
The fatigue life prediction of differential gear in drive axle of loader has great significance to the structural design of the driver axle, because of the complicated structure and force of the loader, the prediction and actual life of the gap was large. Taking the differential gear of ZL50 wheel loader as the research object, the paper, using the probability statistics, the non-linear contact finite element analysis and the fatigue theory, in-depth and systematically studied the nonlinear contact finite element analysis and fatigue life prediction method of the differential gear, and analyzed the impact of fatigue life prediction which the load spectrum, the gear solid model and the uncertainty of material parameters of mechanical properties produced.
By analyzing the wheel loader of the actual working conditions, according the engine and the torque converter characteristic curves of match together, the paper determined the maximum working load of the loader. On this basis, based on the normal distribution function with loader loads and the principle of classification with the load program spectrum, the paper used“3σ”theorem and probability statistics to write the torque program spectrum block of the differential gear.
Based on the profile curve and the tooth root transition curve equation of the differential gear, the paper utilized the capability of Pro/E parametric modeling to create a precise differential gear solid model for the finite element analysis and the fatigue life analysis.
Adopting the non-linear contact finite element method to numerically simulate the whole contact process in gear for the differential gears, the paper discussed the influence of the non-linear calculation convergence and the accuracy of the results for cell types and mesh quality, constraints, and contact with real constant set, and created the stress spectrum for fatigue life analysis.
For the fatigue life analysis with the finite element actual stress spectrum, based on the material S-N fatigue curves, the paper respectively discussed the influence of the part fatigue life with stress concentration and size effect and surface conditions, and founded the equation of the part S-N fatigue curves, and explored the scope of the critical fatigue damage of steel materials DC R; the paper respectively estimated the bending fatigue life of the differential gear using the modified Miner theory by the Elementary Miner rule and the Haibach rule, received the middle reliability life scope of half axle gear, and explored the impact of load statistical analysis on the fatigue life.
The results showed that under the 3D virtual environment of the finite element, the dynamics analysis had enough precision when using the gear solid model with the exact surface equation of the gear tooth. When the loader loads obeyed the normal distribution and the differential gear obeyed symmetrical cyclic loading, in the whole contact period of a pair of tooth, we can get the stress spectrum of gear weaknesses, and predicted the gear’s fatigue life using the fatigue cumulative damage theory. In actual working environment, the test showed that the prediction results were consistent with the actual situation, which verified the credibility of the research methods. At the same time, the paper provided a new method and theory for the fatigue life prediction of the gear.
通过分析轮式装载机的实际工况,依据发动机与液力变矩器共同作用的匹配特性曲线,确定了装载机最大工作载荷。在此基础上,以装载机载荷的正态分布函数为依据,运用“3σ”法则和概率统计法,并根据程序载荷谱的分级原则,编制了装载机差速器齿轮的程序转矩载荷谱。
依据差速器齿轮的齿廓曲线与齿根过渡曲线方程,利用Pro/E参数化建模功能创建了精确的差速器齿轮三维实体模型,为其有限元分析与疲劳寿命分析打下了基础。
采用非线性接触有限元法对差速器齿轮进行齿轮接触全过程的数值模拟,探讨了单元类型与网格质量、约束方式和接触实常数的设置对非线性计算的收敛性和结果精度的影响,并建立了疲劳寿命分析相应的应力谱。
对基于差速器齿轮有限元实际应力谱的疲劳寿命分析,以材料的S-N疲劳特性曲线为基础,分别讨论了应力集中、尺寸效应和表面状况对零件疲劳寿命的影响,建立了零件的S-N曲线方程;探讨了钢材料临界疲劳损伤DC R的取值范围;运用Elementary Miner法则和Haibach法则修正后的Miner理论,分别对差速器半轴齿轮进行弯曲疲劳寿命预测,得到了半轴齿轮的中位使用寿命区间,并探讨了载荷数据统计对疲劳寿命分析的影响。
研究结果表明:利用准确的齿面方程建立的齿轮三维模型,在有限元三维虚拟环境下进行力学分析,精度是足够的。当装载机的载荷服从正态分布,差速器齿轮的载荷谱为对称循环载荷时,在一对轮齿从接触到分离的啮合周期内,可以得到齿轮薄弱环节的应力谱,利用疲劳累积损伤理论,即可预测出齿轮的疲劳寿命。装载机在实际工作环境的试验表明:寿命预测结果与实际情况相符,验证了研究方法的可信性。同时,为其它齿轮寿命预测提供了新的方法和理论。
The fatigue life prediction of differential gear in drive axle of loader has great significance to the structural design of the driver axle, because of the complicated structure and force of the loader, the prediction and actual life of the gap was large. Taking the differential gear of ZL50 wheel loader as the research object, the paper, using the probability statistics, the non-linear contact finite element analysis and the fatigue theory, in-depth and systematically studied the nonlinear contact finite element analysis and fatigue life prediction method of the differential gear, and analyzed the impact of fatigue life prediction which the load spectrum, the gear solid model and the uncertainty of material parameters of mechanical properties produced.
By analyzing the wheel loader of the actual working conditions, according the engine and the torque converter characteristic curves of match together, the paper determined the maximum working load of the loader. On this basis, based on the normal distribution function with loader loads and the principle of classification with the load program spectrum, the paper used“3σ”theorem and probability statistics to write the torque program spectrum block of the differential gear.
Based on the profile curve and the tooth root transition curve equation of the differential gear, the paper utilized the capability of Pro/E parametric modeling to create a precise differential gear solid model for the finite element analysis and the fatigue life analysis.
Adopting the non-linear contact finite element method to numerically simulate the whole contact process in gear for the differential gears, the paper discussed the influence of the non-linear calculation convergence and the accuracy of the results for cell types and mesh quality, constraints, and contact with real constant set, and created the stress spectrum for fatigue life analysis.
For the fatigue life analysis with the finite element actual stress spectrum, based on the material S-N fatigue curves, the paper respectively discussed the influence of the part fatigue life with stress concentration and size effect and surface conditions, and founded the equation of the part S-N fatigue curves, and explored the scope of the critical fatigue damage of steel materials DC R; the paper respectively estimated the bending fatigue life of the differential gear using the modified Miner theory by the Elementary Miner rule and the Haibach rule, received the middle reliability life scope of half axle gear, and explored the impact of load statistical analysis on the fatigue life.
The results showed that under the 3D virtual environment of the finite element, the dynamics analysis had enough precision when using the gear solid model with the exact surface equation of the gear tooth. When the loader loads obeyed the normal distribution and the differential gear obeyed symmetrical cyclic loading, in the whole contact period of a pair of tooth, we can get the stress spectrum of gear weaknesses, and predicted the gear’s fatigue life using the fatigue cumulative damage theory. In actual working environment, the test showed that the prediction results were consistent with the actual situation, which verified the credibility of the research methods. At the same time, the paper provided a new method and theory for the fatigue life prediction of the gear.
引文
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[2]杨占敏,王智明,张春秋等.轮式装载机[M].北京:化学工业出版社,2006:194-195
[3]何正忠.装载机[M].北京:冶金工业出版社,1996: 299
[4]田志成,王东升,陈英杰.国内外装载机可靠性与使用寿命分析[J].建筑机械,2005(11):63-65
[5]刘惟信.机械可靠性设计[M].北京:清华大学出版社,1996: 221
[6]张洪武,关振群,李云鹏,顾元宪.有限元分析与CAE技术基础[M].北京:清华大学出版社,2004:
[7]曾攀.有限元分析及应用[M].北京:清华大学,2004:3
[8]曹雪梅,方宗德,张金良,邓效忠.弧齿锥齿轮的齿面主动设计[J].机械工程学报,2007,47(8): 155-158
[9]麻连荣.基于Pro/E的圆柱齿轮减速器参数化CAD系统的研究与开发[D]. [硕士论文].同济大学,2007
[10]王晓勇.基于UG的章动齿轮减速器建模和仿真研究[D]. [硕士论文].昆明理工大学,2006
[11]刘昆民.圆柱齿轮减速器的快速设计技术[D]. [硕士论文].太原理工大学,2005
[12] Kousaku Ohno, Naoyuki Tanaic. A Contact Stress Analysis for Helical Gear with 3-Dimensional Finite Element Method [J]. Finite Elements in Analysis and Design. 2001: 1-7
[13] J Wang and I Howard. The Torsional Stiffness of Involute Spur Gears [J]. Mechanical Engineering Science. 2004(218.C14902):1-12
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