基于模糊综合评判的重载齿轮热胶合和稳态温度场的研究
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摘要
重载齿轮是国民经济各部门中大型成套设备的关键基础件,本文以国内某重型机械企业生产的大型减速器中重载齿轮为研究对象,对其抗胶合承载能力设计问题进行了研究。本文完成的主要工作如下:
1.采用多级模糊综合评判法优化齿轮载荷系数
结合企业的实际设计生产能力和设备的安装调试情况,通过三级模糊综合评判方法,优化了齿轮的齿向载荷分布系数和齿间载荷分配系数,并编写了该算法基于Matlab的可执行程序。优化结果显示,该算法可根据企业提供的实际情况,降低齿轮载荷系数的取值。
2.采用积分温度法进行齿轮热胶合计算
根据GB/Z6413.2—2003标准,采用积分温度法,建立了渐开线斜齿轮的胶合承载能力计算模型,利用C++Builder程序设计语言开发了该模型的计算软件,通过该软件可快速得到齿轮热胶合承载能力计算结果。
3.建立渐开线斜齿轮的参数化实体模型
在ANSYS环境下,利用APDL语言,根据渐开线齿廓曲线方程,编写了渐开线斜齿轮参数化实体建模的程序。该程序通过输入齿轮的法面模数、齿数、齿宽和螺旋角等主要的几何参数,能快速生成齿轮实体模型。
4.分析齿轮稳态温度场并与积分温度法的计算结果进行对比
在ANSYS环境下,利用齿轮的参数化实体模型建立了相应的有限元模型,并求得了边界条件和热载荷条件,分析了齿轮的稳态温度场,求得了啮合面的最高温度值。通过与积分温度法计算结果的对比,发现重载工况下积分温度法的结果比有限元分析结果普遍偏高,普通载荷工况下两者符合较好。在采用多级模糊综合评判对积分温度结果进行优化后,两者在重载工况下的结果差距得到了显著的减小。结果还表明,重载齿轮啮合温度会随着法面模数增大、齿数增加、工作齿宽增大和螺旋角减小而降低,给企业在齿轮的设计和制造上提供了一定的理论依据。
The heavy-load gear is the basic and key part of many large equipment in the country. This paper has investigated the scuffing load capacity of heavy-load gear. The main completed work is as follows:
(1) Choosing load factor of gear teeth with fuzzy synthesis judgement
By three phase fuzzy synthesis judgement , the load factor of gear optimization was done in combination with the design production capacity and equipment installation, and the executable program of this method has been done based on MATLAB. The results show that the load factor has been decreased by the program.
(2) Calculation of scuffing load capacity of gear on integral temperature.
The calculation model of scuffing load capacity of gear has been done with the formula in GB/Z6413.2—2003.The program of the calculation model has been done based on C++Builder. This program shows the result of scuffing load capacity quickly.
(3) Building of the parametric solid model of involutes helical gears
The modeling program has been done based on APDL in ANSYS for equation of involutes tooth profile. The solid model of gear could be built by module, tooth number, tooth width and helix angle of gear quickly.
(4) Analysis of the steady temperature field of gear.
The finite element model of gear has been built by the solid model in ANSYS, also the boundary condition and thermal load has been obtained. The analysis for steady temperature field of gear has been done, and the maximum temperature of gearing face has been obtained. Contrasting the maximum temperature and the result of integral temperature shows that, the maximum temperature is higher than the result. After the optimization of the integral temperature has been done, the gap of two temperatures has been narrowed. The result also shows that, the temperature would get higher by increasing of module, tooth number, tooth width and helix angle.
1.采用多级模糊综合评判法优化齿轮载荷系数
结合企业的实际设计生产能力和设备的安装调试情况,通过三级模糊综合评判方法,优化了齿轮的齿向载荷分布系数和齿间载荷分配系数,并编写了该算法基于Matlab的可执行程序。优化结果显示,该算法可根据企业提供的实际情况,降低齿轮载荷系数的取值。
2.采用积分温度法进行齿轮热胶合计算
根据GB/Z6413.2—2003标准,采用积分温度法,建立了渐开线斜齿轮的胶合承载能力计算模型,利用C++Builder程序设计语言开发了该模型的计算软件,通过该软件可快速得到齿轮热胶合承载能力计算结果。
3.建立渐开线斜齿轮的参数化实体模型
在ANSYS环境下,利用APDL语言,根据渐开线齿廓曲线方程,编写了渐开线斜齿轮参数化实体建模的程序。该程序通过输入齿轮的法面模数、齿数、齿宽和螺旋角等主要的几何参数,能快速生成齿轮实体模型。
4.分析齿轮稳态温度场并与积分温度法的计算结果进行对比
在ANSYS环境下,利用齿轮的参数化实体模型建立了相应的有限元模型,并求得了边界条件和热载荷条件,分析了齿轮的稳态温度场,求得了啮合面的最高温度值。通过与积分温度法计算结果的对比,发现重载工况下积分温度法的结果比有限元分析结果普遍偏高,普通载荷工况下两者符合较好。在采用多级模糊综合评判对积分温度结果进行优化后,两者在重载工况下的结果差距得到了显著的减小。结果还表明,重载齿轮啮合温度会随着法面模数增大、齿数增加、工作齿宽增大和螺旋角减小而降低,给企业在齿轮的设计和制造上提供了一定的理论依据。
The heavy-load gear is the basic and key part of many large equipment in the country. This paper has investigated the scuffing load capacity of heavy-load gear. The main completed work is as follows:
(1) Choosing load factor of gear teeth with fuzzy synthesis judgement
By three phase fuzzy synthesis judgement , the load factor of gear optimization was done in combination with the design production capacity and equipment installation, and the executable program of this method has been done based on MATLAB. The results show that the load factor has been decreased by the program.
(2) Calculation of scuffing load capacity of gear on integral temperature.
The calculation model of scuffing load capacity of gear has been done with the formula in GB/Z6413.2—2003.The program of the calculation model has been done based on C++Builder. This program shows the result of scuffing load capacity quickly.
(3) Building of the parametric solid model of involutes helical gears
The modeling program has been done based on APDL in ANSYS for equation of involutes tooth profile. The solid model of gear could be built by module, tooth number, tooth width and helix angle of gear quickly.
(4) Analysis of the steady temperature field of gear.
The finite element model of gear has been built by the solid model in ANSYS, also the boundary condition and thermal load has been obtained. The analysis for steady temperature field of gear has been done, and the maximum temperature of gearing face has been obtained. Contrasting the maximum temperature and the result of integral temperature shows that, the maximum temperature is higher than the result. After the optimization of the integral temperature has been done, the gap of two temperatures has been narrowed. The result also shows that, the temperature would get higher by increasing of module, tooth number, tooth width and helix angle.
引文
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[3]张涵孚,何正嘉.模糊诊断原理及应用.西安:西安交通大学出版社,1992
[4]陈国权.模糊数学在经济管理中的应用.合肥:安徽科学技术出版社,1987
[5]于秀平.齿轮设计有关问题的探讨.电动工具,2004,(2):16,29
[6]李光辉,陈绍云.齿面胶合及对润滑油的选择.工业技术,2006,17:83
[7]张建峰,王翠玲,吴玉萍.ANSYS有限元分析软件在热分析中的应用.冶金能源,2004,23(5):9-12
[8]沈允文,王彤,王三民,等.弧齿锥齿轮传动的稳态本体温度场分析.机械传动,2001,25(3):1-4
[9]钱作勤,厉海祥,陆瑞松,等.ANSYS在求解点线啮合齿轮稳态温度场中的应用.武汉造船,1999,(4):20-22
[10]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(12):164-167
[11]赵宁,孙晓玲,陈国定,等.双圆弧齿轮传动的有限元热分析.现代制造工程,2006,4:50-52
[12]汪培庄.模糊数学简介(Ⅰ).数学的实践与认识,1980,(2):45-59
[13]陈永义,刘云丰,汪培庄.综合评判的数学模型.模糊数学,1983,(1):61-69
[14] Chen Y Y. An approach to fuzzy operators. Busefal, 1982, (9):59-65
[15]王道勇.模糊综合评判的失效与消除.系统工程理论方法应用,1998,7(2):66-69
[16] Dubois D, Prade H. Operationson fuzzy numbers. Intern J of Systerms Science, 1978, (9):613-626
[17] Sugeno M. Theory of fuzzy integrals and its applications. Toyko: Tokyo Institute of Technology,1974
[18]赵汝怀.模糊积分.数学研究与评论,1981,(2):55-72
[19]黄金丽.An application of fuzzy integrals in sports appaise.Palmade Malloca: Communication of First IFSACongress, 1985, Paralle Session 2:112-127
[20]刘文奇.均衡函数及其在变权综合中的应用.系统工程理论与实践,1997,(4):58-64
[21]苗壮,徐俊彦,王寒菊.部分变权综和评判模型研究.预测,1997,(4):51-52
[22]汪培庄,李洪兴.知识表示的数学理论.天津:天津科学技术出版社,1994
[23]陈守煜,赵瑛琪.系统层次分析模糊优选模型.水利学报,1988,(10):1-10
[24]饶正富.模糊多准则评价决策分析方法.系统工程学报,1991,(1):69-73
[25]高宏,应援明,左小德.基于次约束的模糊综合评判方法.决策与决策支持系统,1997,7(3):84-91
[26]张雅波,张跃龙,王抵修.模糊系统综合评判模型.松辽学刊(自然科学版), 1999,(4):52-54
[27]王光远,欧进萍.动态模糊集.模糊数学与系统,1988,(1):15-21
[28]钮晓鸣.带置信因子的模糊综合评判.系统工程理论方法应用,1997,6(2):71-80
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