机车高圆簧刚度矩阵计算应用分析
|
摘要
高圆簧广泛应用于机车车辆中,其刚度作为车辆的主要悬挂参数,仿真时刚度矩阵的选择和简化处理对计算结果有直接影响。在一般机车模型的动力学仿真中只考虑了高圆簧刚度矩阵6个对角元素,未考虑非对角元素的影响。通过推导高圆簧的完整矩阵,并分别以弹簧振子和机车作为对象进行对比分析。计算结果表明,仿真结果与理论分析结果吻合;高圆簧采用完整刚度矩阵的机车动力学性能优于高圆簧只采用对角元素的机车,其差异主要表现在与高圆簧轴向垂直的方向上,轴向性能基本一致;机车高圆簧只考虑矩阵对角元素时仿真结果较考虑完整刚度矩阵时偏于安全,但二者最大差值都未超过10%,可以用于机车模型的计算分析。
The stiffness of flex-coil springs,which are widely used in rolling stocks,is the major suspension parameter of the vehicle.The choice and simplification of the stiffness matrix during simulation have a direct influence on the calculation results.Normally,the dynamic simulations of locomotive only take the six diagonal elements of the spring matrix into consideration,while the effects of non-diagonal elements are ignored.In this paper,the complete matrix of flex-coil springs has been discussed,and the comparison and analysis have been conducted based on the study of the spring oscillator and the locomotive.The results show that the simulation results are in agreement with the theoretical results.The dynamic performance of the locomotive using the flex-coil springs with complete matrixes is better than that with only diagonal matrixes.Moreover,the difference is mainly in the direction perpendicular to the axial direction of the spring,while the axial performance is basically the same.The simulation results of the flex-coil springs with only diagonal matrixes,are safer than those with complete stiffness matrixes,nevertheless,the maximum difference that does not exceed10%,is acceptable in the calculation and analysis of locomotive model.
The stiffness of flex-coil springs,which are widely used in rolling stocks,is the major suspension parameter of the vehicle.The choice and simplification of the stiffness matrix during simulation have a direct influence on the calculation results.Normally,the dynamic simulations of locomotive only take the six diagonal elements of the spring matrix into consideration,while the effects of non-diagonal elements are ignored.In this paper,the complete matrix of flex-coil springs has been discussed,and the comparison and analysis have been conducted based on the study of the spring oscillator and the locomotive.The results show that the simulation results are in agreement with the theoretical results.The dynamic performance of the locomotive using the flex-coil springs with complete matrixes is better than that with only diagonal matrixes.Moreover,the difference is mainly in the direction perpendicular to the axial direction of the spring,while the axial performance is basically the same.The simulation results of the flex-coil springs with only diagonal matrixes,are safer than those with complete stiffness matrixes,nevertheless,the maximum difference that does not exceed10%,is acceptable in the calculation and analysis of locomotive model.
引文
[1]FAKHREDDINE D.Finite Element Method for the Stress Analysis of Isotropic Cylindrical Helical Spring[J].European Journal of Mechanics,2005,24(6):1068-1078.
[2]王时龙,雷松,周杰,等.两端并圈多股弹簧的冲击响应研究[J].振动与冲击,2011(3):64-68.WANG Shilong,LEI Song,ZHOU Jie,et al.Impact Response of Stranded Wires Helical Springs with Closed Ends[J].Journal of Vibration and Shock,2011(3):64-68.
[3]米彩盈,李芾.并联高圆簧一端串联橡胶弹簧系统水平方向刚度及稳定性分析[J].铁道机车与动车,2001(10):5-9.MI Caiying,LI Fu.Analysis of Horizontal Stiffness and Stability of High Parallel Spring with One End Have the Series Rubber Spring[J].Railway Locomotive and Motor Car,2001(10):5-9.
[4]邹景超,李安生,刘建秀,等.截锥螺旋压缩弹簧在SS8电力机车上的应用研究[J].机械设计与制造,2009(12):94-95.ZOU Jingchao,LI Ansheng,LIU Jianxiu,et al.Applied Research of Conical Helical Compression Spring on the SS8E-lectric Locomotive[J].Machinery Design&Manufacture,2009(12):94-95.
[5]丘盛昌,安琦.圆柱螺旋弹簧横向刚度的计算方法[J].华东理工大学学报,2015,41(6):846-851.QIU Shengchang,AN Qi.Calculation Method of Lateral Stiffness of Cylindrical Helical Spring[J].Journal of East China University of Science and Technoloy,2015,41(6):846-851.
[6]ZEBDI O,BOUKHILI R,TROCHU F.Optimum Design of a Composite Helical Spring by Multi-criteria Optimization[J].Journal of Reinforced Plastics and Composites,2009,28(14):1713-1732.
[7]CHOI B L,CHOI B H.Numerical Method for Optimizing Design Variables of Carbon-fiber-reinforced Epoxy Composite Coil Springs[J].Composites Part B:Engineering,2015,82:42-49.
[8]熊志远,宋瑞祥,康钟绪,等.复合材料螺旋弹簧刚度及其影响因素分析[J].工程力学,2015,32(9):216-228.XIONG Zhiyuan,SONG Ruixiang,KANG Zhongxu,et al.Analysis on Rigidity of Composite Helical Spring and Its Influence Factors[J].Engineering Mechanics,2015,32(9):216-228.
[9]商跃进,王红.变刚度弹簧组系统优化设计[J].铁道学报,2006,28(6):51-54.SHANG Yuejin,WANG Hong.Optimized Design of Variable-stiffness Spring Combinations System[J].Journal of the China Railway Society,2006,28(6):51-54.
[10]杨永宝.碳纤维复合材料圆柱螺旋弹簧的刚强度设计方法研究[D].北京:清华大学,2013.
[11]WAHL A M.Mechanical Spring[M].北京:国防工业出版社,1981:320-322.
[12]朱勋,吕坤勇,宋成利,等.基于ABAQUS分析圆柱螺旋弹簧几何参数对弹簧刚度的影响[J].机械设计与研究,2015,31(4):95-98.ZHU Xun,LKunyong,SONG Chengli,et al.Study on the Influence of Cylinder Helical Spring’s Geometrical Parameters on Spring Constant Based on ABAQUS[J].Machine Design and Research,2015,31(4):95-98.
[13]米彩盈,李芾.轴箱螺旋压缩圆弹簧横向刚度分析[J].铁道机车车辆,2003,23(5):33-35.MI Caiying,LI Fu.Transverse Stiffness Analysis of Axle Box Cylindrical Helical Compression Spring[J].Railway Locomotive&Car,2003,23(5):33-35.
[14]李艳.高速列车动力学参数影响度的研究与应用[D].成都:西南交通大学,2008.
[15]严隽耄.车辆工程[M].北京:中国铁道出版社,2008.
[16]中华人民共和国建设部.GB 50090-2006铁路线路设计规范[S].北京:中国计划出版社,2006.
[2]王时龙,雷松,周杰,等.两端并圈多股弹簧的冲击响应研究[J].振动与冲击,2011(3):64-68.WANG Shilong,LEI Song,ZHOU Jie,et al.Impact Response of Stranded Wires Helical Springs with Closed Ends[J].Journal of Vibration and Shock,2011(3):64-68.
[3]米彩盈,李芾.并联高圆簧一端串联橡胶弹簧系统水平方向刚度及稳定性分析[J].铁道机车与动车,2001(10):5-9.MI Caiying,LI Fu.Analysis of Horizontal Stiffness and Stability of High Parallel Spring with One End Have the Series Rubber Spring[J].Railway Locomotive and Motor Car,2001(10):5-9.
[4]邹景超,李安生,刘建秀,等.截锥螺旋压缩弹簧在SS8电力机车上的应用研究[J].机械设计与制造,2009(12):94-95.ZOU Jingchao,LI Ansheng,LIU Jianxiu,et al.Applied Research of Conical Helical Compression Spring on the SS8E-lectric Locomotive[J].Machinery Design&Manufacture,2009(12):94-95.
[5]丘盛昌,安琦.圆柱螺旋弹簧横向刚度的计算方法[J].华东理工大学学报,2015,41(6):846-851.QIU Shengchang,AN Qi.Calculation Method of Lateral Stiffness of Cylindrical Helical Spring[J].Journal of East China University of Science and Technoloy,2015,41(6):846-851.
[6]ZEBDI O,BOUKHILI R,TROCHU F.Optimum Design of a Composite Helical Spring by Multi-criteria Optimization[J].Journal of Reinforced Plastics and Composites,2009,28(14):1713-1732.
[7]CHOI B L,CHOI B H.Numerical Method for Optimizing Design Variables of Carbon-fiber-reinforced Epoxy Composite Coil Springs[J].Composites Part B:Engineering,2015,82:42-49.
[8]熊志远,宋瑞祥,康钟绪,等.复合材料螺旋弹簧刚度及其影响因素分析[J].工程力学,2015,32(9):216-228.XIONG Zhiyuan,SONG Ruixiang,KANG Zhongxu,et al.Analysis on Rigidity of Composite Helical Spring and Its Influence Factors[J].Engineering Mechanics,2015,32(9):216-228.
[9]商跃进,王红.变刚度弹簧组系统优化设计[J].铁道学报,2006,28(6):51-54.SHANG Yuejin,WANG Hong.Optimized Design of Variable-stiffness Spring Combinations System[J].Journal of the China Railway Society,2006,28(6):51-54.
[10]杨永宝.碳纤维复合材料圆柱螺旋弹簧的刚强度设计方法研究[D].北京:清华大学,2013.
[11]WAHL A M.Mechanical Spring[M].北京:国防工业出版社,1981:320-322.
[12]朱勋,吕坤勇,宋成利,等.基于ABAQUS分析圆柱螺旋弹簧几何参数对弹簧刚度的影响[J].机械设计与研究,2015,31(4):95-98.ZHU Xun,LKunyong,SONG Chengli,et al.Study on the Influence of Cylinder Helical Spring’s Geometrical Parameters on Spring Constant Based on ABAQUS[J].Machine Design and Research,2015,31(4):95-98.
[13]米彩盈,李芾.轴箱螺旋压缩圆弹簧横向刚度分析[J].铁道机车车辆,2003,23(5):33-35.MI Caiying,LI Fu.Transverse Stiffness Analysis of Axle Box Cylindrical Helical Compression Spring[J].Railway Locomotive&Car,2003,23(5):33-35.
[14]李艳.高速列车动力学参数影响度的研究与应用[D].成都:西南交通大学,2008.
[15]严隽耄.车辆工程[M].北京:中国铁道出版社,2008.
[16]中华人民共和国建设部.GB 50090-2006铁路线路设计规范[S].北京:中国计划出版社,2006.