组合阶梯梁振动特性计算方法及应用
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摘要
在机械加工过程中,对机床主轴进行结构优化或者合理选择刀柄刀具可以改善机床主轴刀柄刀具系统的振动特性,从而提高加工质量和效率.针对机床主轴刀柄刀具系统的振动特性问题,提出了一种基于组合阶梯梁模型的计算方法.基于伯努利-欧拉梁模型,提出了悬臂梁状态下的变截面阶梯梁的固有频率和振型的计算方法;基于实际应用中的刀柄铣刀配合系统,将阶梯梁模型进一步改进为组合阶梯梁模型,提出了梁组合部分的等效弯曲刚度和密度的计算方法,并将该方法应用于刀柄装夹铣刀系统的振动特性分析中,通过有限元法和实验结果验证了该方法的有效性.结果表明:与铁木辛柯梁理论相比,本文算法在计算机床刀柄刀具系统等具有大长径比并且考虑模态阶次较低的情况下,计算误差小,计算效率提高1倍.
In the process of machining,vibration characteristics of the machine tool spindle tool system can be improved by structure optimization of machine tool spindle and appropriate selection of tool and toolholder,reaching a higher machining quality and efficiency with good vibration characteristics. To study the vibration characteristics of the machine tool spindle,this paper proposed a method based on combined stepped beam model. The method for solving bending vibration natural frequency and mode of stepped cantilever beam was developed with the use of Euler-Bernoulli beam theory. Based on the tooltoolholder coupled system from the practical condition,this paper refined the stepped beam model to the combined stepped beam and gave the equivalent bending rigidity and density of the combined part. This method was applied to calculate the vibration characteristics of the tool-toolholder coupled system and it was verified though the finite element method( FEM) and experiment. Results show that compared withthe Timoshenko beam theory,this method doubles the computational efficiency whereas calculation error keeps small in condition of large ratio of length to diameter and low order of modal is considered like the machine tool spindle tool system.
In the process of machining,vibration characteristics of the machine tool spindle tool system can be improved by structure optimization of machine tool spindle and appropriate selection of tool and toolholder,reaching a higher machining quality and efficiency with good vibration characteristics. To study the vibration characteristics of the machine tool spindle,this paper proposed a method based on combined stepped beam model. The method for solving bending vibration natural frequency and mode of stepped cantilever beam was developed with the use of Euler-Bernoulli beam theory. Based on the tooltoolholder coupled system from the practical condition,this paper refined the stepped beam model to the combined stepped beam and gave the equivalent bending rigidity and density of the combined part. This method was applied to calculate the vibration characteristics of the tool-toolholder coupled system and it was verified though the finite element method( FEM) and experiment. Results show that compared withthe Timoshenko beam theory,this method doubles the computational efficiency whereas calculation error keeps small in condition of large ratio of length to diameter and low order of modal is considered like the machine tool spindle tool system.
引文
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[10] QIBO M. Free vibration analysis of multiple-stepped beams by using adomian decomposition method[J].Mathematical&Computer Modelling,2011,54(1/2):756-764
[11]杨骁,刘璐.悬臂组合梁大挠度弯曲的挠度分析[J].力学季刊,2012,33(4):665-671.YANG X, LIU L. Deflection analysis ofcantilever composite beam for large deflection bending[J]. Chinese Quarterly of Mechanics,2012,33(4):665-671.(in Chinese)
[12]崔灿,李映辉.变截面铁木辛柯梁振动特性快速计算方法[J].动力学与控制学报,2012,10(3):258-262.CUI C,LI Y H. A solution for vibration characteristic of Timoshenko beam with variable cross-section[J]. Journal of Dynamic and Control,2012,10(3):258-262.(in Chinese)
[13] DONG X J,MENG G,LI H G,et al. Vibration analysis of a stepped laminated composite Timoshenko beam[J].Mechanics Research Communications,2005,32(5):572-581.
[14]张曙.机床产品创新与设计[M].南京:东南大学出版社,2014:210-212.
[2] YANG Y,YU Y. Design and simulation of long slender end mill embedded with passive damper[C]∥Procedia Engineering of 2014 Asia-Pacific International Symposium on Aerospace Technology. Amsterdam:Elsevier Ltd,2015,99:1380-1384.
[3]李超,沈春根,范燕萍.基于阻尼减振器的铣削过程稳定性研究[J].工具技术,2016,50(9):12-16.LI C,SHEN C G,FAN Y P. Study on stability of milling process based on damping absorber[J]. Tool Engineering,2016,50(9):12-16.(in Chinese)
[4]胡李波,王民,李刚.动力减振镗杆的减振性能研究[J].机械设计与制造,2009(1):131-133.HU L B, WANG M, LI G. Research of dynamical vibration absorber for a boring bar[J]. Machinery Design and Manufacture,2009(1):131-133.(in Chinese)
[5]王跃辉,王民.金属切削过程颤振控制技术的研究进展[J].机械工程学报,2010,46(7):166-174.WANG Y H,WANG M. Advances on machining chatter suppression research[J]. Journal of Mechanical Engineering,2010,46(7):166-174.(in Chinese)
[6]杜立群,颜云辉,王德俊,等.非均质阶梯梁的横向自由振动精确解[J].沈阳工业学院学报,1998,17(3):63-66.DU L Q,YAN Y H,WANG D J,et al. An accurate solution for transverse free vibration of nonhomogeneous stepped beam[J]. Journal of Shenyang Institute of Technology,1998,17(3):63-66.(in Chinese)
[7]夏季,朱目成,马德毅.阶梯轴弯曲固有振动分析及应用[J].冲击与振动,2000,17(2):22-24.XIA J,ZHU M C,MA D Y. The analysis and application of stepped shaft bending vibration[J]. Journal of Vibration and Chock,2000,17(2):22-24.(in Chinese)
[8] GIUSEPPE F,ADOLFO S. A solution method for EulerBernoulli vibrating discontinuous beams[J]. Mechanics Research Communications,2008,35(8):517-529.
[9] YUCHENG L, CHANDRA S G. The use of He's variational iteration method for obtaining the freevibration of an Euler-Bernoulli beam[J]. Mathematical&Computer Modelling,2009,50(11/12):1545-1552.
[10] QIBO M. Free vibration analysis of multiple-stepped beams by using adomian decomposition method[J].Mathematical&Computer Modelling,2011,54(1/2):756-764
[11]杨骁,刘璐.悬臂组合梁大挠度弯曲的挠度分析[J].力学季刊,2012,33(4):665-671.YANG X, LIU L. Deflection analysis ofcantilever composite beam for large deflection bending[J]. Chinese Quarterly of Mechanics,2012,33(4):665-671.(in Chinese)
[12]崔灿,李映辉.变截面铁木辛柯梁振动特性快速计算方法[J].动力学与控制学报,2012,10(3):258-262.CUI C,LI Y H. A solution for vibration characteristic of Timoshenko beam with variable cross-section[J]. Journal of Dynamic and Control,2012,10(3):258-262.(in Chinese)
[13] DONG X J,MENG G,LI H G,et al. Vibration analysis of a stepped laminated composite Timoshenko beam[J].Mechanics Research Communications,2005,32(5):572-581.
[14]张曙.机床产品创新与设计[M].南京:东南大学出版社,2014:210-212.
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