识别动力减振镗杆主系统等效参数的数学计算方法
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摘要
采用动力减振镗杆是解决深孔加工颤振的有效技术途径,为设计减振镗杆内部吸振器的最优参数,需要识别镗杆主系统在吸振器安装位置的等效质量和等效刚度。针对采用实验和仿真的传统等效参数识别方法效率不高的问题,提出一种新的简单高效的数学计算方法:基于欧拉—伯努利梁理论和分段连续条件,将镗杆视为非等截面梁,建立主系统模态的数学模型,求解出固有频率和固有振型函数;再根据最大动能不变原则,推导出了主系统等效质量的求解公式;求解出镗杆主系统所有等效参数。数值仿真结果表明,新的数学计算方法可简便高效地计算出动力减振镗杆的主系统参数,从而提高动力减振镗杆的设计效率,同时也适用于其他不等截面梁等效动力学参数的求解。
Dynamic damping boring bar is an effective approach to avoid chatter in deep hole boring. In order to design the vibration absorber, it is necessary to identify the equivalent mass and stiffness at the location where the absorber is installed.Due to the low identification efficiency of the traditional method accompanied with both experiments and simulations, a new efficient mathematical model method was proposed to identify the equivalent parameters. Based on the Euler-Bernoulli beam theory and the maximum kinetic energy conservation principle, the mathematical model was established, and the formula for deriving the equivalent mass of damping boring bar's main system was presented. Then, all the equivalent parameters were calculated. Compared with the traditional identification method, the new mathematical method can accurately calculate the equivalent parameters, and improve the design efficiency of dynamic damping boring bars. Besides, the new mathematical method can also be applied to identify the kinetic equivalent parameters for other beams.
Dynamic damping boring bar is an effective approach to avoid chatter in deep hole boring. In order to design the vibration absorber, it is necessary to identify the equivalent mass and stiffness at the location where the absorber is installed.Due to the low identification efficiency of the traditional method accompanied with both experiments and simulations, a new efficient mathematical model method was proposed to identify the equivalent parameters. Based on the Euler-Bernoulli beam theory and the maximum kinetic energy conservation principle, the mathematical model was established, and the formula for deriving the equivalent mass of damping boring bar's main system was presented. Then, all the equivalent parameters were calculated. Compared with the traditional identification method, the new mathematical method can accurately calculate the equivalent parameters, and improve the design efficiency of dynamic damping boring bars. Besides, the new mathematical method can also be applied to identify the kinetic equivalent parameters for other beams.
引文
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[5]HOUCK III L,SCHMITZ T L,SMITH K S.A tuned holder for increased boring bar dynamic stiffness[J].Journal of Manufacturing Processes,2011,13(1):24-29.
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[7]RASHID A,NICOLESCU C M.Design and implementation of tuned viscoelastic dampers for vibration control in milling[J].International Journal of Machine Tools&Manufacture,2008,48(9):1036-1053.
[8]HENRIK A,TATIANA S,LARS H.Analysis of dynamic properties of boring bars concerning different clamping conditions[J].Mechanical Systems and Signal Processing,2009,23(8):2629-2647.
[9]SORTINO M,TOTIS G,PROSPERI F.Modeling the dynamic properties of conventional and high-damping boring bars[J].Mechanical Systems and Signal Processing,2013,34(1/2):340-352.
[10]MOETAKEF-IMANIB,YUSSEFIAN N Z.Dynamic simulation of boring process[J].International Journal of Machine Tools&Manufacture,2009,49(14):1096-1103.
[11]何山,杨志坚,丁康,等.基于正交多项式法的动力吸振器安装点的等效质量识别[J].振动与冲击,2014,33(24):211-214.HE Shan,YANG Zhijian,DING Kang,et al.Estimating equivalent mass of a dynamic vibration absorber at mounting point based on method of orthogonal polynomials[J].Journal of Vibration and Shock,2014,33(24):211-214.
[12]KAZUTO S,MASAAKI O,SHIGEO Y,et al.Method of estimating equivalent mass of multi-degree-of-freedom system[J].JSME International Journal,1987,30(268):1638-1644.
[2]罗红波,李红梅,程宏伟,等.内置式减振镗杆动力学模型的参数优化[J].四川大学学报,2009,41(6):200-204.LUO Hongbo,LI Hongmei,CHENG Hongwei,et al.Parameter optimization of built-in damping boring bar kinetic mode[J].Journal of Sichuan University,2009,41(6):200-204.
[3]MIGUELEZ M H,RUBIO L,LOYA J A.Improvement of chatter stability in boring operations with passive vibration absorbers[J].International Journal of Mechanical Sciences,2010,52(10):1376-1384.
[4]RUBIO L,LOYA J A,MIGUELEZ M H.Optimization of passive vibration absorbers to reduce chatter in boring[J].Mechanical Systems and Signal Processing,2013,41(1/2):691-704.
[5]HOUCK III L,SCHMITZ T L,SMITH K S.A tuned holder for increased boring bar dynamic stiffness[J].Journal of Manufacturing Processes,2011,13(1):24-29.
[6]杨月婷,高国生,张作良.半主动动力吸振镗杆系统的颤振抑制机理[J].石家庄铁道大学学报,2014,27(3):55-58.YANG Yueting,GAO Guosheng,ZHANG Zuoliang.Chatter suppression mechanism of semi-active damping boring bar system[J].Journal of Shijiazhuang Tiedao University,2014,27(3):55-58.
[7]RASHID A,NICOLESCU C M.Design and implementation of tuned viscoelastic dampers for vibration control in milling[J].International Journal of Machine Tools&Manufacture,2008,48(9):1036-1053.
[8]HENRIK A,TATIANA S,LARS H.Analysis of dynamic properties of boring bars concerning different clamping conditions[J].Mechanical Systems and Signal Processing,2009,23(8):2629-2647.
[9]SORTINO M,TOTIS G,PROSPERI F.Modeling the dynamic properties of conventional and high-damping boring bars[J].Mechanical Systems and Signal Processing,2013,34(1/2):340-352.
[10]MOETAKEF-IMANIB,YUSSEFIAN N Z.Dynamic simulation of boring process[J].International Journal of Machine Tools&Manufacture,2009,49(14):1096-1103.
[11]何山,杨志坚,丁康,等.基于正交多项式法的动力吸振器安装点的等效质量识别[J].振动与冲击,2014,33(24):211-214.HE Shan,YANG Zhijian,DING Kang,et al.Estimating equivalent mass of a dynamic vibration absorber at mounting point based on method of orthogonal polynomials[J].Journal of Vibration and Shock,2014,33(24):211-214.
[12]KAZUTO S,MASAAKI O,SHIGEO Y,et al.Method of estimating equivalent mass of multi-degree-of-freedom system[J].JSME International Journal,1987,30(268):1638-1644.