辨识主轴转子系统能量传递特性的矢量匹配平衡方法研究
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摘要
为了有效抑制主轴转子系统由于不平衡引起的振动,并且克服传统动平衡方法效率低下的问题。以180SD35Q15高速磨削主轴为研究对象,利用有限元法,建立了主轴转子系统的动力学模型,并且利用模态测试试验对模型进行了修正,实现转子系统结构特征参数的获取;通过动力学方程证明了加重影响系数实际是由转子系统结构参数决定,是能够反映转子系统能量传递特性的参数,并且利用结构参数对其实现了辨识,利用矢量合成原理对配重方案进行寻优匹配,快速、准确的获取了配重质量和相位,采用矢量匹配平衡法和影响系数法进行了对比试验研究。结果表明:在15 000 r/min,18 000 r/min以及21 000 r/min时采用矢量匹配平衡方法进行动平衡,抑振幅度分别达到64.85%,49.57%和60.59%,抑振效果相较于影响系数法更好,且无需试重,一次配重成功,有效的缩短了平衡时间,大大地提高了平衡效率。
In order to suppress the vibration caused by the imbalance of a spindle rotor system, and to overcome the low efficiency of the conventional dynamic balancing method, the dynamic model of a spindle rotor system was established by using the finite element method. The model was modified by the modal test experiment and the identification of the structural parameters of the rotor system was realized, taking the 180 SD35 Q15 high-speed grinding spindle as the research object.It is proved that the influence coefficient is determined by the rotor structure parameters which can reflect the energy transfer characteristics of the rotor system. Using the principle of vector synthesis to match the weight, the weight and phase can be quickly and accurately obtained. The experimental results of the vector matching balance method were compared with those of the influence coefficient method. The results show that: the amplitude at the running frequency is reduced by 64.85%, 49.57% and 60.59% at the speed of 15 000 r/min, 18 000 r/min and 21 000 r/min, respectively. The balancing effect is better than the influence coefficient method, and it needs no trial weights, which shortens the balance time and greatly improves the balance efficiency.
In order to suppress the vibration caused by the imbalance of a spindle rotor system, and to overcome the low efficiency of the conventional dynamic balancing method, the dynamic model of a spindle rotor system was established by using the finite element method. The model was modified by the modal test experiment and the identification of the structural parameters of the rotor system was realized, taking the 180 SD35 Q15 high-speed grinding spindle as the research object.It is proved that the influence coefficient is determined by the rotor structure parameters which can reflect the energy transfer characteristics of the rotor system. Using the principle of vector synthesis to match the weight, the weight and phase can be quickly and accurately obtained. The experimental results of the vector matching balance method were compared with those of the influence coefficient method. The results show that: the amplitude at the running frequency is reduced by 64.85%, 49.57% and 60.59% at the speed of 15 000 r/min, 18 000 r/min and 21 000 r/min, respectively. The balancing effect is better than the influence coefficient method, and it needs no trial weights, which shortens the balance time and greatly improves the balance efficiency.
引文
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[10] 章云,梅雪松,邹冬林,等.应用模态分析及傅里叶变换的柔性转子无试重动平衡方法[J].振动与冲击,2012,31(11):7-10.ZHANG Yun,MEI Xuesong,ZOU Donglin,et al.A field balancing method of a flexible rotors based on modal analysis and fourier transformation[J].Journal of Vibration and Shock,2012,31(11):7-10.
[11] 章云,梅雪松,邹冬林,等.应用动力学模型的高速主轴无试重动平衡方法[J].西安交通大学学报,2011,45(7):34-37.ZHANG Yun,MEI Xuesong,ZOU Donglin,et al.Model based balancing method for high speed machine tool spindle without trial weights[J].Journal of Xi’an Jiaotong University,2011,45(7):34-37.
[12] CAO H,LI Y,CHEN X.A new dynamic model of ball-bearing rotor systems based on rigid body element[J].Journal of Manufacturing Science & Engineering,2016,138(7):071007.
[13] CAO H,LI B,HE Z.Finite element model updating of machine-tool spindle systems[J].Journal of Vibration and Acoustics,Transactions of the ASME,2013,135(2):024503.
[14] 田久良,洪军,朱永生,等.机床主轴-轴承系统热-力耦合模型及其动态性能研究[J].西安交通大学学报,2012,46(7):63-68.TIAN Jiuliang,HONG Jun,ZHU Yongsheng,et al.Thermo-mechanical coupling model and dynamical characteristics of machining spindle bearing system[J].Journal of Xi’an Jiaotong University,2012,46(7):63-68.
[ 2 ] GOODMAN T P.A least-squares method for computing balance corrections[J].ASME Transactions,Journal of Engineering for Industry,1964,8:273-279.
[ 3 ] LUND J W,ORCUTT F K.Calculations and experiments on the unbalance response of a flexible rotor[J].Journal of Engineering for Industry,1967,89(4):774-785.
[ 4 ] 章璟旋,唐云冰,罗贵火.最小二乘影响系数法的优化改进[J].南京航空航天大学学报,2005,37(1):110-113.ZHANG Jingxuan,TANG Yunbing,LUO Guihuo.Improved least square influence coefficient methods[J].Journal of Nanjing University of Aeronautics & Astronautics,2005,37(1):110-113.
[ 5 ] 雷文平,韩捷,陈宏,等.进动分解及其在转子动平衡中的应用[J].振动与冲击,2012,31(11):133-136.LEI Wenping,HAN Jie,CHEN Hong,et al.Procession decomposition and its application in rotor dynamic balancing[J].Journal of Vibration and Shock,2012,31(11):133-136.
[ 6 ] 王星星,吴贞焕,杨国安,等.基于改进粒子群算法的最小二乘影响系数法的理论及实验研究[J].振动与冲击,2013,32(8):100-104.WANG Xingxing,WU Zhenhuan,YANG Guoan,et al.Theory and tests for least square influence coefficient method based on an improved particle swarm optimization algorithm[J].Journal of Vibration and Shock,2013,32(8):100-104.
[ 7 ] BISHOP R E D.The vibration of rotating shafts[J].Journal of Mechanical Engineering Science,1959,1(1):50-65.
[ 8 ] 宾光富,李学军,沈意平,等.基于动力学有限元模型的多跨转子轴系无试重整机动平衡研究[J].机械工程学报,2016,52(21):78-86.BIN Guangfu,LI Xuejun,SHEN Yiping.Whole machine dynamic balancing method without trial weights for multi-span rotor shafting based on dynamic finite element modal[J].Journal of Mechanical Engineering,2016,52(21):78-86.
[ 9 ] 张西宁,赵明,温广瑞.一种轴系全息动平衡配重的多目标优化方法[J].中国机械工程,2000,21(16):1974-1977.ZHANG Xining,ZHAO Ming,WEN Guangrui.A multi objective optimization method for holo-balancing weights of rotor set[J].China Mechanical Engineering,2000,21(16):1974-1977.
[10] 章云,梅雪松,邹冬林,等.应用模态分析及傅里叶变换的柔性转子无试重动平衡方法[J].振动与冲击,2012,31(11):7-10.ZHANG Yun,MEI Xuesong,ZOU Donglin,et al.A field balancing method of a flexible rotors based on modal analysis and fourier transformation[J].Journal of Vibration and Shock,2012,31(11):7-10.
[11] 章云,梅雪松,邹冬林,等.应用动力学模型的高速主轴无试重动平衡方法[J].西安交通大学学报,2011,45(7):34-37.ZHANG Yun,MEI Xuesong,ZOU Donglin,et al.Model based balancing method for high speed machine tool spindle without trial weights[J].Journal of Xi’an Jiaotong University,2011,45(7):34-37.
[12] CAO H,LI Y,CHEN X.A new dynamic model of ball-bearing rotor systems based on rigid body element[J].Journal of Manufacturing Science & Engineering,2016,138(7):071007.
[13] CAO H,LI B,HE Z.Finite element model updating of machine-tool spindle systems[J].Journal of Vibration and Acoustics,Transactions of the ASME,2013,135(2):024503.
[14] 田久良,洪军,朱永生,等.机床主轴-轴承系统热-力耦合模型及其动态性能研究[J].西安交通大学学报,2012,46(7):63-68.TIAN Jiuliang,HONG Jun,ZHU Yongsheng,et al.Thermo-mechanical coupling model and dynamical characteristics of machining spindle bearing system[J].Journal of Xi’an Jiaotong University,2012,46(7):63-68.