高速电主轴动力学分析与实验研究
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摘要
高速加工能显著地提高生产率、降低生产成本和提高产品加工质量,是制造业发展的重要趋势,也是一项非常有前景的先进制造技术。实现高速加工的首要条件是高质量的高速机床,而高速机床的核心部件是高速电主轴单元,它实现了机床的“零传动”,简化了结构,提高了机床的动态响应速度,是一种新型的机械结构形式,其性能好坏在很大程度上决定了整台机床的加工精度和生产效率。
本文在国家自然科学基金项目《高速电主轴机电耦合动力学分析及仿真与实验研究》(项目编号50675233)、重庆市重大科技攻关项目《装备制造业典型基础部件关键技术研究及产业化》(项目编号CSTC, 2006AA3010)和重庆市科技攻关项目《高速高性能主轴系统关键技术及典型应用》(项目编号CSTC, 2005AC3029)的资助下,对高速电主轴进行了动力学分析和实验研究,主要做了以下几个方面的工作:
针对高速电主轴系统具有复杂机电系统的特点,提出对高速电主轴系统进行机电耦合分析的观点;从机电耦合动力学出发,提炼并归纳了高速电主轴系统中存在的多物理过程、多参数耦合现象;讨论了高速电主轴系统中存在的全局机电耦合关系,给出了高速电主轴系统的全局耦合结构;分析并研究了高速电主轴电机—主轴子系统的结构和局部耦合情况,建立其物理模型,采用变分原理法推导其数学模型,建立了该子系统的动力学方程,并进行了实例验证。
基于传递矩阵法对高速电主轴进行动力学分析,简化其结构并进行分段建模,对轴系中典型单元的状态进行了数学描述;针对电主轴结构的特殊性,修改了简化模型中部分典型单元的状态向量,得到电主轴的传递矩阵方程即轴系的频率方程;以60 000 r/min电主轴为例,描述了用修改后的传递矩阵方程对其进行求解的计算过程,得到了该电主轴的固有频率及振型。
在应用传递矩阵法对电主轴进行机械动力学分析的基础上,针对电主轴的偏心状态,结合电磁学对电主轴进行的力学分析,建立此时轴系的传递矩阵方程;综合电磁学与机械动力学的分析结果,修改典型单元的状态向量,推出偏心电主轴的传递矩阵方程,将轴系的边界条件代入传递矩阵方程,得到轴系的频率方程;并利用机电动力学的方法分析了电主轴发生偏心时由电磁力激发的振动,应用拉格朗日—麦克斯韦方程,导出电主轴偏心状态下的振动方程和转动方程。
基于模态分析理论,对同一60 000 r/min高速电主轴进行了自由模态实验,介绍了实验方法和过程,并分析了实验结果,提取了该电主轴的模态参数(固有频率、阻尼和振型);实验结果与传递矩阵法的计算结果基本吻合。
针对高速电主轴高转速难加载的问题,提出了使用经改造的测功机对电主轴进行加载实验的方案;根据电主轴转速的不同,提出了对拖式和非接触式两种不同的动态加载测试方法;详细描述了对拖式加载方法的系统构成和加载原理,该系统不但可以完成对电主轴的加载,还可以测出加载过程中电主轴的基本参数,并绘制出相应的曲线,使电主轴在不同工作点的状态一目了然;应用该系统对最高转速为15 000 r/min的电主轴进行加载实验,得到其特性曲线,分析并处理实验数据,得出被测电主轴本身所具有的特性及其存在的问题;解决了高速电主轴无法进行准确加载实验的问题。
High speed machining (HSM) has become the mainstream of manufacturing for drastically increasing productivity, reducing production costs and improving the product quality. HSM is also a promising advanced manufacturing technology. In the realization of HSM, machine tool generally plays an all-important role and high speed motorized spindle is the key technology for a machine tool. The machine tool equipped with high speed motorized spindle has characteristic of the zero-transmission and simplified of the machine structure. With use of new mechanical structure, the high speed motorized spindle has much better dynamic performance in response to the high demands in this machine. In general, overall performance of high speed machine in terms of the machining precision and productivity is largely dependent upon the performance of the equipped high speed motorized spindle.
This thesis is funded by the National Natural Science Foundation, China (No.50675233), Chongqing Municipal Important Science and Technology Key Project, China (CSTC, No.2006AA3010) and Chongqing Municipal Important Science and Technology Key Project, China (CSTC, No.2005AC3029). The dynamic analysis and experiment on high speed motorized spindle are researched. The major contribution of the work is summarized as followings.
Due to the high speed motorized spindle system has characteristic of the complex electromechanical system, the view of electromechanical coupling analyses on high speed motorized spindle is put forward. Grounded on the electromechanical coupling dynamics, several physical processes and multidimensional coupling parameters that exist in the high speed motorized spindle system are extracted and summed up. The global coupling relation of high speed motorized spindle system has also been discussed and its frame is given. The physical model of the subsystem is set up based upon the analysis of the structure and local coupling of motor-spindle subsystem in high speed motorized spindle. The mathematical model is developed base on variance principle. The dynamical equation of the subsystem is established and the validation of equation is made by experimental data from the examples.
The dynamic analysis is carried out on the high speed motorized spindle with use of the transfer matrix method, which includes the structure simplification and modeling segmentation. Typical elements’states of the shafting are described by mathematical method. For the special structure of the high speed motorized spindle, some state vectors of typical elements in the simplified model are modified. Then transfer matrix model of the high speed motorized spindle, which is also the frequency model of the shafting, is derived. As a case study, the natural frequency and critical speed of the high speed motorized spindle with 60 000 rpm are calculated by the modified model. Meantime the calculation course is also described.
On the condition that the transfer matrix method is applied to do the mechanical dynamic analyses of the high speed motorized spindle, mechanical analysis on high speed motorized spindle under the eccentric state is carried out through electromagnetic method. Then the transfer matrix equation for the shafting is set up. Combining the analytic results of electromagnetics and mechanical dynamics, state vectors of typical elements are modified. The transfer matrix equation of the eccentric high speed motorized spindle is obtained. Putting the boundary condition of the entire shafting into the transfer matrix equation, the frequency equation of the shafting is gained. Electromechanical dynamics is used to analyze the eccentric motorized spindle’s vibration which caused by the electromagnetic force. Lagrange-Maxwell equation is made use of educing its vibration equation and rotation equation.
Based on the theory of mode analysis, a free mode experiment is carried out under the 60 000 rpm high speed motorized spindle in order to acquire the modal parameters, such as natural frequency, damp and mode shape. The experimental results exhibited that modal parameters from the test are matched with the theory calculation. The overall experimental method and procedure are also introduced.
Loading and measuring the load applied on a high speed motorized spindle in the non-machining state is an important issue in performance evaluation of high speed motorized spindle. A new method is developed through modifying a dynamometer to make the loading possible in the experiment. According to the different rotating speed, two types of dynamic loading test ways which are the inter-drag method and the non-contact method are proposed. The structure and principle of the inter-drag loading method are described in detail. The system can not only load to the high speed motorized spindle, but also measure basic parameters of the high speed motorized spindle and present the corresponding curves which make it visible for states of the high speed motorized spindle at different working points. The inter-drag loading system is applied in experiment on the high speed motorized spindle in which the highest rotating speed is 15 000 rpm. The characteristic curve of this high speed motorized spindle is depicted. Analyzing and dealing with the test data, the inherent characteristic and existent problem of the motorized spindle are gained. Proposed method makes it possible to accurately loading on a high speed motorized spindle.
本文在国家自然科学基金项目《高速电主轴机电耦合动力学分析及仿真与实验研究》(项目编号50675233)、重庆市重大科技攻关项目《装备制造业典型基础部件关键技术研究及产业化》(项目编号CSTC, 2006AA3010)和重庆市科技攻关项目《高速高性能主轴系统关键技术及典型应用》(项目编号CSTC, 2005AC3029)的资助下,对高速电主轴进行了动力学分析和实验研究,主要做了以下几个方面的工作:
针对高速电主轴系统具有复杂机电系统的特点,提出对高速电主轴系统进行机电耦合分析的观点;从机电耦合动力学出发,提炼并归纳了高速电主轴系统中存在的多物理过程、多参数耦合现象;讨论了高速电主轴系统中存在的全局机电耦合关系,给出了高速电主轴系统的全局耦合结构;分析并研究了高速电主轴电机—主轴子系统的结构和局部耦合情况,建立其物理模型,采用变分原理法推导其数学模型,建立了该子系统的动力学方程,并进行了实例验证。
基于传递矩阵法对高速电主轴进行动力学分析,简化其结构并进行分段建模,对轴系中典型单元的状态进行了数学描述;针对电主轴结构的特殊性,修改了简化模型中部分典型单元的状态向量,得到电主轴的传递矩阵方程即轴系的频率方程;以60 000 r/min电主轴为例,描述了用修改后的传递矩阵方程对其进行求解的计算过程,得到了该电主轴的固有频率及振型。
在应用传递矩阵法对电主轴进行机械动力学分析的基础上,针对电主轴的偏心状态,结合电磁学对电主轴进行的力学分析,建立此时轴系的传递矩阵方程;综合电磁学与机械动力学的分析结果,修改典型单元的状态向量,推出偏心电主轴的传递矩阵方程,将轴系的边界条件代入传递矩阵方程,得到轴系的频率方程;并利用机电动力学的方法分析了电主轴发生偏心时由电磁力激发的振动,应用拉格朗日—麦克斯韦方程,导出电主轴偏心状态下的振动方程和转动方程。
基于模态分析理论,对同一60 000 r/min高速电主轴进行了自由模态实验,介绍了实验方法和过程,并分析了实验结果,提取了该电主轴的模态参数(固有频率、阻尼和振型);实验结果与传递矩阵法的计算结果基本吻合。
针对高速电主轴高转速难加载的问题,提出了使用经改造的测功机对电主轴进行加载实验的方案;根据电主轴转速的不同,提出了对拖式和非接触式两种不同的动态加载测试方法;详细描述了对拖式加载方法的系统构成和加载原理,该系统不但可以完成对电主轴的加载,还可以测出加载过程中电主轴的基本参数,并绘制出相应的曲线,使电主轴在不同工作点的状态一目了然;应用该系统对最高转速为15 000 r/min的电主轴进行加载实验,得到其特性曲线,分析并处理实验数据,得出被测电主轴本身所具有的特性及其存在的问题;解决了高速电主轴无法进行准确加载实验的问题。
High speed machining (HSM) has become the mainstream of manufacturing for drastically increasing productivity, reducing production costs and improving the product quality. HSM is also a promising advanced manufacturing technology. In the realization of HSM, machine tool generally plays an all-important role and high speed motorized spindle is the key technology for a machine tool. The machine tool equipped with high speed motorized spindle has characteristic of the zero-transmission and simplified of the machine structure. With use of new mechanical structure, the high speed motorized spindle has much better dynamic performance in response to the high demands in this machine. In general, overall performance of high speed machine in terms of the machining precision and productivity is largely dependent upon the performance of the equipped high speed motorized spindle.
This thesis is funded by the National Natural Science Foundation, China (No.50675233), Chongqing Municipal Important Science and Technology Key Project, China (CSTC, No.2006AA3010) and Chongqing Municipal Important Science and Technology Key Project, China (CSTC, No.2005AC3029). The dynamic analysis and experiment on high speed motorized spindle are researched. The major contribution of the work is summarized as followings.
Due to the high speed motorized spindle system has characteristic of the complex electromechanical system, the view of electromechanical coupling analyses on high speed motorized spindle is put forward. Grounded on the electromechanical coupling dynamics, several physical processes and multidimensional coupling parameters that exist in the high speed motorized spindle system are extracted and summed up. The global coupling relation of high speed motorized spindle system has also been discussed and its frame is given. The physical model of the subsystem is set up based upon the analysis of the structure and local coupling of motor-spindle subsystem in high speed motorized spindle. The mathematical model is developed base on variance principle. The dynamical equation of the subsystem is established and the validation of equation is made by experimental data from the examples.
The dynamic analysis is carried out on the high speed motorized spindle with use of the transfer matrix method, which includes the structure simplification and modeling segmentation. Typical elements’states of the shafting are described by mathematical method. For the special structure of the high speed motorized spindle, some state vectors of typical elements in the simplified model are modified. Then transfer matrix model of the high speed motorized spindle, which is also the frequency model of the shafting, is derived. As a case study, the natural frequency and critical speed of the high speed motorized spindle with 60 000 rpm are calculated by the modified model. Meantime the calculation course is also described.
On the condition that the transfer matrix method is applied to do the mechanical dynamic analyses of the high speed motorized spindle, mechanical analysis on high speed motorized spindle under the eccentric state is carried out through electromagnetic method. Then the transfer matrix equation for the shafting is set up. Combining the analytic results of electromagnetics and mechanical dynamics, state vectors of typical elements are modified. The transfer matrix equation of the eccentric high speed motorized spindle is obtained. Putting the boundary condition of the entire shafting into the transfer matrix equation, the frequency equation of the shafting is gained. Electromechanical dynamics is used to analyze the eccentric motorized spindle’s vibration which caused by the electromagnetic force. Lagrange-Maxwell equation is made use of educing its vibration equation and rotation equation.
Based on the theory of mode analysis, a free mode experiment is carried out under the 60 000 rpm high speed motorized spindle in order to acquire the modal parameters, such as natural frequency, damp and mode shape. The experimental results exhibited that modal parameters from the test are matched with the theory calculation. The overall experimental method and procedure are also introduced.
Loading and measuring the load applied on a high speed motorized spindle in the non-machining state is an important issue in performance evaluation of high speed motorized spindle. A new method is developed through modifying a dynamometer to make the loading possible in the experiment. According to the different rotating speed, two types of dynamic loading test ways which are the inter-drag method and the non-contact method are proposed. The structure and principle of the inter-drag loading method are described in detail. The system can not only load to the high speed motorized spindle, but also measure basic parameters of the high speed motorized spindle and present the corresponding curves which make it visible for states of the high speed motorized spindle at different working points. The inter-drag loading system is applied in experiment on the high speed motorized spindle in which the highest rotating speed is 15 000 rpm. The characteristic curve of this high speed motorized spindle is depicted. Analyzing and dealing with the test data, the inherent characteristic and existent problem of the motorized spindle are gained. Proposed method makes it possible to accurately loading on a high speed motorized spindle.
引文
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