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机械专业英语杨亚炬 20100334506
机电103班
考虑磨削力的磁悬浮磨床电主轴转子系统动态特性分析
摘要:以电磁轴承支承的磨床也主轴为研究对象，建立了转子的弹性支承模型，对其进行了模态分析，得出转子固有频率随支承刚度变化的规律;对施加磨削力时转子的稳态响应特性进行了分析，根据危险界面的节点位移，初步确定了主轴系统的稳定性。
关键词:电磁轴承支承系统;磨床电主轴;模态分析;稳态响应特性 引言
电磁轴承具有无摩擦、元磨损、高速度、高精度及可长期免维护等优点，因此被广泛应用于高速旋转类机械中。采用电磁轴承支承的磨床电主轴是典型的机电一体化系统，由于磨削过程的复杂性，其支承主轴系统的影响与其他轴承相比更为突出[1 刀。转子的动态特性是电磁轴承支承特性与转子结构动力学特性综合作用的结果。在对转子实施控制之前，研究转子本身的动力学行为对控制系统的设计是很重要的时。本文以某电磁轴承支承的磨床电主轴为研究对象，建立了转子的弹性支承模型，对其进行了模态分析和施加磨削力时的稳态响应特性分析。轴、砂轮连接杆、前后径向轴颈套、前后平衡环、止推盘和隔磁环等组成，其他部件与转轴之间采用过盈连接。
转子总重5.90kg，总长507mm，稳定悬浮时转子和径向轴承之间的间隙为0.2mm，轴向轴承
1.砂轮2 传感器3.前辅助轴承4.前径向轴承5.转轴6.轴向轴承7.冷却水套
8.电机部分9.后径向轴承10.后辅助轴承间隙为0.3mm。建立有限元模型
电磁轴承支承为典型的弹性支承，有限元分析模型采用16 个弹簧单元模拟径向电磁轴承的16 个磁极。止推盘两侧分别采用8 个弹簧转轴 根据转子的结构形式，用ANSYS 建立起转子的实体有限元分析模型，模态分析
支承刚度对转子固有频率的影晌根据转子的有限元分析模型，用ANSYS 对其进行模态分析[5J。忽略弹簧单元的阻尼，支承刚度在5X106~lXI09N/m 范围内变化阶模态，得到转子的正进动固有频率和负进动固有频率，进一步研究临界转速时，首先剔除负进动固有频率[6J。可以得到转轴前四阶固有频率随刚度变化曲线,转子的正进动固有频率随支承刚度的增大而增大，且转子的低阶固有频率随支承刚度增加的幅度较大。当支承刚度增大到1.6X10 8 N/m 时，转子的2~4 阶固有频率已无多
模态分析完毕后，将磨削激振力施加于砂轮 处进行谐响应分析，在砂轮外圆节点7746 处施加Y 方向力(实部为88.328N、虚部为1.9737N)和Z 方向力(实部为1.9737N、虚部为88.328N)，这样磨削力为一简谐力。COMBIN14 单元的刚度取2.0X10 7 N/m，为分析转子在高频段的响应，将激振力的频率范围扩大至0~1600Hz，分20 个载荷步进行谐响应分析。
当主轴工作在30000r/ min(对应额定工作频率500.0Hz)、48 OOOr/ min(对应最高工作频率800.OHz)，即转速处于一阶与二阶临界转速之间时，由转子的二阶振型(图5)可以看出，转子在砂轮、前保护轴承、前径向轴承和后径向轴承处的中心截面为危险截面。图7~ 图10 分别为砂轮、前保护轴承、前径向轴承和后
径向轴承处的振动幅值一频率响应后径向轴承处节点4484 振动幅值一频率响应曲线移增大幅值在一阶固有频率处最小，二阶固有频率处最大，三阶固有频率处次之。
磨床电主轴的结构参数如下:转子与前后保护轴承的间隙为O.lmm，与前后径向轴承的间隙为0.2mm。由表3 可知，当激振力频率达到转子一阶、三阶固有频率时，转子产生的共振位移在转曲线，在有限元模型上分别对应节点7746、7818、7559 和4484 的振动幅值频率响应。各危险截面的节点Y 方向位移如表3 所示。当激振力频率达到转子的固有频率时，转子的位移(振动幅值)会突然增大，通过前三阶的幅频响应曲线可以看出，转子位子间隙范围之内;但达到转子二阶固有频率时，转子产生的共振位移会超出间隙要求，使得转子与轴承碰撞，发生危险，因此应避免激振力频率达到转子的二阶固有频率。由转子的二阶振型可以看出，转子在后保护轴承处的径向位移小于后径向轴承处的径向位移，故可判定后保护轴承处在Y 方向的位移小于
2.0 X 10 一7 m。各危险截面的节点位移均在间隙范围内，因此可初步判定转子在额定转速和最高
转速下工作时，给其施加Fn = 88.328N、Ft =1.9737N 的磨削力，可稳定工作。结论
(1)完全弹性支承下，电主轴转子固有频率的总体变化趋势随支承刚度的增大而增大，并且在支承刚度较低时，固有频率随支承刚度的变化较大。当支承刚度到达一定值时，转子的前四阶固有频率趋于稳定，在设计控制系统时可控制轴承的刚度高于此值，以便转子具有稳定的临界转速。
(2)在施加了磨削激振力后，通过幅值频率响应分析确定了几个危险界面的节点位移，可初步判断主轴系统的稳定性。
Dynamic Analysis for Electric Spindle Rotor System of Magnetic Levitation Grinder
Considering Grinding Force
Abstract: This paper bui1t an elastic bearing model for the rotor of grinder electric spindlesupported by electromagnet bearing and analyzed the mode of the rotor , educed the laws about therotor inherent frequencies changing along with bearing stiffne.Then, it analyzed steady stateresponse characteristics of the rotor while applying grinding force.According to the nodedisplacements of danger interface ,stability of spindle system is ensured initially.Key words: supporting system of electromagnet bearing;grinder electric spindle;mode analysis;steady state response characteristics.Introduction
Electromagnetic bearings with no friction, wear yuan, high-speed, high precision and long-term maintenance-free, etc., it is widely used in high-speed rotating machinery.The electromagnetic bearing grinder electric spindle is a typical mechatronic systems, due to the complexity of the grinding proce, the supporting spindle system compared with other bearing more prominent [1 knife.The dynamic characteristics of the rotor the electromagnetic bearing characteristics and rotor structure dynamics combined result.Before control of the rotor embodiment, the study rotor dynamic behavior of the control system design is very important.An electromagnetic bearing grinder electric spindle rotor elastic support model, its modal analysis and steady-state response characteristics in the grinding force is applied.Shaft, wheel connecting rod, front and rear radial journal cover, front and rear stabilizer ring, thrust plate, and every other magnetic interference connection between the other components and the shaft.The rotor total weight of 5.90kg, Total length 507mm, stable suspension of the rotor and the radial bearing gap of 0.2mm, and the axial bearingwheel sensor 3.Former auxiliary bearing front radial bearing 5.Shaft axial bearing cooling water jacket motor section 9 after radial bearing 10 after the auxiliary bearing clearance of 0.3 mm.Finite element model
The electromagnetic bearing the typical elastic support, finite element analysis model with 16 spring element to simulate the radial magnetic bearing 16 pole.On both sides of the thrust plate 8 spring pivot
Established with ANSYS based on the structure of the rotor, the rotor solid finite element analysis model, Modal Analysis Support stiffne IMPACT natural frequency
of the rotor based on the finite element analysis model of the rotor, modal analysis using ANSYS its [5J.The damping of the spring element is ignored, the the support stiffne 5X106 ~ lXI09N / m range order modal rotor is preceion natural frequencies and negative preceion natural frequency, further study of the critical speed, the first natural frequency [excluding the negative preceion 6J.Can get the shaft first four natural frequency of the curve with the change in stiffne of the rotor is preceion natural frequency with the support stiffne increases, and the rate of increase of the low-order natural frequency of the rotor with the bearing stiffne.The 2-4 order natural frequency of the rotor Found when the supporting stiffne increases to 1.6X10 8 N / m,Modal analysis after grinding exciting force is applied at the wheel at the harmonic response analysis, the Y direction of the force applied to the wheel outer node 7746(88 328N real part, imaginary part 1 9737N), and Z directions force(the real part of 9737N, the imaginary part of the 88 328N), so that the grinding force of a simple harmonic force.COMBIN14 element stiffne take 2.0x10 7 N / m for the analysis of the response of the rotor at high frequencies, the frequency range of the excitationforce is expanded to 0 to 1600Hz, 20 load step harmonic response analysis.Spindle 30000r / min(corresponding to the nominal operating frequency 500.0Hz), of 48 OOOr / min(corresponding to the maximum operating frequency of 800 OHZ)that speed in the first-order and second-order critical speed, the second rotor vibration type(Figure 5)can be seen, the rotor wheel, the front protective bearings, the radial bearing and the rear radial bearing at the center of a sectional view of the dangerous section.Figures 7 to 10 respectively for the wheel, the front protective bearings, the front radial bearing and a radial bearing at a frequency response of the vibration amplitude of the vibration amplitude of the radial bearing at the node 4484 frequency response curve shift increased amplitude in a The natural frequencies at the minimum, followed by the natural frequency of the second-order, third-order natural frequency.Of Grinder Spindle structure parameters are as follows: rotor protection before and after bearing clearance O.lmm the front and rear radial bearing clearance of 0.2 mm.Seen from Table 3, when the frequency of the excitation force to the rotor-order, third-order natural frequency, the resonance generated by the rotor displacement in the transfer curve in the finite element model, respectively corresponding to the nodes 7746, 7818, 7559 and 4484, the amplitude of vibration frequency response.The nodes in the Y direction of the dangerous section of the displacement shown in Table 3.When the frequency of the excitation force is reached when the natural frequency of the rotor, the rotor displacement(vibration amplitude)will suddenly increases, frequency response curve of the web through the first three can be seen, within the scope of the clearance of the rotor charts;but reached rotor Second Order natural frequency of the rotor of the resonance displacement will exceed the spacing requirements, so that the rotor and the bearing collision danger, the second natural frequency of the exciting force the frequency of the rotor should therefore be avoided.By the second-order vibration of the rotor can be seen, the radial displacement of the rotor after protection of the radial displacement of the bearing
is le than the radial bearing at the displacement of the bearings in the Y direction, it can be determined after protection Smaller
2.0 X 10 a m.Of the dangerous section of the nodal displacements gap preliminary determination rotor at rated speed and maximum
Speed work when applied to its Fn = 88.328N FT = 9737N grinding force can work stably.Conclusions
(1)fully resilient support, the overall trend of the natural frequency of the electro-spindle rotor with bearing stiffne increases, and the supporting rigidity is low, the larger the change of the natural frequency with the support stiffne.When the supporting rigidity reaches a certain value, the first four natural frequencies of the rotor is stabilized in the design of the control system can control the stiffne of the bearing is higher than this value, the stability of the critical speed for the rotor having.(2)In the grinding exciting force is applied by the amplitude frequency response analysis identified several risk interface nodal displacements can determine the initial stability of the spindle system.
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