Developmental Research of Hydrostatic Air Spindle for Ultra-Precision Machine Tools

1)轴承-转子系统共振频率最大阻尼设计的发展：根据挤压膜阻尼的频率特性，通过在径向和推力轴承表面制造点阵槽，建立了轴承-转子系统共振频率最大气膜阻尼的设计方法。考虑转子弹性变形的静压空气主轴振动分析：基于有限元法，开发了考虑转子弹性变形和连接螺栓等效刚度的轴承-转子系统结构模态分析程序。结果表明，在5%的误差范围内，不仅可以准确地预测转子高达11 kHz的三个结构固有频率，而且可以准确地预测气轴承共振。3)开发了一种使各种频谱的加工力引起的转子响应的均方根值最小的气主轴设计方法：首先确定了径向和推力轴承的配置，以使加工点的静位移最小。其次，提出了一种折衷静刚度和共振阻尼比的设计方法，以最小化加工点动态响应的均方根值。举例说明了在窄带和宽频带载荷作用下空气轴承的优化设计。进一步将转子的最低弯曲振动频率提高到7kHz。4)以3 σ表示10nm/N动态柔度的超精密空气主轴的实现：在0.5 ~ 5 kHz的频率范围内，制作了一个动态响应均方根值最小，且振幅均匀的空气主轴样机。从轴承特性的测量中发现，由于加工精度不高，轴承的有效游隙为4至4.5 μ m，因此静刚度为5 μ m标称游隙理论值的50至70%。动态气膜刚度比计算值大20 ~ 30%，阻尼比为计算值的60 ~ 80%。然而，证实了自由支承主轴在径向和推力方向上的动态柔度的3 σ值可以在10nm/N以内。非重复振动的均方根值小于10 nm。少

1) Development of the maximized damping design at resonance frequency of bearing-rotor system : Based on the frequency characterisitics of squeeze film damping, we established a design method of maximizing air film damping at resonance frequency of the bearing-rotor system by fabricating the lattice grooves on the radial and thrust bearing surfaces. From this design concept we can increase the damping ratio at resonance up to more than 0.1.2) Vibration analysis of hydrostatic air spindle including elastic deformation of rotor : Based on the finite element method, we developed the structural modal analysis program of the bearing-rotor system including the elastic deformation of rotor and the equivalent stiffness of the connecting bolts. As a result it is found that not only the three stractural natural frequencies of rotor up to 11 kHz but also air bearing resonances can be predicted more accurately within 5% errors.3) Development o air spindle design method of minimizing the rms value … More of rotor response caused by the machining force with various kinds of frequency spectrum : We first determined the radial and thrust bearing configurations so as for the static displacement at machining point to be minimized. Next we developed a design method of compromizing the static stiffness and resonance damping ratio in order to minimize the rms value of dynamic response at machining point. The optimal air bearing designs for narrow and wide band spectrum external forces are exemplified. Further the lowest bending vibration frequency of rotor can be increased up to 7kHz.4) Realization of ultra-precision air spindle with 10nm/N dynamic compliance in terms of 3 sigma : We made an air spindle prototype whose rms value of the dynamic response is minimized to the imposed machining force with uniform amplitude for the frequencies from 0.5 to 5 kHz. From measurement of the bearing characterisitics, it is found that, because of the machining inaccuracy, the effective bearing clearance is 4 to 4.5 mum, so that the static stiffness is 50 to 70% of the theoretical value for 5 mum nominal clearance. The dynamic air film stiffnesses are larger than the calculated ones by 20 to 30% and the damping ratios are 60 to 80% of the calculated ones. However, it is confirmed that the 3 sigma value of the dynamic compliance of the spindle supported freely can be within 10nm/N in both the radial and thrust directions. It is also found that the rms value of nonrepeatable vibration is less than 10 nm. Less