基于主轴系统动力学的铣削稳定性建模与分析

高速切削技术具有加工精度高和表面质量好的特点,但在切削难加工材料时易发生颤振。基于主轴系统动力学进行铣削稳定性的建模与分析,采用有限元法建立主轴系统动力学模型,重点考虑主轴旋转时产生的离心力对结合面刚度的影响,分析主轴转速对结合面刚度和主轴系统频响函数的影响规律。结合主轴系统动力学特性和动态铣削过程建立铣削动力学模型,利用全离散法进行铣削稳定性预测,分析主轴转速、刀具直径和刀具悬伸量对铣削稳定域的影响规律。     

铣削工况下考虑结合面的主轴系统动态特性

机床主轴系统动态特性直接影响铣削稳定和表面加工质量，而铣削状态下主轴系统动态特性与静止或空转状态下存在差异。针对此问题，建立了铣削工况下主轴系统和结合面动力学耦合模型，获得铣削工况下主轴系统动态特性，并通过铣削过程中机床主轴系统动态特性实验测试进行验证，将静止状态与铣削工况进行对比，预测结果误差平均降低了11.35%。实验结果表明，径向铣削载荷和转速削弱了结合面的刚度特征和系统动态特性，而轴向铣削载荷增强了结合面的刚度特征和系统动态特性，影响最为明显的是主轴转速，其次为径向铣削载荷，然后为轴向铣削载荷。研究结果为铣削状态下主轴系统动态特性和铣削稳定性预测提供了理论支持。     

考虑主轴-刀柄结合面特性的机器人铣削系统刀尖频响预测研究

针对机器人铣削系统刀尖频响具有位姿依赖特性,导致机器人变位姿加工时稳定性难以准确预测、加工颤振难以有效控制的问题,提出一种考虑主轴-刀柄结合面接触刚度的机器人铣削系统刀尖频响预测方法。基于欧拉-拉格朗日法与吉村允孝单位面积法,分别构建了机器人本体动力学模型与主轴-刀柄结合面接触刚度模型,进而基于有限元主副自由度理论将机器人本体动力学模型与主轴-刀柄结合面接触刚度模型结合,构建了机器人铣削加工系统刀尖频响预测模型。开展了机器人不同位姿下刀尖频响预测验证实验,结果表明,仿真与实验得到的刀尖频响函数相比,固有频率最大误差为6.63%,对应幅值最大误差为9.80%,验证了所提出的预测模型的准确性,证明了该模型能够实现机器人任意位姿下的频响函数准确预测。     

主轴—刀柄结合面刚度建模方法

为建立高速旋转状态下的主轴—刀柄结合面刚度模型,提出了经典弹性理论和吉村允孝积分法相结合的半解析方法,求解在高速旋转状态下的主轴一刀柄结合面刚度.采用文献[2]的实验数据验证了该方法的有效性.在此基础上建立了在高速旋转状态下的主轴—刀具耦合系统的动力学模型.采用基于Riccati变换的整体传递矩阵法,对主轴—刀具耦合系统的动态特性进行了分析.考察了主轴转速软化结合面刚度因素对系统动态特性的影响.通过对比说明,高速旋转产生的离心力对主轴—刀具耦合系统的动态特性有较大影响;所提的计算模型和方法可以实现高速旋转状态下的主轴刀柄结合面刚度的求解.     

多因素影响下高速电主轴系统动态特性分析

以某大功率高速铣削加工中心电主轴系统为研究对象,采用有限元法,综合考虑高速状态下主轴系统阻尼比、陀螺力矩效应和轴承刚度软化3种因素,建立了高速电主轴系统的动力学方程。得到了主轴系统由转速引起的陀螺力矩效应,轴承刚度变化两种因素影响下的前6阶固有频率,并进一步得到了上述3种因素影响下的刀尖处频率响应。结果表明在高速状态下,轴承刚度的软化对固有频率的影响大于陀螺力矩效应;而主轴系统的结构阻尼比会减弱轴承刚度软化对刀尖处频率响应的影响。     

高速电主轴运行状态下模态识别及高速效应分析

为了研究电主轴在高速运转状态下的模态及不同转速对主轴固有频率的影响,首先应用有限元法进行电主轴的建模和分析,然后采用环境激励方法对某电主轴进行模态分析。通过实验数据比较,发现随着转速升高,离心力效应和轴承软化效应的综合作用降低了轴承径向支撑刚度,引起前三阶固有频率呈下降趋势,其对高阶固有频率的影响与转速有关。可见以主轴转速所引起的振动作为激振力的环境激励法,能够排除环境及虚模态等复杂干扰,从而准确地对高速运转状态下的主轴系统进行模态参数识别。     

考虑结合面法向刚度的拉杆转子轴向振动特性

针对接触刚度解析模型参数确定困难、精度难以保证等问题,提出了根据弹塑性粗糙表面微体单元受力变形的有限元分析结果确定轮盘结合面法向刚度的方法;为准确获取拉杆转子的轴向振动特性,建立了考虑轮盘结合面法向刚度的集中质量动力学模型;运用上述方法和模型计算了某型实验转子轴向振动的固有频率,并将结果与实测数据进行对比,误差低于5%,证明了该方法的有效性;改变拉杆预紧力,进一步研究预紧力对拉杆转子动力学行为的影响,结果表明：拉杆预紧力对转子的作用效果存在一个饱和区域,可为拉杆预紧力数值的确定提供重要的设计依据。     

主轴转子系统动力学解析建模方法

传统上主轴转子系统动力学模型中的结合部接触刚度和阻尼系数常通过试验识别的方法来获取,针时该方法通用性差的特点,提出一种可以考虑刀具-夹套、夹套-刀柄以及刀柄-主轴结合部接触特性的主轴转子系统动力学解析建模方法。通过对各联接部件的受力分析,建立结合面接触刚度与各结合部夹紧力和几何参数间的影响关系;考虑到转子系统的轴向、径向和弯曲变形,采用均布2节点6自由度的弹簧-阻尼单元来建立结合部动力学模型;通过综合系统各部件和结合部的动力学方程参数,建立起主轴转子系统的动力学模型。以刀具-BT40刀柄-主轴为对象,进行模态测试。试验结果表明,结合部刚性处理时,系统的前三阶固有频率与试验值最大误差为21.7%;而结合部柔性处理时,系统前三阶固有频率与试验值最大误差降为4.8%,并且根据模型计算得出的刀尖点频响函数与试验测试能更好地吻合,验证了该建模方法的准确性。     

高速主轴离心膨胀及对轴承动态特性的影响

以高速主轴系统为对象,将主轴转子和轴承内圈分别等效为等截面梁和空心圆盘,计算离心力作用下主轴转子和轴承内圈的径向弹性变形,并分析主轴转子与轴承连接状态随转速升高的变化趋势。考虑旋转部件的离心膨胀变形,建立高速主轴轴承动力学模型并进行试验验证。在此基础上,研究离心效应对主轴轴承径向预紧状态的影响,揭示高速主轴轴承动态特性随转速的变化规律。研究结果表明,离心力引起的径向膨胀变形使滚动体与轴承内、外圈之间的接触角减小,接触力增加。主轴轴承的轴向刚度和径向刚度均随转速的升高而降低。轴承内圈的离心膨胀变形对轴承轴向刚度的影响可以忽略不计,而能在一定程度上提高轴承的径向刚度。     

轴承预紧力和跨距对主轴动态特性的影响

基于ABAQUS采用有限元分析法分析了主轴动态特性,主要研究了轴承预紧力和支撑跨距对主轴动态特性的影响,在同时考虑轴向预紧和主轴自重对轴承刚度的影响的情况下,计算得到不同预紧力和过盈配合下组配轴承的径向刚度,拟合了固有频率随轴承预紧力和支撑跨距变化的经验公式。结果表明:轴承预紧力相比过盈量对组配轴承刚度的影响更为明显。主轴系统的固有频率随轴承预紧力的增加而增大,相同的刚度下,轴承支承跨距的增加系统固有频率随之增大。     

Centrifugal force induced dynamics of a motorized high-speed spindle

Trend of the high-speed and high efficiency machining has pushed the continuous demand of higher spindle speed and power for the machining center application. Because the extremely high speed produces significant centrifugal force, it creates a need to predict the spindle dynamical characteristics at dynamic states. This work presents analysis results of the spindle dynamic of a motorized high speed spindle with angular ball contact bearings. For a machining center, two major subsystems determining the overall spindle stiffness are the shaft/bearing subsystem and the draw bar mechanism subsystem. Shaft/bearing stiffness as well as the natural frequency decreased at high speeds due to the bearing softening and gyroscopic effect. The bearing softening is the major reason of the reduced spindle stiffness, while the gyroscopic effect plays the secondary effect. Angular contact ball bearing softening at high speed is due to the reduced contact load and increased contact angle at the ball/inner-raceway contact interface caused by the centrifugal force. For the draw bar mechanism, analysis results show that the dynamic draw force at high speeds is significantly increased from that designed at the static state. Because the toolholder/spindle interface stiffness is proportional to the draw force, centrifugal force theoretically contributes a plus to the spindle stiffness at dynamic state. The dynamic draw force, however, is dependent on the friction loss inside the draw bar mechanism. Because of the low friction coefficient, the ball-type mechanism is superior to the wedge type mechanism.     

Acceleration-Dependent Analysis of Vertical Ball Screw Feed System without Counterweight

The distinguishing feature of a vertical ball screw feed system without counterweight is that the spindle system weight directly acts on the kinematic joints.Research into the dynamic characteristics under acceleration and decel-eration is an important step in improving the structural performance of vertical milling machines.The magnitude and direction of the inertial force change significantly when the spindle system accelerates and decelerates.Therefore,the kinematic joint contact stiffness changes under the action of the inertial force and the spindle system weight.Thus,the system transmission stiffness also varies and affects the dynamics.In this study,a variable-coefficient lumped parameter dynamic model that considers the changes in the spindle system weight and the magnitude and direc-tion of the inertial force is established for a ball screw feed system without counterweight.In addition,a calculation method for the system stiffness is provided.Experiments on a vertical ball screw feed system under acceleration and deceleration with different accelerations are also performed to verify the proposed dynamic model.Finally,the influence of the spindle system position,the rated dynamic load of the screw-nut joint,and the screw tension force on the natural frequency of the vertical ball screw feed system under acceleration and deceleration are studied.The results show that the vertical ball screw feed system has obviously different variable dynamics under acceleration and deceleration.The influence of the rated dynamic load and the spindle system position on the natural frequency under acceleration and deceleration is much greater than that of the screw tension force.     

磁悬浮铣削电主轴转子-刀具变质量不平衡系统动态特性研究

针对磁悬浮铣削电主轴在切削过程中因切屑进入刀具容屑槽中而导致“刀具-主轴”系统质量变化,进而引起系统回转精度不稳定的问题,以变质量质点理论为依据建立“切屑-刀具-主轴”系统的变质量动力学模型。分析系统的不平衡质量变化时所引起的系统振动,进而导致磁悬浮轴承定/转子间气隙磁场不均所产生不平衡磁拉力,并利用等效磁路法建立不平衡磁拉力模型。利用Riccati传递矩阵法求解磁悬浮铣削电主轴转子-刀具系统的稳态动力学模型,得到系统的模态参数和初始偏心质量影响下的不平衡响应。考虑铣削力、变质量力、切屑质量不平衡离心力和不平衡磁拉力等因素,采用Newmark-β算法求解磁悬浮铣削电主轴转子-刀具变质量系统的瞬态动力学模型。对系统从起动到切削过程的动态响应进行仿真分析,结果表明,质量不平衡是影响磁悬浮铣削电主轴转子-刀具系统稳态响应的主要因素;在切削过程中,变质量力是影响系统瞬态响应的主要因素;不平衡磁拉力对系统响应的影响与系统的稳定性成负相关与系统的振幅成正相关。     

高速主轴/刀柄联接的离心力效应分析

随着切削速度的提高 ,主轴 /刀柄联接性能在离心力的作用下发生很大变化 ,直接影响工件的加工精度和表面粗糙度。本文通过先进的非线性有限元技术分析了离心力对主轴 /刀柄联接特性的影响。研究表明 ,适当提高过盈量 (轴向拉力 )对于提高主轴 /刀柄联接特性具有积极意义     

永磁同步型磨削电主轴偏心振动分析及实验*

电主轴是将旋转主轴与电机转子集成为一体的主轴单元,结构复杂,由于加工或装配误差等原因,电主轴转子会存在着一定的偏心量,为探求由于电主轴偏心所导致的转子振动特性,建立了电主轴转子偏心模型,采用Maxwell应力张量法计算了偏心造成的不平衡磁拉力(UMP),将UMP解析式代入Jeffcott转子模型,得到了转子偏心振动方程。以某磨床的永磁同步电主轴为研究对象,利用有限元方法分析了UMP,发现作用于转子的UMP始终指向气隙最小的方向,研究了不同转速下转子在质量偏心离心力和UMP作用下的振动响应。研究结果表明,电主轴在低速运行时,UMP为转子振动的主要来源;随着转速的增加,质量偏心离心力对转子振动的影响更加明显,而UMP大小保持不变,其频率随转速增加而增大,对转子振动的作用随之减弱。对某机床厂所研发永磁同步型磨削电主轴在试运行时产生的振动问题进行了实验,对主轴振动频谱分析后判断实验电主轴存在静态偏心,测得主轴轴心轨迹对前述分析进行了验证。     

基于内置力执行器的铣削颤振的主动控制

高速加工中铣削颤振不仅降低工件的表面加工质量,严重时还会造成刀具或者其他加工部件的损坏,因此对电主轴铣削颤振进行控制具有重要的意义。为对电主轴铣削过程中的颤振进行有效控制,在双绕组无轴承感应电动机的基础上,提出一种具有内置力执行器的感应型高速电主轴结构,建立电主轴—刀具系统的有限元模型、动态铣削模型、双绕组感应型电主轴电磁力模型,在对具有内置力执行器的感应型高速电主轴电磁力进行解耦后,提出基于内置力执行器的电主轴铣削颤振的主动控制方案,通过仿真分析控制器的主要参数对电主轴铣削稳定性的影响。结果表明采用具有内置力执行器的感应型高速电主轴能够有效地提高电主轴铣削的稳定区域以及在抑制铣削颤振方面具有明显效果。     

高速电主轴中的离心现象及其影响

对高速电主轴内的离心现象进行了分类,归纳出了离心力的三种表现形式及其对主轴动态、热态特性的影响,指出离心力影响的广泛性和严重性,它不仅是影响主轴动态特性的关键因素,而且能加剧轴承发热;同时指出了旋转部件因离心膨胀而可能带来的其他影响,从离心膨胀这一角度出发,为今后主轴动力学和热力学的研究提出了相关建议。     

A comparative study on the dynamics of high speed spindles with respect to different preload mechanisms

This paper presents the effects of bearing preload mechanisms on the dynamic performance of high speed spindles. The comparisons of two main types of bearing preload????constant?? and ??rigid????mechanisms are provided using a mathematical model as well as experiments. Based on the Timoshenko beam element theory coupled with a nonlinear model of angular contact ball bearings, the dynamics of the spindle shaft, housing, and bearings system is modeled as a nonlinear function of preload mechanism and amplitude, spindle speed, and external cutting loads. The mathematical model of the spindle is experimentally validated by comparing the predicted and measured static displacements, mode shapes, frequency response functions, and natural frequencies under different conditions. The performance of spindles under rigid and constant force preload is investigated systematically using a mathematical model under various conditions. It is shown, among other things, that at high speeds and under cutting loads the rigid preload mechanism is more efficient in maintaining the dynamic stiffness of spindles than constant preload.     

Robust rotor dynamics for high-speed air bearing spindles

For ultra-precision machining machine tool components need to operate outside critical frequencies of the machining system to avoid insufficient surface finish caused by vibrations. This particularly applies to tooling spindles as those are generally the component of a machine tool with low stiffness and damping values. Surface finish and shape of a machined part rely directly on the overall accuracy in motion of the tooling spindle over the entire machining parameter and speed range. Thus spindle designs for an operation outside critical frequencies combined with high stiffness and damping values are crucial for ultra-precision machining.For sufficient stiffness properties bearing gaps of gas bearings have to have a size of only a few microns and show a distinct sensitivity on temperature and for journal bearings also on speed. This again means that bearing properties change with temperature and speed. Considering a spindle system comprising a rigid shaft rotating in a radial/axial bearing system with changing stiffness and damping properties leads to a resonance speed map with changing rigid mode resonance speeds.This paper treats the influence of shaft speed and temperature on bearing gaps from which rigid mode resonance speeds for a shaft spinning in a bearing system are derived. The quoted influence of centrifugal load and temperature on bearing stiffness, damping and load capacity can be applied to any kind of gas bearing. Therefore the calculation of bearing stiffness, damping or load capacity is not treated in detail. The reader will be shown that there are simple design rules for air bearing systems and shafts of high-speed tooling spindles to avoid critical speeds through the entire speed range. Finally, methods of how to prove the initial design goals and how to verify dynamics of high-speed spindles in production will be presented to the reader. It will also be shown that there are production high-speed spindles available which do not include any critical speed within their speed range and thus show robust rotor dynamics with extremely low errors in motion.Procedures in design, validation and application treated in this paper shall give the reader not only design guidelines for spindles to avoid critical spindle speeds within its speed range, but also recommendations for machine tool builders and end-users for a machine operation taking machine and rotor dynamics into account. As the knowledge for this paper is predominantly based on the experience and work of the author himself only a few references are used. However presented testing results entirely confirm the approach presented in this paper.