The nonlinear and ball pass effects of a ball bearing on rotor vibration

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.     

球头铣刀数控加工表面形貌几何仿真的研究

几何仿真是建立铣削力预测模型的基础,而传统的几何仿真只考虑刀具的平动而忽略其转动。本文在同时考虑刀具平动和转动的基础上,利用工件Z-Map表示模型和刀刃离散表示法,提出了一种球头铣刀三轴数控铣削的微观几何仿真算法。该算法鲁棒性好、适用范围广,不仅能高效而准确地仿真铣削表面形貌,而且能准确提供切屑的轮廓,为建立精确的切削力预测模型提供了重要的几何参数。     

The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings

The paper deals with the structural dynamic response of rotor supported by ball bearings. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force, surface waviness, varying compliance and internal radial clearance resulting transition from no contact to contact state between rolling elements and races. In terms of the feature that the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. The effects of speed of balanced rotor in which ball bearings show periodic, quasi-periodic and chaotic behavior are analyzed. The results are presented in the form of time displacement responses, frequency spectra and Poincarè maps. It is implied from the frequency spectra that peak amplitude of vibrations appear at the varying compliance frequency.     

Cutting speed modelling in ball nose milling applications

Cutting speed is a key factor that influences machined surface quality and tool life in milling. To date, the study of its distribution over a machined surface has not been established. This paper presents a mathematical model to evaluate cutting speed on the machined surface in 3-axis ball nose milling. The approximation errors introduced by surface shape, step-over and CNC interpolation are analysed. The model is used to predict visible areas which have different colour intensities on finished surfaces in the machining of a wood-plastic composite. A good agreement is obtained between the prediction and experimental results.     

Effect of tool stiffness upon tool wear in high spindle speed milling using small ball end mill

Longer tool life can be tentatively achieved at a higher feed rate using a small ball end mill in high spindle speed milling (over several tens of thousands of revolutions per minute), although the mechanism by which tool life is improved has not yet been clarified. In the present paper, the mechanism of tool wear is investigated with respect to the deviation in cutting force and the deflection of a ball end mill with two cutting edges. The vector loci of the cutting forces are shown to correlate strongly with wear on both cutting edges of ball end mills having various tool stiffnesses related to the tool length. The results clarified that tool life can be prolonged by reducing tool stiffness, because the cutting forces are balanced, resulting in even tool wear on both cutting edges as tool stiffness is lowered to almost the breakage limit of the end mill. A ball end mill with an optimal tool length showed significant improvement in tool life in the milling of forging die models.     

3D FE modelling of high-speed ball nose end milling

The paper details research and development of a Lagrangian-based, 3D finite element (FE) model to simulate the high-speed ball nose end milling of Inconel 718 nickel-based superalloy using the commercial FE package ABAQUS Explicit. The workpiece material was modelled as elastic plastic with isotropic hardening and the flow stress defined as a function of strain, strain rate and temperature. Workpiece material data were obtained from uniaxial compression tests at elevated strain rates and temperatures (up to 100/s and 850°C, respectively) on a Gleeble 3500 thermo-mechanical simulator. The data were fitted to an overstress power law constitutive relationship in order to characterise flow behaviour of the material at the level of strain rates found in machining processes (typically up to 10⁵/s). Evolution of the chip was initially seen to progress smoothly, with the predicted machined workpiece contour showing good correlation with an actual chip profile/shape. Cutting force predictions from the FE model were validated against corresponding experimental values measured using a piezoelectric dynamometer, while modelled shear zone/chip temperatures were compared with previously determined experimental data. The model was successful in predicting the forces in the feed and step-over direction to within 10% of corresponding experimental values but showed a very large discrepancy with the thrust force component (～90%). Modelled shear-plane temperatures calculated at the point of maximum cutting force were found to demonstrate very good agreement with measured values, giving a discrepancy of ～5%. The simulation required a computational time of approximately 167 h to complete one full revolution of the ball end mill at 90 m/min cutting speed.     

Chatter and dynamic cutting force prediction in high-speed ball end milling

Machine tool chatter is a serious problem which deteriorates surface quality of machined parts and increases tool wear, noise, and even causes tool failure. In the present paper, machine tool chatter has been studied and a stability lobe diagram (SLD) has been developed for a two degrees of freedom system to identify stable and unstable zones using zeroth order approximation method. A dynamic cutting force model has been modeled in tangential and radial directions using regenerative uncut chip thickness. Uncut chip thickness has been modeled using trochoidal path traced by the cutting edge of the tool. Dynamic cutting force coefficients have been determined based on the average force method. Several experiments have been performed at different feed rates and axial depths of cut to determine the dynamic cutting force coefficients and have been used for predicting SLD. Several other experiments have been performed to validate the feasibility and effectiveness of the developed SLD. It is found that the proposed method is quite efficient in predicting the SLD. The cutting forces in stable and unstable cutting zone are in well agreement with the experimental cutting forces.     

全液压铣刨机铣刨系统速度刚度问题研究

为提高全液压铣刨机铣刨鼓切削速度稳定性,采用理论分析与试验相结合的方法,对影响铣刨鼓切削速度稳定性的因素及提高铣刨鼓切削速度稳定性的方法进行了研究.指出铣刨液压系统的速度刚度是影响铣刨鼓切削速度稳定性的重要因素,采用高性能元件、加大液压马达排量和合理配置液压元件的工作点是提高液压系统速度刚度的重要措施,其中液压系统的速度刚度与液压马达排量的平方呈正比关系.     

Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

高速铣床主轴和进给系统特性与分析

介绍了高速电主轴、高速磁力轴承主轴和高速进给系统的结构和特性，并对它们的特性进行分析。     

A force-model-based approach to estimating cutter axis offset in ball end milling

Cutter runout due to cutter axis offset is quite common in a milling process, yet it is difficult to directly measure the runout geometry of a ball end cutter during the cutting process. This paper presents an analytical method for the estimation of cutter radial offset via forces in ball end milling. Closed form expression for the total milling force in the presence of cutter offset is first obtained. Fourier series coefficients for the offset related force component are shown to be expressed explicitly in terms of the offset geometry and serve as the basis for the identification of the offset geometry from the measured cutting forces. The offset geometry including its magnitude and the phase angle are directly calculated from the measured force component at the spindle frequency through two algebraic expressions. The identification method is finally validated by milling experiments.     

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.Nomenclature b damping coefficient: mass-spring-damper representation - b _e equivalent damping coefficient: mass-spring-damper representation - C compliance element - CWD chip with density function - D diameter of cutter - d _a axial depth of cut - d _r radial depth of cut - average total cutting force - K _r radial specific cutting pressure constant - K _t tangential specific cutting pressure constant - k spring constant - k _e equivalent spring constant - m mass: mass-spring-damper representation - m _e equivalent mass: mass-spring-damper representation - n number of flutes on the cutter - p _x,y elemental cutting forces - P _1,2 elemental cutting force functions - R cutter radius - s Laplace variable - TS tooth sequencing function - chip thickness - t _c average chip thickness - t _x feed per tooth - helix angle - _x actual displacement of cutter tip - unit impulse function - _d damped circular frequency of vibration - damping ratio - spindle speed     

Investigation on ball end milling of P20 die steel with cutter orientation

The generation mechanism of machining-induced residual stresses is a complex nonlinear and thermal–mechanical coupling problem. The cutting forces and cutting temperature produced in machining process must be considered simultaneously. The influence of cutter orientation and feed per tooth on the cutting speed, cutting forces, cutting temperature, and residual stresses is discussed in the present study. Effective cutting speed in accordance with the inclination angle in feed direction is analyzed. The cutting forces are gained by milling experiment, and the cutting temperature is obtained by finite element method. Moreover, the influence of the effective cutting speed on the cutting forces and cutting temperature is stated, and the relationship among the cutting forces, cutting temperature, and residual stresses is discussed. The experimental and numerical methods are both adopted in this study to give a better understanding of the milling process. After analysis of the phenomenon, several conclusions are made. The inclination angle in feed direction affects the effective cutting speed, and then the cutting forces, cutting temperature, and residual stresses are affected. Priority selection of inclination angle in feed direction is suggested from 5° to 30° in order to reduce the cutting forces. The overall trend of the workpiece temperature presents the parabolic shape, while the chip temperature increases with the increasing inclination angle in feed direction. Residual stress in feed direction almost increases with the increasing feed per tooth, which is not obvious in the general scope of the feed rate. The inclination angle of 5° and 15° is the priority in order to produce residual compressive stresses in cross feed direction.     

基于ANSYS的铣刨转子楔形刀具应力分析

利用有限元分析软件ANSYS对楔形刀具进行应力分析得出楔形刀具的应力分布图。分析结果表明,应用ANSYS可直观地掌握楔形刀具上各节点的受力情况,确定刀具内部应力的分布规律,从而为改进刀具受力状况和结构设计提供理论依据。     

燃气涡轮转子盘-片系统三维非线性循环应力-应变分析

燃气涡轮转子盘—片系统的几何形状和结构形式比较复杂,在高温、高转速的恶劣条件下工作,准确的应力分析是进行强度计算和疲劳寿命预测的重要前提。使用ANSYS有限元结构分析软件,建立了燃气涡轮盘—片接触系统三维循环对称有限元模型,考虑了叶片材料的各向异性、涡轮盘与叶片榫头之间的接触非线性、材料的弹塑性变形和温度不均匀引起的热应力等情况,数值模拟涡轮盘—叶片组件的受力状态及边界条件,进行三维非线性循环应力—应变分析。     

基于不同铣削方式的球头铣刀切削性能的研究

利用Third Wave Advant Edge软件针对球头铣刀的平面和斜面铣削建立铣削模型,采用单因素的方法对球头铣刀铣削7075-T6进行有限元仿真试验,得到铣削力和铣削温度在不同铣削方式下随转速、进给量及切削深度变化的规律,为球头铣刀铣削7075-T6的铣削方式和铣削参数的合理选择提供依据。     

A microcontroller-based end milling cutter monitoring and management system

The monitoring of end milling cutting operations for tool breakage is achieved using a low-cost microcontroller-based system. The system is based upon acquiring and analysing machine tool-based signals for characteristic responses to tool breakage. Spindle speed and load signals are shown to be responsive to tool condition and thus capable of supporting the deployed approach. The resulting system operates in real time with tool breakage detection consistently diagnosed within two revolutions. The monitoring function is extended to consider tool wear using analysis methods applied in the time and frequency domains. Decisions about tool condition are made by integrating all relevant information into a rule base. Higher-level tool management functions supported by the deployed system are identified.     

Analysis of cutting force coefficients in high-speed ball end milling at varying rotational speeds

In high-speed ball end milling, cutting forces influence machinability, dimensional accuracy, tool failure, tool deflection, machine tool chatter, vibration, etc. Thus, an accurate prediction of cutting forces before actual machining is essential for a good insight into the process to produce good quality machined parts. In this article, an attempt has been made to determine specific cutting force coefficients in ball end milling based on a linear mechanistic model at a higher range of rotational speeds. The force coefficients have been determined based on average cutting force. Cutting force in one revolution of the cutter was recorded to avoid the cutter run-out condition (radial). Milling experiments have been conducted on aluminum alloy of grade Al2014-T6 at different spindle speeds and feeds. Thus, the dependence of specific cutting force coefficients on cutting speeds has been studied and analyzed. It is found that specific cutting force coefficients change with change in rotational speed while keeping other cutting parameters unchanged. Hence, simulated cutting forces at higher range of rotational speed might have considerable errors if specific cutting force coefficients evaluated at lower rotational speed are used. The specific cutting force coefficients obtained analytically have been validated through experiments.     

薄壁零件高速铣削振动试验与分析

切削速会加强振动随针对薄壁零件在高速铣削加工过程中存在的振动问题,为有效抑制加工振动,采用单因素试验,对每齿进给量、度、工彳车径向轴向切深、径向切深等加工参数进行了研究。试验结果显示：每齿进给量并不是越小越好;转速过高过低都振动：切深增随轴向切深增大振动增强;随径向切深增大振动逐渐减弱,较大轴向切深下,径向切深小于1mm时,大而增强。综合数据优选：薄壁零件高速铣削时,每齿进给量在0．1～0．15mm之间;转速在11000—14000r／min之间;较小的轴向切深和较大径向切深会有效抑制加工振动。     

300MW汽轮机调速系统模型与非线性分析

本文以某典型的300MW汽轮发电机组为例,详细地分析了它的汽轮机调速系统的构成.工作机理和主要特征.建立了DEH系统各个环节的数学模型,对可能包含的非线性环节进行了详细地探讨,为分析调速系统与电力系统稳定的关系打下了基础.