Analysis of bearing configuration effects on high speed spindles using an integrated dynamic thermo-mechanical spindle model

This work presents the effects of bearing configuration on the thermo-dynamic behavior of high speed spindles using the comprehensive dynamic thermo-mechanical model. The dynamic thermo-mechanical model consists of a comprehensive bearing dynamic model, a shaft dynamic model and a thermal model. The thermal model is coupled with the spindle dynamic model through bearing heat generation and thermal expansion of the whole system based on the bearing configuration. Thus the entire model becomes a comprehensive dynamic thermo-mechanical model. The new thermo-mechanical model also considers a pertinent mapping between bearing stiffness and shaft stiffness matrices based on bearing configurations, so that more general cases of bearing configurations can be modeled. Based on this model, the effects of bearing orientation on the spindle dynamics are systematically described and experimentally validated. It is shown that bearing orientation has a significant effect on spindle stiffness. Finally, the effects of various bearing configurations on spindle thermal and dynamic behavior are illustrated through numerical analysis with three different spindles.     

Rotary-axial spindles for ultra-precision machining

By combining pressurized fluid journal bearings with a novel magnetic thrust bearing, a rotary-axial spindle design is presented to achieve both rotary motion for cutting and mm-range linear motion along the axial direction for feeding. The advantages of such rotary-axial spindles include stiffer structure loops, fewer components, higher accuracy and resolution, and less heat generation. Our first prototype has demonstrated 9000 rpm, 600 N axial load capacity, 100 N/μm dynamic stiffness, 1 mm axial stroke, and 5 nm resolution. These are significant improvements over aerostatic spindles of comparable size.     

Anisotropic plasticity model coupled with strain dependent plastic strain and stress ratios

It is necessary to describe properly anisotropic material behavior for realistic numerical analyses of sheet metal forming processes. The implementation of many yield criteria in finite element analysis is very complicated. Various material tests are also required to determine yield function coefficients. Stress ratios and anisotropy coefficients are not constant during forming processes due to deformation induced anisotropy. This paper introduces a yield function using strain dependent plastic strain ratios and stress ratios. The main advantage is to fully utilize the data of uniaxial tensile tests. The described material behavior shows a significantly improved agreement with experimental data.     

Error correction in hydrostatic spindles by optimal bearing tuning

In this paper a high precision grinding wheel is considered as a rigid rotor mounted on two hydrostatic bearings. The equations for small perturbations of the wheel on the bearings are derived in the form of a multi-input, multi-output transfer function matrix, enabling the frequency response function of the wheel to be determined. Thereafter an optimisation algorithm is proposed which considers speed, load and dimensions of the spindle, and computes optimal stiffness and damping of the bearings. The dynamic characteristics of the bearings, tuned for minimum radial displacement of the spindle, is achieved maximising thereby the accuracy of the grinding process. Simulation results show that by stiffness coarse adjustment, and fine adjustment of the damping in the bearings, a spindle with 35 μm manufacturing error, can produce components with 3 μm accuracy.     

Modelling of angular contact ball bearings and axial displacements for high-speed spindles

This paper presents modelling of moving sleeve and spindle tip displacements in spindle bearing systems equipped with angular contact ball bearings. The balance of axial forces produced in high-speed bearings is examined, with a particular consideration of centrifugal forces, gyroscopic moments, contact deformations, and contact angles. It has been shown that centrifugal forces acting on bearing balls do not cause sleeve axial shifts. Those sleeve shifts can only result from gyroscopic moments, and changes in spindle dimensions due to centrifugal forces. The proposed model has been verified experimentally, and can be used for compensation of spindle tip displacements.     

Model-based chatter stability prediction for high-speed spindles

The prediction of stable cutting regions is a critical requirement for high-speed milling operations. These predictions are generally made using frequency response measurements of the tool/holder/spindle set, obtained from a non-rotating spindle. However, significant changes in system dynamics occur during high-speed rotation. In this paper, a dynamic model of a high-speed spindle-bearing system is elaborated on the basis of rotor dynamics predictions, readjusted with respect to experimental modal identification. Variations in dynamic behaviour according to speed range are then investigated and determined with accuracy. Dedicated experiments are carried out in order to confirm model results. By integrating the proposed speed-dependant transfer function into the chatter vibration stability approach of Budak–Altintas [S. Tobias, W. Fishwick, Theory of regenerative machine tool chatter, The Engineer February (1958)] a dynamic stability lobes diagram is predicted. The proposed method enables a new stability lobes diagram to be established that takes into account the effect of spindle speed on dynamic behaviour. Significant variations are observed and allow the accurate prediction of cutting conditions. Finally, experiments are performed in order to validate chatter boundary predictions in practice. The proposed modelling approach can also be used to qualify a spindle design in a given machining process and can easily be extended to other types of spindle.     

Radial error measuring device based on auto-collimation for miniature ultra-high-speed spindles

This study has developed a radial error measuring device for miniature ultra-high-speed spindles because it is very difficult to measure the radial error motion of miniature ultra-high-speed spindles by the conventional measurement method using capacitive-type displacement sensors. The authors have proposed an optical measurement method based on auto-collimation, which evaluates the radial error motion according to the movements of a laser beam reflected from a target sphere attached to the spindle end. This optical measurement method is suitable for radial error measurements of miniature ultra-high-speed spindles because of its applicability to a small target sphere, high-speed response and minor susceptibility to electric noise. In this paper, the measurement principle, and basic characteristics of the optical measurement method in addition to an approximate analysis are shown. The radial error motion of a miniature ultra-high-speed spindle with a steel ball 1 mm in diameter are measured by an optical measuring device designed and manufactured to implement the proposed method. The measurement results show that the optical measuring device is able to measure the radial error motion of ultra-high-speed spindles with a maximum rotational speed of 200 krpm.     

Vibration monitoring of high speed spindles using spectral analysis techniques

A significant source of noise and vibration in precision high speed machine tool spindles is bearing induced vibration, which is caused by inherent geometrical characteristics, as well as out-of-balance assembly and interactions between rolling mating members with surface irregularities. The multitude of causes often makes a diagnostic approach quite arduous, particularly due to insufficient information obtained from frequency domain analysis alone. Furthermore, the averaging nature of Fourier analysis and its poor frequency resolution make the task in complex vibration spectra more difficult. The paper presents a new approach in use of auto-correlation analysis with good frequency resolution, combined with windowing capability to isolate significant causes for subsequent remedial actions. The method is applied to a routing spindle with special reference to primary induced bearing frequencies.     

铝合金轧制过程中的热力耦合分析

通过铝合金在Gleeble-1500上的实验数据,建立了本构方程.根据弹塑性热力耦合大变形有限元理论,获得了热轧过程中的数值仿真模型,分析了压下率、轧制速度以及接触传热系数等参数对温度和流动应力变化规律的影响,并与某铝厂热轧板带生产过程中不同压下率下的力能参数变化进行了对比,计算结果表明模拟值与实测值吻合较好,误差低于15%.     

ANALYSIS OF DISTRIBUTIONS OF RESIDUAL STRESS AND STRAIN BENEATH A NOTCH AFTER ROLLING

The fatigue property of the notched part can be improved significantly by introducingcompressive residual stress resulting from surface plastic deformation at the notch.Theresidual stress and strain distributions beneath the notch is predicted by using finite elementmethed (FEM) of large strain elasto-plastic analysis in this paper.It is investigatedwheather the rolling process could be replaced by a plane-strain indenting with a model inthe analysis.The effects of material strength.notch radius r.and indentation and depth Δhon the distribution of residual stress and strain are discussed.The agreement of predictedand experimental results is good enough.     

Finite element analysis of die wear in hot forging processes

Design optimization of hot forging dies requires an accurate estimation of die wear. The presented paper introduces a finite element model for wear estimation that includes the process related thermal effects on hardness of the tool material. Fundamental investigations concerning the hardness evolution due to thermal softening of the tool material are presented. To obtain necessary data for model calibration by means of statistical analysis, optical measurements are performed on several industrial forging dies. The introduced model is proved to be applicable in wear estimation of hot forging dies over a large number of operating cycles.     

机械主轴热特性分析

以机械主轴为研究对象,运用HyperMesh、Abaqus等有限元分析软件,研究了机械主轴的热特性。通过确定热分析的边界条件、计算皮带轮以及轴承的发热量,建立了机械主轴热力学有限元模型,并通过计算得到了其稳态热、温升变化以及温度场分布情况。结果表明:仿真计算得到的温度场与实验测得的温度分布数据基本吻合,因而采用有限元方法可以较准确预测机械主轴温度变化,皮带轮处的发热在机械主轴中是不能忽略的。而热变形分析显示机械主轴的变形较小,证明该机械主轴结构设计合理。     

Thermo-mechanical coupled analysis of hot ring rolling process

A 3D rigid-plastic and coupled thermo-mechanical FE model for hot ring rolling（HRR） was developed based on DEFORM 3D software, then coupled heat transferring, material flow and temperature distribution of the ring in HRR were simulated and the effects of process parameters on them were analyzed. The results show that the deformation nonuniformity of ring blank increases with the increase of the rotational speed of driver roll and friction factor or the decrease of the feed rate of idle roll and initial temperature of ring blank. The temperature nonuniformity of ring blank decreases with the increase of the feed rate of idle roll or the decrease of initial temperature of ring blank and friction factor. There is an optimum rotational speed of driver roll under which the temperature distribution of ring blank is the most uniform. The results obtained can provide a guide for forming parameters optimization and quality control.     

Optimum process parameters to produce green ceramic complex parts

The fragility of green ceramic compacts introduces considerable difficulties during green or bisque machining. This paper demonstrates methods developed to manufacture thin wall-thin floor, complex green ceramic parts to close tolerance. Hybrid finite element (FE)/mechanistic models were utilized in the development of the green machining process. An FE model was used to define cutting edge geometry and machining parameters that would reliably produce crack free parts. Mechanistic model was used to direct cutter path generation of a 5-axis milling machine having a large axial depth of cut, and to prevent edge chipping. The optimized cutter path eliminated any need for hand work before densifying the machined part.     

模切板刀片复合弯曲成形中的回弹研究

复合弯曲成形是一种高柔性的板料成形工艺。运用有限元方法分析了模切板刀片的复合弯曲成形,对成形过程中的回弹进行了研究。建立了外环转角与弯曲回弹角的度的关系。分析了内环圆角半径与对回弹的影响,对模切刀片的成形具有一定的指导意义。     

Analysis of workpiece thermal behaviour in cut-off grinding of high-strength steel bars to control quality and efficiency

Cut-off grinding is a machining process for separating various components and materials. The application of this trimming technology for high-strength steel bars leads to thermally induced defects such as grinding burrs and residual stresses. By means of a developed and empirically validated FE model it is possible to control the temperature distribution in the workpiece. The implementation of a CBN grinding wheel along with the optimization of the cutting parameters allows a significant decrease of the thermal load in the machined bar. As a consequence, thermal defects are reduced, thus leading to a high-quality trimming process.     

Modelling vibration transmission in the mechanical and control system of a precision machine

The relative vibration between tool and workpiece factors significantly to the performance of a precision machine. This paper develops a model for predicting the vibration transmission from two major excitation sources, ground vibration and fluid bearing force, to the tool and the workpiece position through the mechanical and control system of a precision machine. We synthesised the frequency response functions obtained from a finite element analysis of the machine to create transmissibility matrices that define the dynamic behaviours of the electromechanical system. The validity of the developed model was checked by comparing the measured relative vibrations to the results calculated from the measured excitations.     

AZ31B镁合金矫直过程中热力耦合模型下中性层偏移规律分析

为了提高镁合金板材的矫直精度,需要对镁板的中性层偏移规律进行分析。在室温下,镁合金的塑性较差且拉压不对称性也较大。并且镁板在室温下矫直时,压下量的控制不当会导致板材的矫直效果受到严重影响,因此,镁板常采用温矫的方法来提高矫直精度而且温度是影响镁板拉压不对称性的重要因素。本文基于CaBa2004拉压不对称性屈服准则,利用弹塑性力学的基本理论,推导了AZ31B镁板在矫直过程中中性层偏移量计算公式,运用ABAQUS有限元建立了热力耦合矫直模型,得出了不同温度下的中性层偏移规律,并利用实验,对中性层偏移理论进行实验验证。     

Flexible Sheet Forming Technology by Double-sided Simultaneous Shot Peen Forming

The exceptionally flexible forming technology shot peen forming is used primarily on large, three-dimensionally curved sheet metal in the aircraft and aerospace industries. Depending on the kinetic shot energy, both convex and concave curvatures will be generated. The most recent development, double-sided simultaneous shot peen forming, brings about a higher productivity of the entire process. FEM simulations of single and multiple impacts are presented in order to evaluate the characteristics of concave curvatures generated by both single and double-sided peen forming.