Measurement and compensation of error motions of a diamond turning machine

This paper describes the measurement and compensation of error motions of a diamond turning machine for nanofabrication of large sinusoidal metrology grids. The diamond turning machine has a T-base design, which consists of a spindle with its rotation axis along the Z-direction and a cross-slide with its movement direction along the X-direction. A fast-tool-servo (FTS) unit is mounted on the X-slide to generate sinusoidal microstructures on a flat workpiece surface mounted on the spindle. The error motions of the X-slide and the spindle, which introduce Z-directional profile errors (out-of-flatness) on the grid surface, are measured and compensated. The out-of-straightness of the X-slide is measured to be approximately 60 nm over a travel of 80 mm by using the reversal method. It is also confirmed that the out-of-straightness of the X-slide has a 10-nm periodic component with a period of 11 mm corresponding to the diameter of the needles used in the roller bearing of the X-slide. The angular motion of the spindle is measured to be approximately 0.3″ by using an autocollimator, which can cause a 73-nm out-of-flatness over a workpiece 100 mm in diameter. The axial motion of the spindle is measured to be approximately 5 nm, which is the smallest error motion. The out-of-flatness of the workpiece is reduced from 0.27 to 0.12 μm through compensating for the error motions by utilizing the FTS unit based on the measurement results of error motions.     

金属切削机床主轴运动误差影响的数学分析

在研究金属切削机床加工误差的基础上,针对机床主轴回转运动误差中的径向跳动误差、角度摆动误差和轴向窜动误差,以车床和镗床主轴为例,建立了主轴回转运动误差数学分析模型,从数学几何角度分别对上述主轴回运动城的加工精度影响结果进行了定量分析,并推导出了由此产生的各类加工几何误差不同的数学表达式。通过这些数学表达式可以定量地计算出机床主轴由于回转运动误差产生的加工几何误差数值。     

A novel surface analytical model for cutting linearization error in fast tool/slow slide servo diamond turning

Fast tool/slow slide servo (FTS/SSS) technology plays an important role in machining freeform surfaces for the modern optics industry. The surface accuracy is a sticking factor that demands the need for a long-standing solution to fabricate ultraprecise freeform surfaces accurately and efficiently. However, the analysis of cutting linearization errors in the cutting direction of surface generation has received little attention. Hence, a novel surface analytical model is developed to evaluate the cutting linearization error of all cutting strategies for surface generation. It also optimizes the number of cutting points to meet accuracy requirements. To validate the theoretical cutting linearization errors, a series of machining experiments on sinusoidal wave grid and micro-lens array surfaces has been conducted. The experimental results demonstrate that these surfaces have successfully achieved the surface accuracy requirement of 1 μm with the implementation of the proposed model. These further credit the capability of the surface analytical model as an effective and accurate tool in improving profile accuracies and meeting accuracy requirements.     

A theoretical and experimental investigation of orthogonal slow tool servo machining of wavy microstructured patterns on precision rollers

Precision cylinders, or rollers, with patterned microstructures on the surface are the key tooling component in the Roll-to-Roll and Roll-to-Plane fabrication process for precision manufacturing of microstructured plastic films. These films are widely used in optical applications such as the backlight guide and brightness enhancement films in LCD and LED displays. Compared with other fabrication processes, such as lithography, Single-Point Diamond Turning (SPDT), using a Fast Tool Servo (FTS) or Slow Tool Servo (STS) process, is an enabling and efficient machining method to fabricate microstructures. Most studies of the tool servo machining process focus on either machining microstructures in the axial direction for face machining of flat parts or in the radial direction on the surface of a precision roller. There is relatively little research work found on the machining of patterned microstructures on the surface of precision rollers using the tool servo in the axial direction. This paper presents a pilot study on the development of a tool path generator for machining wavy microstructure patterns on precision rollers by using an Orthogonal Slow Tool Servo (OSTS) process. The machining concept of OSTS is first explained, and then the tool path generator is developed in detail for machining wavy microstructure patterns on a roller surface. Modelling and simulation of pattern generation for different microstructures with different wavy patterns and grooves are presented based on the proposed tool path generator. Preliminary experimental work using SPDT on a 4-axis ultra-precision machine tool is presented and clearly shows the generation of unique wavy microstructure patterns on a precision roller. The machined wavy microstructures on the roller surface are measured and analyzed to evaluate the validity of the proposed tool path generator.     

Optimal selection of machining parameters for fast tool servo diamond turning

Ultraprecision machined components with micro-structured surfaces in micrometer or nanometer range have gained wide applications especially in optical industry. A technique called fast tool servo (FTS) diamond turning is superior in fabricating precision and complicated micro-structured surfaces with wavelength above tens of microns. However, in order to obtain optimal machined surface quality, the machining parameters need to be selected carefully. In this paper, optimal selection of the machining parameters, including spindle speed, sampling number, feedrate and tool geometry, for fabricating micro-structured surfaces by FTS diamond turning is presented. A simulation system is developed to select feedrate and tool geometry by computing the theoretical surface roughness, spindle speed, and sampling number based on the FTS dynamics and the motion controller capability. Experiments have been carried out to show the effect of the machining parameters. In addition, machining of typical micro-structured surfaces with machining parameters selected by the presented approach proves the effectiveness of the proposed optimal machining parameters selection method and the designed FTS diamond turning machine.     

Thermal error of a hydrostatic spindle

This paper proposes a thermo-mechanical error model of a hydrostatic spindle for a high precision machine tool. By predicting the variation of motion error induced by thermal effects on a machine worktable during machining, this model allows deeper insights into the underlying mechanisms that result in evolutions of the spindle accuracy. The heat power generated in the spindle elements and the coefficients of convection heat transfer over its outer surface have been evaluated. Then, the distribution of temperature and deformation of the spindle have been simulated by a finite element coupled thermo-elastic model, from which the influence on notably spindle stiffness variation was deduced. Experimental measurement of the thrust plate axial displacement under thermal expansion is in close agreement with the computed axial thermal expansion.     

立式加工中心空间几何误差辨识解析及定位误差补偿研究

为大幅提升立式加工中心加工精度,满足当代数控机床对高精度的需求,针对立式加工中心3个运动轴,深入分析了其轴向运动空间几何误差,提出了可有效辨识运动轴轴向运动空间6项几何误差的辨识方法.建立了空间6项几何误差辨识模型,并针对关联轴联动垂直度误差进行了有效分析,建立了垂直度误差辨识解析模型.同时,针对3个独立运动轴轴向定位...     

A method for evaluating spindle rotation errors of machine tools using a laser interferometer

This paper presents a method for assessing radial and axial error motions of spindles. It uses the Hewlett Packard 5529A laser interferometer. The measurement is made using reflection directly from a high-precision sphere. Such object is used as the optical reflector. The sphere is affixed at the end of a wobble device, which is clamped in the spindle. The principle of measurement is similar to that of a linear interferometer, except that the high-precision sphere is used in place of the usual retroreflector. A convergent lens is utilized to focus the laser beam to a small spot on the sphere surface. This minimizes the dispersion of the beam due to the reflection on the spherical surface. A software package has been developed for data acquisition and presentation of the error motion polar plots of the spindle. Application of this spindle error calibrator on a CNC machining centre is undertaken. The results are presented and discussed.     

A flexure-based long-stroke fast tool servo for diamond turning

This paper describes the development of the fast tool servo (FTS) in detail and categorizes existing FTSs according to different principles. The characteristics and differences of these FTSs have been analyzed. A flexure-based long-stroke FTS system for diamond turning is presented with displacement range of 1?mm and bandwidths of 10?Hz. The vertical jump is about 0.045?μm, and the full stroke tracking error is less than 0.15%. A voice coil motor and a piezoelectric actuator are used as the driving elements, and two flexure hinges are developed as the guide mechanisms. The FTS utilizes a linear encoder and a capacitive sensor to measure the displacement of the tool for closed-loop control. The electromechanical design of the FTS and its motion analysis are described. Experimental tests have been carried out to verify the performance of the FTS system. This long-stroke FTS has the advantage of easy machining, high resonance frequency, and error compensation in y-axis direction.     

螺旋铣孔工艺的切削稳定性及工艺参数规划

以螺旋铣孔工艺时域解析切削力建模、时域与频域切削过程动力学建模、切削颤振及切削稳定性建模为基础,研究了螺旋铣孔的切削参数工艺规划模型和方法。切削力模型同时考虑了刀具周向进给和轴向进给,沿刀具螺旋进给方向综合了侧刃和底刃的瞬时受力特性;动力学模型中同时包含了主轴自转和螺旋进给两种周期对系统动力学特性的影响,并分别建立了轴向切削稳定域和径向切削稳定域的预测模型,求解了相关工艺条件下的切削稳定域叶瓣图。在切削力和动力学模型基础之上,研究了包括轴向切削深度、径向切削深度、主轴转速、周向进给率、轴向进给率等切削工艺参数的多目标工艺参数规划方法。最后通过试验对所规划的工艺参数进行了验证,试验过程中未出现颤振现象,表面粗糙度、圆度、圆柱度可以达到镗孔工艺的加工精度。     

Influence of tool eccentricity on surface roughness in gear skiving

Gear skiving is a state-of-the-art technique for machining internal gears with high efficiency. Numerical simulation method being able to analyze the eccentricity error e of cutter is critical to the understanding on the formation of surface roughness in skiving process. In this work, we proposed a novel Z-map-based numerical model to calculate the surface of gear flanks with eccentricity errors up to 9 μm. Correlation between eccentricity error and gear flank profile was clarified by numerical simulation and supported by experimental verification. The results show that the eccentricity error imposed a low-frequency motion during the generation of scallop height, leading to a surface roughness with a maximal error about four times that of the theoretical roughness. The e-induced scallop height became the majority factor account for variation of surface roughness when e exceeds 1.4 and 2.3 μm for feed rates of 0.4 and 0.8 mm/rev, respectively. The experimental result further supported the capability of proposed simulation model in providing detail surface features of gear flanks in skiving process.     

高精度无心车床主轴系统动力学建模研究

针对无心车床加工时主轴系统的振动导致加工精度不足的问题,该文以无心车床主轴系统为研究对象,考虑了实际加工中存在的棒料s弯问题,建立了主轴系统动力学模型,并在simulink中进行了动力学分析,得到了主轴在径向1(x向),径向2(y向),轴向(z向)振动信号。通过对主轴参数轴承游隙的改变来观察主轴x方向,y方向,z方向振动的变化趋势,以及改变轴套磨损量来观察主轴z方向的振动变化趋势。分析结果表明,主轴在三个方向上的振动z向最大。最后将试验信号与模型信号进行对比分析,振动实验值与理论值的误差均在5%以内,所得实验结果与模型结果基本一致,z向振动最大,可通过调整主轴参数来提高加工精度,验证了所建立模型的准确性。     

<Emphasis Type="Bold">Roundness Error Prediction with a Volumetric Error Model Including Spindle Error Motions of a Machine Tool</Emphasis>

This paper proposes a modified volumetric error model that includes spindle error motions as well as geometric errors. The model is constructed using rigid-body kinematics and homogeneous transformation matrices and an additional error matrix describing spindle error motions is included. The suggested model predicts the positioning errors at a given axis position as a function of both the axis position and the engaged spindle rotation angle. Two circular interpolation tests (inner and outer circle of the same radius) are simulated and the machined part profiles are predicted. To verify the simulation results, machining tests are performed according to the ISO 10791-7 standard. The error model with spindle errors shows a better agreement, between the simulated and measured roundness errors, than the simple geometric model. It can be seen that the geometric errors determine the basic part profiles and the spindle errors change the basic profiles according to the magnitude of the errors and the spindle rotation angle.     

液体静压主轴热态特性多物理场耦合仿真与实验研究

液体静压主轴在加工过程中受热源影响发生热变形,会影响机床加工精度。针对一种超精密卧式辊筒加工机床的液体静压主轴,建立主轴生热与散热的理论模型,采用有限体积法与有限单元法建立主轴的流-热-固耦合仿真模型,考虑油膜区域散热条件,分析主轴工作到稳态下的温度场以及产生的轴向热误差,并通过试验验证仿真模型的正确性和准确性。应用该模型分析主轴转速、供油压力、液压油黏度、油膜间隙以及轴向封油边长度对主轴温升的影响。结果表明,主轴温升随主轴转速、液压油黏度、封油边长度的增大而增大,随供油压力、油膜间隙的增大而减小。因此,在满足主轴性能的前提下,使用较低的主轴转速、较大的供油压力,选择小黏度的液压油、较大的油膜间隙以及较短的封油边长度可以有效地降低主轴的温升。     

Characterization of surface defects in fast tool servo machining of microlens array using a pattern recognition and analysis method

Microlens array (MLA) is a type of structured freeform surfaces which are widely used in advanced optical products. Fast tool servo (FTS) machining provides an indispensible solution for machining MLA with superior surface quality than traditional fabrication process for MLA. However, there are a lot of challenges in the characterization of the surface defects in FTS machining of MLA. This paper presents a pattern recognition and analysis method (PRAM) for the characterization of surface defects in FTS machining of MLA. The PRAM makes use of the Gabor filters to extract the features from the MLA. These features are used to train a Support Vector Machine (SVM) classifier for defects detection and analysis. To verify the method, a series of experiments have been conducted and the results show that the PRAM produces good accuracy of defects detection using different features and different classifiers. The successful development of PRAM throws some light on further study of surface characterization of other types of structure freeform surfaces.     

Thermal influence of the Couette flow in a hydrostatic spindle on the machining precision

Hydrostatic spindles are increasingly used in precision machine tools. Thermal error is the key factor affecting the machining accuracy of the spindle, and research has focused on spindle thermal errors through examination of the influence of the temperature distribution, thermal deformation and spindle mode. However, seldom has any research investigated the thermal effects of the associated Couette flow. To study the heat transfer mechanism in spindle systems, the criterion of the heat transfer direction according to the temperature distribution of the Couette flow at different temperatures is deduced. The method is able to deal accurately with the significant phenomena occurring at every place where thermal energy flowed in such a spindle system. The variation of the motion error induced by thermal effects on a machine work-table during machining is predicated by establishing the thermo-mechanical error model of the hydrostatic spindle for a high precision machine tool. The flow state and thermal behavior of a hydrostatic spindle is analyzed with the evaluated heat power and the coefficients of the convective heat transfer over outer surface of the spindle are calculated, and the thermal influence on the oil film stiffness is evaluated. Thermal drift of the spindle nose is measured with an inductance micrometer, the thermal deformation data 1.35 μm after running for 4 h is consistent with the value predicted by the finite element analysis's simulated result 1.28 μm, and this demonstrates that the simulation method is feasible. The thermal effects on the processing accuracy from the flow characteristics of the fluid inside the spindle are analyzed for the first time.     

龙门数控机床主轴热误差及其改善措施

依据ISO和ASME标准建立龙门数控(Numerical control,NC)机床热误差测试条件,通过主轴恒转速和变转速热误差试验分析主轴箱温度场分布及其对主轴热误差的影响趋势。建立龙门机床误差元素模型,分析影响机床各坐标轴加工精度的主轴热误差分量。研究发现,主轴热误差和主轴箱温度存在单调对应关系,温度对主轴轴向的热伸长误差的影响要远大于主轴径向的热漂移误差,但温度变化相对各坐标变形存在热延迟和热惯性等特性。对主轴径向精度影响最大的热误差分量是由机床生热产生的同方向的偏移误差和与之垂直的偏转误差;对轴向精度影响最大的则是轴向的偏移误差。针对热误差特点和分布规律,提出结构优化、热平衡、误差补偿建模等3种减小热误差的措施,并对其各自优点进行了分析。     

Examination of surface location error due to phasing of cutter vibrations

The purpose of this research is to investigate the relative importance of spindle speed, system dynamics, and cutting conditions on the accuracy of surface location in computer numerical-control (CNC) finish machining operations. The relationship between the spindle speed, the most flexible modes of the machine/cutting tool system and the final part dimensions is rather complex. The underlying theory, based on the situation of forced vibrations, is outlined. It is shown that the critical factor is the ratio of the tooth passing frequency to the system most flexible mode and corresponding natural frequency. Simple analytical calculations are carried out to illustrate the overcut/undercut surface error phenomenon. A simple simulation for end milling operations is also described which calculates the force on the cutter, the resulting cutter deflection, and the final error of surface. A comparison between the simulated and experimental results is presented. From experimental data, it shown that a change in surface location (and part dimension) of up to 50 μm is seen for a set of given conditions (i.e., cutter, material, chip load) simply by changing spindle speeds. Furthermore, it is seen that certain spindle speeds produce surfaces with no error introduced by the machining process.     

A spiral scanning probe system for micro-aspheric surface profile measurement

This paper presents a novel spiral scanning probe measurement system which is developed to achieve precise profile measurements of micro-aspheric surfaces. The system consists of a scanning stage (a spindle and a linear slide) and a contact-type displacement sensor. The contact-type sensor is employed for the scanning of the micro-aspheric surface. The micro-aspheric object is set on the spindle, and the contact-type displacement sensor is set on the linear slide. The motions of the spindle and the linear slide are controlled synchronously so that the micro-aspheric object is scanned spirally for high-speed measurement. The motions of the stage are used as the scanning datum for the profile measurement. Because the error motions of the stage are estimated to be on the order of tens of nanometer, these errors are measured and compensated to achieve precise measurements. The alignment error between the spindle rotation axis and the probe tip of the contact-type displacement sensor, which is called the centering error, is confirmed to cause considerable measurement error of the micro-aspheric surface profile. Methods are proposed to make the alignment accurately. Experiments of surface profile measurement of a micro-aspheric lens are also carried out in the measurement system.