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.     

Precision evaluation of surface form error of a large-scale roll workpiece on a drum roll lathe

This paper presents on-machine evaluation of surface form error components of a large-scale roll workpiece, including the out-of-roundness, the out-of-straightness, the taper angle and the diameter deviation, on a drum roll lathe. A pair of capacitive-type displacement probes is mounted on the carriage slide to target the two sides of the roll workpiece mounted on the spindle, which has a length of 2000 mm, a diameter of 320 mm and a mass of 350 kg. The outputs of the probes are employed to accurately evaluate the surface form error components through separating the influences of the motion errors of the spindle and the carriage slide of the lathe. It has been difficult to apply the reversal error-separation method for measurement of the out-of-roundness component of such a large workpiece because it is difficult to reverse the workpiece with respect to the spindle on the lathe due to its large size and heavy mass. An improved reversal operation technique, in which the spindle is rotated with respect to the stationary roll workpiece being held by a crane, is therefore proposed to solve this problem. Measurement uncertainty analysis is carried out to verify the reliability of the new technique for on-machine evaluation of the out-of-roundness component. The out-of-straightness component and the taper angle component of the roll workpiece are then evaluated by using a previously developed method. A simple and effective algorithm for evaluation of the diameter deviation component is also presented.     

Investigation of error separation for three dimensional profile rotary measuring system

High precision 3D profile rotary measuring systems for large diameter workpieces are urgently needed in precision engineering. Error separation is critical for improving the accuracy of the system. In order to obtain higher accuracy for 3D profile rotary measuring systems, the random and systematic errors are analyzed and separated in this paper. In the measuring system, roll and pitch caused by the probe tilt violate the Abbe principle. Roll is removed by using two probes and pitch is separated by the interferometer method. The radial run-out and the perpendicularity error between the probe and the spindle axis are compensated by a two-probe-two-step method carried out on a standard hemisphere artifact. As the form error of the artifact is mixed with the perpendicularity error, the least-squares method is applied to fit the hemisphere and work out the perpendicularity error and the profile error of the hemisphere. Finally, numerical validation is presented using Matlab program to demonstrate the effectiveness and correctness of the proposed method.     

用于大尺寸工件的动态长度测量系统

针对移动大尺寸工件的表面形貌特点,利用二维激光三角法构造出水平和垂直虚拟测量基准面;结合多传感器融合准则,建立了一种新型的大尺寸工件测量模型,并利用该模型实现了移动工件两端端面到虚拟测量基准面的位移非接触测量。采用误差分离方法自修正理论误差和运动误差的影响;结合人机交互界面,研制了高精度、低成本的移动大尺寸工件长度自动检测系统。利用该系统对在(1 000±25)mm内以不同速度运动的圆柱体大尺寸工件长度进行检测,得到的检测分辨力为10μm、检测精度为100μm、工件移动速度为5cm/s。实际运行结果表明,该系统安全、稳定、快速,可满足工业在线生产中对同类型规则的大尺寸工件控制和检测的要求。     

Repetitive Measurement and Compensation to Improve Workpiece Machining Accuracy

Achieving workpiece high accuracy at low cost is one of the greatest challenges in the manufacturing industry. A repetitive error measurement and compensation scheme to improve the workpiece diameter accuracy for machining centres is des-cribed. The scheme entails an on-machine measurement and error compensation technology between machining processes. The workpiece diameters are measured along the workpiece length by using a fine touch sensor. The workpiece diameters in the compensation program are modified for implementation of next pass error correction. The technology is realised on a CNC turning centre. This method works well in hard machining and turned workpieces with large length–diameter ratios where the machining process induced errors are significantly greater than errors from other sources. It demonstrates that the work-piece can obtain maximum possible machining accuracy by this repetitive measurement and compensation technique.     

Pitch deviation measurement of an involute spur gear by a rotary profiling system

This paper presents surface-profiling based gear pitch deviation measurement for an involute spur gear. A rotary profiling system, which consists of an air-bearing spindle and a displacement sensor with a diamond stylus, is employed to measure gear pitch deviation. In measurement of gear pitch deviation, an eccentric error between a gear axis and a motion axis of the rotary stage in the profiling system would affect accuracy of gear profile measurement. In this paper, at first, the influence of the eccentric error on measurement of gear pitch deviation is estimated in computer simulation based on a geometric model of the profiling system. After that, a new scanning method named “opposite-direction dual scanning method” is proposed so that a steep profile of gear flank surface with a local slope of up to 90° can be measured by the developed rotary profiling system. For compensating distortions in the measured gear tooth profile, which are induced not only by the eccentric error but also by a probe offset introduced by the proposed scanning method, a self-calibration and compensation method is applied. To verify the feasibility of the proposed method, measurement of gear pitch deviation of a master involute spur gear with a certificate data is carried out. Measurement uncertainty of the proposed method is also analyzed.     

凸轮轴数控磨削工件主轴转速优化建模与实验研究

根据凸轮轴X-C轴联动恒线速度磨削加工数学模型,建立了砂轮架进给位移与速度、凸轮工件主轴转速的理论方程。根据数控凸轮轴磨床加工能力的约束条件,对砂轮架进给中速度、加速度或加加速度值超出限定值的凸轮转角区间,通过积分反求方法求解出相应转角区间工件主轴所允许的转速值,并以该段转速值替换对应的转角区间上凸轮轴恒线速度磨削时理论转速值。对优化计算前后的工件主轴转速曲线进行了凸轮轴磨削加工实验。实验结果表明：采用优化后的凸轮工件主轴转速进行加工,相比于恒线速度理论转速加工,其升程最大误差与最大相邻误差减小,工件表面粗糙度降低,提高了凸轮轴高效精密磨削加工质量。     

Optical,in situ,three-dimensional,absolute shape measurements in CNC metal working lathes

Temperature drifts, tool deterioration, unknown vibrations, as well as spindle play are major effects which decrease the achievable precision of CNC lathes and lead to shape deviations of the processed workpieces. Since currently no measurement system exists for precise, in situ, 3D shape monitoring, much effort is required to simulate and compensate these effects. In this article, we propose an optical measurement principle for first part quality manufacturing. The absolute shape, meaning the diameter and surface profile, of the workpiece is determined from its tangential velocity and the surface distance. In order to allow keyhole access, both measurands are determined simultaneously with a single sensor. Measurements inside a metal working lathe show that the standard uncertainty for the absolute shape measurement is below 1 μm. The measurement uncertainty is nearly independent of the lateral surface velocity and roughness. The in situ measurements are compared to measurements with a tactile coordinate measurement machine for reference.     

Development of a rapid profilometer with an application to roundness gauging

This paper presents the development of a real-time, contact-based, high frequency, response profilometer employed as a roundness gauge for measuring circular form error for 100% part inspection on the shop floor with an accuracy of better than 0.5 μm with measurement times of less than 1 s. The gauge head is a closed-loop controlled mechanism comprising a contact force probe that is rigidly attached to a high bandwidth linear translator. The gauge head assembly is, in turn, attached to a precision spindle. The objective of the complete tool is to contact the sidewall of the circular feature, translate the probe tip to produce a defined contact force with the workpiece and rotate the gauge head assembly. During rotation of the spindle, this contact force is maintained at a nominally constant value by dynamically translating the force probe along a radial direction to follow surface deviations. The gauge head assembly (including force probe and servo drive) has a fundamental mode natural frequency of 330 Hz while scanning the workpiece with a constant contact force typically less than 100 mN. Form error (deviation from a nominal circle) is measured using a capacitance-based displacement sensor measuring the relative radial displacement of the probe with the spindle rotating at a constant rotation speed. This paper discusses the design and characterization of this metrology tool.     

A comprehensive technique for measuring the three-dimensional positioning accuracy of a rotating object

A method for measuring the accuracy of rotating objects was studied. Rotating axis errors are significant; such as the spindle error of a machine tool which results in increased surface roughness of machined work pieces. Three capacitance-type displacement sensors were used to measure the position of a rotating master ball. The sensors were mounted at the three orthogonal points on the spindle axis. The measurement data were analysed for rotating spindle accuracy, not only for the average roundness error but also for the spindle volumetric positional error during rotation. This method is simple and economical for industrial field use for regular inspection of spindles using portable equipment. The time taken for measurement and analysis using this method is only about two hours. This method can also measure microscopic amplitudes in 3-D directions of vibrating objects.     

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.     

Least squares evaluations for form and profile errors of ellipse using coordinate data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.     

基于三维激光扫描的移动大尺寸圆柱体工件长度快速检测系统

针对移动大尺寸圆柱体工件两端的表面形貌特征,利用三维激光扫描仪设计了一种快速长度在线检测系统。基于三维激光扫描仪可在短时间内连续高速获取大量测量数据的特点,系统在虚拟环境下构造出自适应测量形状的虚拟测量基准面,采用二维误差分离方法抑制系统误差和运动误差,识别定位工件两端端点并计算其到虚拟测量基准面的位移;最后结合多传感器融合模型获取三维位移场测量结果。另外,测试前用三坐标测量机精密测量过的相似形状圆柱体工件对系统进行了校准修正。为验证系统的精度和可靠性,分别对处于（1 000±25）mm内不同直径的圆柱体工件进行了长度检测。结果显示,系统可在1 s完成直径约为50 mm工件的长度测量,检测分辨力为0.010 mm,检测精度达到0.050 mm。实际运行结果表明,该设计系统具有高自动性和高效性,可满足在线生产中对大尺寸工件控制和检测的要求。     

Correcting capacitive displacement measurements in metrology applications with cylindrical artifacts

Metrology applications commonly require non-contact, capacitive sensors for displacement measurements due to their nanometer resolution. In some metrology applications, for example, the measurement of roundness and spindle error motion, the displacements of stationary and rotating cylindrical artifacts are measured. Error from using a conventionally calibrated sensor with a non-flat (e.g., cylindrical) target is typically neglected, but these errors cannot be ignored for nanometer-level accuracy. The capacitance between a sensor and a cylindrical target is less than that of a sensor with a flat target, which causes four effects. As the diameter of the target shrinks, the sensitivity of the sensor increases, the sensing range decreases, the sensing range shifts towards the target, and the nonlinearity increases. These errors can be greatly reduced by either calibrating sensors with the correct target surface or by determining corrections for post-processing data. This paper quantifies and experimentally verifies these errors for a commonly used sensor, and a simulation of a nanometer-level measurement of out-of-roundness and spindle error motion demonstrates that measurement accuracy is improved with corrected sensitivities.     

On-machine profile measurement of a micro cutting edge by using a contact-type compact probe unit

A new contact-type on-machine measurement system is designed and developed for the evaluation of a micro cutting edge profile. The measurement system is composed of a compact probe unit having a sharp stylus mounted on a flexible beam, an inner displacement sensor for the detection of the stylus displacement, and a two-axis precision positioning system. For the evaluation of tool faces having a steep slope, a new probing procedure with the enhancement of the inner displacement sensor integrated into the probe unit is newly proposed. After the design and development of the probe unit, the feasibilities of the developed measurement system and the proposed probing procedure are demonstrated through some basic experiments. Regarding the out-of-straightness and angular error motion of the two-axis positioning system employed in the developed measurement system, a pair of length gauges is newly employed to reduce the influences of error motions of the stage system. The topographic profile of the micro cutting edge obtained by the measurement system with the modified probe unit is then compared with those obtained by a commercial stylus profiler and a laser confocal microscope. The feasibility and effectiveness of the developed on-machine tool edge profile measurement system are also demonstrated through uncertainty analysis based on the GUM with the Monte-Carlo method.     

An identification method for spindle rotation error of a diamond turning machine based on the wavelet transform

This paper presents an identification method for the spindle rotation error from the flatness error in the workpiece surface. The spindle rotation error is identified by the wavelet transform, Weierstrass function, and power spectral density (PSD). The flatness error comprises various errors of the machine tool, such as spindle rotation error, guideway error, motor error, and ball screw error, therefore, wavelet transform is used to process the measured result of the workpiece and the signal is decomposed into high-frequency and low-frequency signal. Weierstrass function is used to fit the spindle rotation error. According to the PSD analysis of the processed signal in the frequency domain, the spindle rotation error is identified from the measured flatness error, this method provides a basis for the identification of machine tool errors.     

Form Error Characterisation by an Optical Profiler

Form errors are deviations of the machined surface from the geometrical surface excluding position errors, waviness and roughness. From a functional point of view, as for surface roughness, form error characterisation is also important. In the present work, an optical profiler is used to measure and numerically characterise form errors such as roundness and cylindricity of cylindrical surfaces. A double orientation method using mean value analysis has been applied to separate the workpiece error from the spindle error during roundness measurement. Software is developed for data generation, fitting the reference data for assessing form errors in terms of statistical and functional parameters including new parameters. An optical profiler measures all the surface irregularities and hence can be used to study both micro and macro errors of the profile measured. A study of both roughness and roundness parameters along the circumferential direction is made for the unfiltered signal using different filter cut-off values. It is known that filtering greatly affects the value of the form error parameters measured. The form measurements obtained by the optical profiler are compared with the stylus profiler and the results are presented.     

Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage

This paper describes the measurement of straightness error motions (vertical straightness and horizontal straightness) and rotational error motions (pitch, yaw and roll) of a commercial precision linear air-bearing stage actuated by a linear motor. Each of the error motions was measured by two different methods for assurance of reliability. The stage was placed in the XY-plane and moved along the X-direction. The pitch error and yaw error, which were measured by an autocollimator and the angle measurement kit of a laser interferometer, were about 8.7 and 1.6 arc-s, respectively, over a travel of 150 mm with a moving speed of 10 mm/s. The roll error was measured by the autocollimator through scanning a flat mirror along the X-direction. The second method for roll error measurement was to scan two capacitance-type displacement probes along the flat surface placed in the XZ-plane. The two probes with their sensing axes in the Y-direction were aligned with a certain spacing along the Z-axis. The roll error can be obtained by dividing the difference of the outputs of the two probes by the spacing between the two probes. The roll error was measured to be approximately 11.8 arc-s over the 150 mm travel. The horizontal straightness error and the vertical straightness error (Y- and Z-straightness errors) were measured by using the straightness measurement kit of the laser interferometer. The second method for straightness measurement was to scan the flat surface with a capacitance-type displacement probe. The horizontal and vertical straightness errors of the stage over the 150 mm travel were measured to be approximately 207 and 660 nm, respectively.     

平行三点法圆度误差分离技术的精度分析

阐述了一种能临床测量与分离工件圆度误差和主轴系统回转误差的新方法——平行三点法误差分离技术的测量原理 ,定量分析了测量装置的结构参数、传感器初始调零误差、传感器随机误差和标定误差对圆度测量精度的影响 ,给出了误差传播方程。并讨论了一些消除或减小上述误差的方法。     

一种新型滚动轴承表面形貌测量仪

介绍了一种新型的滚动轴承表面形貌测量仪,它采用一种全新的能越过陡峭表面的二维位移传感器和垂直扫描三维工作台组成一个闭环控制系统,将传统的触针移动扫描方式改变为工作台移动扫描方式。在测量工件时,二维位移传感器的测量杠杆总是不断地回到平衡位置,因此即使增大量程,由杠杆转动所引起的测量非线性误差也非常小。该仪器不仅可进行二维轮廓测量,还可进行三维形貌测量,具有大量程、高精度、小测量力和更多测量参数等特点。