Measurement of form error of a probe tip ball for coordinate measuring machine (CMM) using a rotating reference sphere

This study presents a method of measurement of the form error of the tip ball in the tactile probing systems of a coordinate measuring machine (CMM) by using a rotating reference sphere. The measurement of the form error of the CMM probe tip was conducted without the use of additional external measuring instruments or sensors. The form errors of the probe tip ball and the reference sphere were separated from the probing coordinates of CMM by rotation of the reference sphere. The effectiveness of the proposed method was evaluated based on an uncertainty analysis. The uncertainty in measurement of diameter of the probe tip ball was estimated to be less than 0.5 μm.     

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.     

Precision tracking control of a horizontal arm coordinate measuring machine in the presence of dynamic flexibilities

One of the major sources that affect measurement accuracy and limit the use of high motion speeds in coordinate measuring machines (CMM) is the position error. In fact, static and dynamic probe errors are more direct factors in measuring machine accuracy, but are not the subject of this research. However the accuracy of acquisition of component position errors using a CMM in motion is also of importance, hence the dynamics of a CMM need to be considered. Therefore, this research aims to model the dynamics of a horizontal arm CMM by considering drive flexibility at joints and evaluates the characteristics of the system for fine motion control purposes. Design of a precision tracking controller (PTC) to perform superior tracking for enhancing the measurement accuracy and the probing speed in providing less inspection time at high motion speeds is carried out. A dynamic model for the CMM is developed including drive flexibilities represented with lumped springs at the joints. Due to the non-collocated nature of the control scheme in the flexible CMM dynamics, a non-minimum phase system is observed in the proposed CMM model. Using the derived CMM model with joint flexibilities, tracking motion control simulations are conducted at different probing speeds for the cases where a PI controller and a feedback PTC are employed. A comparison of the PI controller with the feedback PTC is also performed. Results demonstrate that the effects of joint flexibilities on the contour error and probing speeds are significant and the PI controller is not capable of providing good accuracy during challenging tasks such as corner tracking. However, the simulation results indicated that by using the proposed feedback precision tracking controller, contour errors in corner tracking that are caused by joint flexibilities can be reduced effectively .     

Influence of linear-axis error motions on simultaneous three-axis controlled motion accuracy defined in ISO 10791-6

Five-axis machine tools, which combine three linear axes and two rotary axes, are required for accuracy in machining complex shapes. In this paper, to clarify the influence of simultaneous three-axis control motion measurements as specified in ISO 10791-6, the measured results using a ball bar and R-test are compared. As the motion trajectories of the linear axes are not identical in both measurement devices, it is expected that the error motions of the linear axes cause different measurement results depending on the measurement devices. Thus, the squareness errors between the linear axes and the error motions of the linear axes are assumed as error factors that influence the measured results in this study. A mathematical model of a five-axis control machine tool that considers the error motions and squareness errors of the linear axis is constructed, and the influence of those error factors on motion accuracy is examined using an experiment and a simulation. As a result, the squareness errors and error motions of the linear axis are observed to greatly affect simultaneous three-axis controlled motion accuracy.     

Development of nanopositioning mechanism with real-time compensation algorithm to improve the positional accuracy of a linear stage

A compensation mechanism with six degrees of freedom (DOF) was developed to enable precise control of a linear stage. Geometric, thermally induced, and dynamic errors in the linear stage were compensated for in real time by the nanopositioning stage. A stage-based hinge with high structural stiffness and rapid response characteristics was modified for parallel operation. The stage’s full range of motion was measured and kinematics was used to calculate the displacement required by each actuator to compensate for the errors. Except for the displacement error of the linear stage, the contribution of each error source was measured by a reference mirror and five capacitive sensors. A compensation algorithm, based on a recursive method, was used to improve the positioning accuracy of the system. The performance of the stage presented here was investigated by measuring, and compensating for, the five-DOF linear stage errors in real time. In practice, the peak-to-valley errors of the translational and rotational errors were reduced by 89% and 93%, respectively.     

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.     

激光测量几何误差补偿算法

激光技术作为重要的测量手段,已经被广泛的应用到精密运动控制系统中。激光测量误差直接影响到运动控制系统的控制精度,其中阿贝与余弦误差等几何误差对激光测量精度影响显著,在精密运动控制中必须予以补偿与校正。以精密运动台多维激光测量模型为基础,介绍了阿贝与余弦误差产生原因。在不考虑激光干涉仪的加工和安装误差的情况下,推导了运动台存在倾斜角度下的阿贝与余弦误差计算模型,在此基础上给出了激光测量数据误差补偿模型,以实现测量数据的实时补偿与修正。算法已经成功应用在实例中,表明该算法的有效性与可靠性。     

A 6-degree-of-freedom measurement system for the accuracy of X-Y stages

A precision 6-degree-of-freedom measurement system has been developed for simultaneous on-line measurements of six motion errors of an X-Y stage. The system employs four laser Doppler scales and two quadrant photo detectors to detect the positions and the rotations of an optical reflection device mounted on the top of the X-Y stage. Compared to the HP5528A system, the linear positioning accuracy of the developed measurement system is better than ±0.1 μm to the range of 200 mm and the vertical straightness error is within ±1.5 μm for the measuring range of ±0.1 mm. The yaw and pitch errors are about ±1 arcsec, and the roll error is about ±3 arcsec within the range of ±50 arcsec.     

Development of a three-degree-of-freedom laser linear encoder for error measurement of a high precision stage

In this study, a laser linear encoder with three degrees of freedom (3-DOFs) based on diffraction and interference was developed to measure the linear displacement and two angular errors of a linear moving stage. Parts of the linear motion errors induced from the two angular errors can be calculated by this prototype 3-DOF laser encoder. It was an effective method for online error calculation and compensation to improve precision stage performance. This new function was superior to other laser encoders. The verification results showed that the resolution is 20 nm. It detected displacements relative to an external grating scale with accuracy of about +/-150 nm for a measuring range of +/-1 mm, and detected the angular errors with related accuracy of about +/-1 arc sec for a measuring range of +/-100 arc sec.     

几何误差和倾覆力矩对双螺母滚珠丝杠副载荷分布的影响#br#

建立了一种考虑几何误差（滚珠尺寸误差、丝杠导程误差和滚道齿形误差）和倾覆力矩的双螺母滚珠丝杠副载荷分布模型;通过试验测得4010型滚珠丝杠副的力与位移变形曲线,验证了理论模型的正确性;通过仿真分析研究了轴向外载荷、几何误差和倾覆力矩对双螺母滚珠丝杠副载荷分布的影响。研究结果表明：轴向外载荷一定时,倾覆力矩会导致双螺母滚珠丝杠副的载荷分布迅速变差;滚珠尺寸误差和滚道齿形误差会使双螺母滚珠丝杠副中滚珠的受载显著增大或减小;由于丝杠轴向误差累计的作用,导程误差会使双螺母滚珠丝杠副中一侧螺母受载增大,另一侧螺母受载减小;在误差大小一定的情况下,导程误差对载荷分布的影响程度大于尺寸误差和齿形误差,即双螺母滚珠丝杠副的载荷分布对导程误差的敏感度更高。     

A low cost, high accuracy roundness measuring system

This work presents a new architecture of a roundness measuring system in which the roundness measuring accuracy is not dependent on motion accuracy of the rotary element. In this architecture, the influence of motion errors on roundness measurement is minimized by applying a new error separation technique developed by Horikawa et. al. [1 and 2], the improved Reversal Method — IRM. A prototype that uses: a rotary table supported by ball bearings, non-contact gap sensors and a computer system that collects and process sensor readings has been developed. Experimental results have shown that even using a rotary table supported by ball bearings, that has non-repetitive motion errors larger than 2μm, the final measurement repeatability is better than 0.3μm of peak-to-peak value. In order to ensure the same levels of accuracy of the proposed system, a traditional roundness measuring system design must use a more precise and therefore more expensive type of bearing with a motion error no larger than 0.1μm.     

Laser interferometric system for six-axis motion measurement

This article presents the development of a precision laser interferometric system, which is designed to achieve six-axis motion measurement for real-time applications. By combining the advantage of the interferometer with a retroreflector and that of the interferometer with a plane mirror reflector, the system is capable of simultaneously measuring large transverse motions along and large rotational motions about three orthogonal axes. Based on optical path analysis along with the designed kinematics of the system, a closed form relationship between the six-axis motion parameters of the object being measured and the readings of the six laser interferometers is established. It can be employed as a real-time motion sensor for various six-axis motion control stages. A prototype is implemented and integrated with a six-axis magnetic levitation stage to illustrate its resolution and measurement range.     

精密滚珠丝杠副丝杠滚道磨损异常的原因分析

实践中发现,精密滚珠丝杠副丝杠轴滚道的磨损明显大于螺母滚道,本文从弹性接触和润滑状态两方面分析了产生这一现象的原因。研究表明,滚珠与丝杠轴滚道的接触应力高于滚珠与螺母滚道的接触应力,而滚珠与螺母滚道接触面的润滑状态优于滚珠与丝杠轴滚道接触面。该研究结果为滚珠丝杠副的合理设计和适当润滑提供了理论依据。     

Active Profiling and Polishing Model and Validation Based on Rotor Spiral Groove

When a spiral groove is formed using superplastic molding, precision casting, additive manufacturing, or other non?mechanical processing technology, it is diffcult to meet the molding precision required for direct use, and the surface quality and accuracy of the shape need to be improved through a finishing process. In view of the poor reachability of the current tool?based polishing process, a tool?less polishing method using free?abrasive grains for complex spiral grooves is proposed. With this method, by controlling the movement of the workpiece, the design basis and relative motion of the abrasive particles along a helical path remain consistent, resulting in a better polishing profile. A spiral groove of a revolving body is taken as the research object; the influence of the installation method and the position of the parts, as well as the effect of the rotational speed of the abrasive ball on its relative motion along a helical trajectory, are studied, and the polishing cutting process of an abrasive ball is reasonably simplified. A consistent math?ematical model of the trajectory of an abrasive ball relative to the design helix is constructed. The grooved drum parts are verified through a polishing experiment. The spiral groove of the revolving body is modified and polished. Experiments show that the process not only corrects the shape a spiral groove error, but also reduces the surface roughness of a spiral groove. This study provides a theoretical basis for achieving free?abrasive, tool?free polishing.     

滚动轴承弹性接触动态特性有限元分析

滚动轴承弹性滚动接触动态特性直接影响转子系统的精度及动态特性,针对滚动轴承弹性滚动接触动态特性问题,以深沟球轴承61914为例,在同时考虑内环、外环、滚珠及保持架变形的情况下,建立滚动轴承三维弹性滚动接触有限元模型,采用有限单元法计算滚动轴承在不同转速、径向力及轴向力等载荷工况下滚动轴承的接触应力及滚珠与内环的运动状态。结果表明,有限单元法能在满足高精度计算的情况下求解各种复杂工况下的滚动轴承动力学特性,为进一步研究滚动轴承弹性滚动接触动态特性提供有力的研究方法。     

在机测量激光测头位姿的线性标定

针对在机激光扫描测量中激光测头安装位置和姿态引起的测量误差,提出了一种适用于在机激光测量的测头标定方法。构造了在机激光扫描测量原型系统,建立了激光测头随机床运动的测量模型;通过多角度扫描标准球球面拟合球心,给出了一种线性求解测头安装位姿参数的算法,避免了非线性优化求解中的大量计算和不稳定问题。分析了测量过程中机床各个轴的运动误差对测量结果的影响,建立了误差模型,并给出补偿机床系统误差的方法。实验显示,对直径已知的标准球进行测量时,测头在不同摆角测得的标准球直径误差小于0.05 mm,误差补偿后球心位置误差减小了83%。实验结果验证了该标定方法的可行性,以及机床误差对测量精度影响的模型及补偿方法的正确性。     

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.     

In-plane vibration analysis of cantilevered circular arc beams undergoing rotational motion

Equations of motion of cantilevered circular arc beams undergoing rotational motion are derived based on a dynamic modeling method developed in this paper. Kane’s method is employed to derive the equations of motion. Different from the classical linear modeling method which employs two cylindrical deformation variables, the present modeling method employs a non-cylindrical variable along with a cylindrical variable to describe the elastic deformation. The derived equations (governing the stretching and the bending motions) are coupled but linear, so they can be directly used for vibration analysis. The coupling effect between the stretching and the bending motions, which could not be considered in the conventional modeling method, is considered in this modeling method. The effects of rotational speed, arc angle, and hub radius ratio on the natural frequencies of the rotating circular arc beam are investigated through numerical analysis.     

三面静压转台回转精度干涉测量与误差处理

介绍了激光干涉法测三面静压转台回转精度的原理及测量方法,分析了激光干涉仪在回转轴运动位置精度测量中的主要误差诱因;作出了角度测量中正弦近似误差特性曲线,并建立了该测量误差的数学模型,为机床的运动精度误差补偿提供了数据。经现场检验,该方案简便易行,成效显著。     

三坐标测量机动态误差的建模方法

为了提高三坐标测量机的测量速度,缩短测量周期,分析了影响给定的三坐标测量机动态误差的因素。对三坐标测量机的具体和了分析,用电感测微仪进行了动态偏转角的测量,并推导出由动态偏转误差得到测头处的动态位移误差的方法。同时,对由导轨的直线度造成的误差进行了讨论。指出动态误差主要是由各构件绕气浮导轨连接处的偏转和各运动构件本身的弯曲变形造成挫理论上可以证明,在气浮导轨力矩刚度和横梁弯曲刚度已知的情况下,只要