Misalignment Angle Calculation Accuracy Analysis of Three-Axis Stabilized Geostationary Satellite

The most challenging problem of navigation in three-axis stabilized geostationary satellite is accurate calculation of misalignment angles, deduced by orbit measurement error, attitude measurement error, thermal elastic deformation, time synchronization error, and so on. Before the satellite is launched, the misalignment model must be established and validated. But there were no observation data, which is a non-negligible risk of yielding the greatest returns on investment. On the basis of misalignment modeling using landmarks and stars, which is not available between different organizations and is developed by ourselves, experimental data are constructed to validate the navigation processing flow as well as misalignment calculation accuracy. In the condition of using landmarks, the maximum misalignment calculation errors of roll, pitch, and yaw axis are 2, 2, and 104 micro radians, respectively, without considering the accuracy of image edge detection. While in the condition of using stars, the maximum errors of roll, pitch, and yaw axis are 1, 1, and 3 micro radians, respectively, without considering the accuracy of star center extraction. Results are rather encouraging, which pave the way for high-accuracy image navigation of three-axis stabilized geostationary satellite. The misalignment modeling as well as calculation method has been used in the new generation of geostationary meteorological satellite in China, FY-4 series, the first satellite of which was launched at the end of 2016.

Modification Design Method for an Enveloping Hourglass Worm Gear with Consideration of Machining and Misalignment Errors

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG).However,a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported.The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing.Also,the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling.The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile.A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact.The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors.This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

Identification of Kinematic Errors of Five-axis Machine Tool Trunnion Axis from Finished Test Piece

Compared with the traditional non-cutting measurement,machining tests can more accurately reflect the kinematic errors of five-axis machine tools in the actual machining process for the users.However,measurement and calculation of the machining tests in the literature are quite difficult and time-consuming.A new method of the machining tests for the trunnion axis of five-axis machine tool is proposed.Firstly,a simple mathematical model of the cradle-type five-axis machine tool was established by optimizing the coordinate system settings based on robot kinematics.Then,the machining tests based on error-sensitive directions were proposed to identify the kinematic errors of the trunnion axis of cradle-type five-axis machine tool.By adopting the error-sensitive vectors in the matrix calculation,the functional relationship equations between the machining errors of the test piece in the error-sensitive directions and the kinematic errors of C-axis and A-axis of five-axis machine tool rotary table was established based on the model of the kinematic errors.According to our previous work,the kinematic errors of C-axis can be treated as the known quantities,and the kinematic errors of A-axis can be obtained from the equations.This method was tested in Mikron UCP600 vertical machining center.The machining errors in the error-sensitive directions can be obtained by CMM inspection from the finished test piece to identify the kinematic errors of five-axis machine tool trunnion axis.Experimental results demonstrated that the proposed method can reduce the complexity,cost,and the time consumed substantially,and has a wider applicability.This paper proposes a new method of the machining tests for the trunnion axis of five-axis machine tool.

MODELING AND COMPENSATION TECHNIQUE FOR THE GEOMETRIC ERRORS OF FIVE-AXIS CNC MACHINE TOOLS

One of the important trends in precision machining is the development ofreal-time error compensation technique. The error compensation for multi-axis CNC machine tools isvery difficult and attractive. The modeling for the geometric error of five-axis CNC machine toolsbased on multi-body systems is proposed. And the key technique of the compensation―identifyinggeometric error parameters―is developed. The simulation of cutting workpiece to verify the modelingbased on the multi-body systems is also considered.

Spindle Thermal Error Optimization Modeling of a Five-axis Machine Tool

Aiming at the problem of low machining accu- racy and uncontrollable thermal errors of NC machine tools, spindle thermal error measurement, modeling and compensation of a two turntable five-axis machine tool are researched. Measurement experiment of heat sources and thermal errors are carried out, and GRA（grey relational analysis） method is introduced into the selection of tem- perature variables used for thermal error modeling. In order to analyze the influence of different heat sources on spindle thermal errors, an ANN （artificial neural network） model is presented, and ABC（artificial bee colony） algorithm is introduced to train the link weights of ANN, a new ABC- NN（Artificial bee colony-based neural network） modeling method is proposed and used in the prediction of spindle thermal errors. In order to test the prediction performance of ABC-NN model, an experiment system is developed, the prediction results of LSR （least squares regression）, ANN and ABC-NN are compared with the measurement results of spindle thermal errors. Experiment results show that the prediction accuracy of ABC-NN model is higher than LSR and ANN, and the residual error is smaller than 3 pm, the new modeling method is feasible. The proposed research provides instruction to compensate thermal errors and improve machining accuracy of NC machine tools.

MOTION ERROR ESTIMATION OF 5-AXIS MACHINING CENTER USING DBB METHOD

In order to estimate the motion errors of 5-axis machine center, the double ball bar （DBB） method is adopted to realize the diagnosis procedure. The motion error sources of rotary axes in 5-axis machining center comprise of the alignment error of rotary axes and the angular error due to various factors, e.g. the inclination of rotary axes. From sensitive viewpoints, each motion error is possible to have a particular sensitive direction in which deviation of DBB error trace arises from only some specific error sources. The model of the DBB error trace is established according to the spatial geometry theory. Accordingly, the sensitive direction of each motion error source is made clear through numerical simulation, which is used as the reference patterns for rotational error estimation. The estimation method is proposed to easily estimate the motion error sources of rotary axes in quantitative manner. To verify the proposed DBB method for rotational error estimation, the experimental tests are carried out on a 5-axis machining center M-400 （MORISEIKI）. The effect of the mismatch of the DBB is also studied to guarantee the estimation accuracy. From the experimental data, it is noted that the proposed estimation method for 5-axis machining center is feasible and effective.

Laser Interferometer Based Measurement for Positioning Error Compensation in Cartesian Multi-Axis Systems

Accuracy is one of the most important key indices to evaluate multi-axis systems’ (MAS’s) characteristics and performances. The accuracy of MAS’s such as machine tools, measuring machines and robots is adversely affected by various error sources, including geometric imperfections, thermal deformations, load effects, and dynamic disturbances. The increasing demand for higher dimensional accuracy in various industrial applications has created the need to develop cost-effective methods for enhancing the overall performance of these mechanisms. Improving the accuracy of a MAS by upgrading the physical structure would lead to an exponential increase in manufacturing costs without totally eliminating geometrical deviations and thermal deformations of MAS components. Hence, the idea of reducing MAS’s error by a software-based alternative approach to provide real-time prediction and correction of geometric and thermally induced errors is considered a strategic step toward achieving the full potential of the MAS. This paper presents a structured approach designed to improve the accuracy of Cartesian MAS’s through software error compensation. Four steps are required to develop and implement this approach: (i) measurement of error components using a multidimensional laser interferometer system, (ii) tridimensional volumetric error mapping using rigid body kinematics, (iii) volumetric error prediction via an artificial neural network model, and finally (iv) implementation of the on-line error compensation. An illustrative example using a bridge type coordinate measuring machine is presented.

Research on Contour Error Based on CNC Multi-axis Motion Control System

The contour error was analyzed based on CNC multi-axis motion control, the contour error model was obtained focused on beeline and different radius of curvature and common contour of curve, for a CNC biaxial motion control system and the mechanism of producing contour error and the relationship between tracking error and contour error were presented. The theoretical and practical significance of modeling error and controlling error in motion control systems was carried out.

ACCURATE MEASUREMENT OF ROTARY MACHINE AXIS CENTER TRACE

Four methods aiming at measuring rotary machine axis center trace arediscussed in detail. The comparative analysis is made on some aspects such as measurement accuracy,on-machine characteristics, feasibility, practical operation convenience and the integrity ofmeasurement information. In order to simplify measurement, the axis profile error is ignored intraditional condition, while the measurement accuracy will be reduced. The 3-point method that theaxis profile error is firstly separated has better real time character, at the same time, not onlythe axis motion error but also the axis profile error can be measured. All of those information canbe used to diagnose the fault origin. The analysis result is proved to be correct by the experiment.

Axis intersection measurement of three-axis turntable with two crosshair targets

In order to measure three-axis intersection error, two crosshair targets were fixed in the inner axis frame of a three-axis turntable. Also a theodolite was used to point its telescope to the targets and to measure the horizontal angles when three axes were on equi-spaced angle positions. The calculation equations of the axis intersection were deduced from the mounting position of the theodolite, positions of two targets, angular positions of three axes, and the measured horizontal angles with the theodolite. Finally, a practical measurement is carried out on a horizontal three-axis turntable and error analysis is conducted.

Study on Initial Alignment Under Large Misalignment Angle

Misalignment angle error model describing the SINS mathematical platform error is presented in this paper following the idea of small misalignment angle error model and large azimuth misalignment angle error model.It can be considered that the three misalignment angles are independent of the rotational sequence in the misalignment error model,but not suitable in the large misalignment error model.The error angle of Euler platform is used to represent the three misalignment angles from theoretical navigation coordinate system to computational navigation coordinate system.The Euler platform error angle is utilized to represent the mathematical platform error and its physical meaning is very clear.The SINS nonlinear error model is deduced by using the error angle of Euler platform and is simplified under the condition of large azimuth error and small error.The simplified results are more comprehensive and accurate than the large azimuth misalignment error model.The damping SINS algorithm and its error model are proposed to change the structure of the strapdown inertial navigation algorithm by using the external damping information.The accuracy of SINS error model of large Euler platform error angle is simulated,and has strong practicability in initial alignment and is conducive to reducing the amount of calculation.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

新型旋转激光扫描系统轴系调整与误差标定

旋转激光扫描系统是一种基于精密转台结合多路激光的空间多目标并行角度传感系统。为改善系统光源性能,设计了一种采用光纤从外部导入光源的新型轴系结构。但是当激光以一定角度穿过中空的转轴进入镜组后,若倾斜入射柱镜,将导致出射的扫描光面型发生变化。针对此问题,研究了一种基于平行线的传递性的激光光轴姿态的调整方法,并借助激光跟踪仪测量平台,分别对光轴与转轴轴系进行拟合,建立了对光轴倾斜误差的标定方法。实验结果表明,调整后光轴与转轴轴线的空间夹角优于0.15°,完全满足扫描光截面中心直线度对激光入射柱镜的角度要求。该调整方案可用于系统的装配环节,使扫描光更加接近理想平面,有助于系统测量精度的提升。

精密镗床旋转轴几何误差完备性测量与辨识

针对四轴卧式镗床旋转轴需测几何误差的数目不统一与完备性缺失的问题,提出了基于形状创成函数的四轴卧式镗床旋转轴PIGEs形成机理分析方法与旋转轴完备几何误差测量辨识方法。基于形状创成机理构建了卧式镗床几何误差创成函数,确定了旋转轴可通过误差补偿进行调整的最少与位置无关的几何误差(Position-independent geometric error, PIGEs)数目。建立了卧式镗床旋转轴4项PIGEs、6项与位置有关的几何误差(Position-dependent geometric error, PDGEs)、6项安装误差(Setup error, SEs)与球杆仪(Double ball bar, DBB)测量轨迹半径之间的完备性函数模型,设计了基于DBB的四轴联动Viviani曲线测量轨迹,构建了旋转轴6项PDGEs的NURBS表征与PIGEs、SEs辨识方法。开展了误差补偿对比实验验证,结果表明,利用几何误差完备性测量与辨识结果进行误差补偿,较仅单一补偿6项PDGEs可提升圆轨迹测量精度40.69%。

五轴数控机床旋转轴综合误差测量与辨识

针对五轴数控机床旋转轴的运动误差和几何误差的综合评估问题,在不考虑直线轴运动误差影响的情况下,提出了一种采用R-test测量仪的测量及其辨识方法。首先,测量过程按照参考球的两种不同高度设置进行,仅移动旋转轴,而不移动直线轴。其次,利用R-test测量仪对旋转轴的运动精度进行了测量。此外,假设旋转轴位置几何误差和工作台上参考球的设置误差是影响测量结果的因素,并通过最小二乘法对这些因素进行分离。采用IBS公司的R-test测量仪,对米克朗公司UCP800Duro立式五轴加工中心C轴的运动误差和几何误差进行了测量实验。研究结果表明,该方法能够正确识别旋转轴的运动误差和几何误差,可以有效地综合评估旋转轴的运动精度,并有助于进一步提高旋转工作台的精度。

数控机床旋转轴多自由度静/热误差同步测量与建模

针对现有的数控机床旋转轴误差测量与建模方法仅考虑多自由度静态几何误差或单自由度热误差单独作用的影响,未考虑几何误差和热误差耦合影响的问题,提出了一种基于球杆仪的数控机床旋转轴多自由度静/热误差同步测量与建模方法。首先基于齐次坐标变换建立球杆仪杆长变化模型,再基于该模型使用非齐次线性方程组建立静/热误差辨识模型;其次设计了适应多自由度静/热误差同步测量的球杆仪安装模式以缩短测量时间,减少热逸散对测量结果的影响;再次基于卷积长短期记忆神经网络(CNN-LSTM)建立旋转轴多自由度静/热误差预测模型;最后在数控蜗杆砂轮磨齿机的C轴上进行误差测量实验,对多种转速下的旋转轴多自由度误差进行快速辨识,并通过CNN-LSTM静/热误差预测模型对多自由度误差和球杆仪杆长变化进行预测,以验证所建模型的准确性。

高精度五轴龙门数控加工中心综合误差建模与辨识

针对五轴数控机床在加工过程产生的多类别融合误差影响着机床加工精度的问题,提出一种基于误差耦合的综合误差模型建立方法。从误差源的角度出发,分析影响机床加工精度的主要因素,探究不同误差对机床加工精度的影响。在此基础上建立了目标机床的拓扑结构和低序体阵列,从而完成了基于多体系统理论的理想状态和实际状态下的综合误差齐次坐标变换矩阵的推导,由此建立起目标机床的综合误差模型,并给出了综合误差模型正确性的验证。提出了一种先插值后拟合方法对五轴数控机床误差进行拟合。实验结果表明,该方法可有效地处理误差波动较大的数据,相较而言,拟合偏差降低了3.04%,提高了五轴数控机床综合误差模型精度。

基于多项式混沌的机床几何误差灵敏度分析

为解决目前灵敏度分析方法普遍存在的样本需求量大且计算效率不高的问题,提出了一种基于多项式混沌展开的全局灵敏度分析方法。首先,以AC型双转台五轴数控机床为研究对象,根据旋量理论建立了完备的空间误差模型。其次,构建了机床几何误差的多项式混沌展开模型,采用正交匹配追踪实现模型的稀疏化,并给出了基于该方法的Sobol灵敏度指数。进而,对五轴数控机床几何误差进行了实例分析,测量并统计出41项误差的近似概率分布,分析了影响各方向位姿误差分量的关键几何误差。通过与蒙特卡洛法和拉丁超立方法进行对比,多项式混沌展开方法的正确性得到验证,且在不降低计算精度的前提下,样本量从1×10^(5)降低到1×10^(3),计算时间分别减少96.8%和98.1%,计算效率显著提高。

数控机床几何误差单轴五次测量与辨识方法

针对数控机床几何误差项的准确测量与辨识问题,提出了一种基于激光干涉仪的机床空间几何误差单轴五次测量与辨识方法。首先,针对X、Y、Z轴分别设置了一条测量线,测量了3条划定线上除滚转误差外的其他15项几何误差,共计15次测量;然后,分析了转角误差对直线度误差以及直线度误差对定位误差的耦合影响,并建立了误差辨识方程组;最后,根据误差辨识方程组,得到了机床21项几何误差;并进行了单轴五次测量法的测量和辨识实验,并将所得结果与空间九线法测量辨识结果进行了对比分析。研究结果表明:单轴五次测量法与空间九线法测量辨识结果的空间误差向量最大偏差为1.93μm,平均偏差为0.58μm,该结果验证了单轴五次测量法是准确和有效的。该方法考虑了实际测量过程中的误差耦合情况,因此相比于空间九线法,该方法减少了测量线数与测量次数,简化了误差项的求解过程;同时,采用单轴运动方式可以有效避免其他轴对当前运动轴误差的影响。

双转台五轴数控机床旋转轴位置无关几何误差辨识

针对双转台五轴数控机床旋转轴几何误差辨识精度问题,提出一种在机床坐标系下的旋转轴位置无关几何误差(PIGEs)辨识模型。建立了刀具球与工件球在机床坐标系下的实际初始坐标,通过逆矩阵得到工件球在所测轴的实际初始位置,基于4种测量模式建立了包含球杆仪安装误差与旋转轴PIGEs的杆长变化量数学模型。仿真分析了PIGEs对测量模式的影响,结果表明刀具球在两旋转轴轴线交点位置时,平行度误差不影响球杆仪杆长变化量。最后,通过实验辨识出旋转轴8项PIGEs,并对旋转轴PIGEs的4项位置误差进行补偿。实验结果表明,补偿后的位置误差最大绝对值由203.5μm减小至5.1μm,所提出的辨识模型可以有效提高五轴机床精度。