一种新型三自由度虚轴坐标测量机机构的误差建模与仿真

设计了一种新型三自由度虚轴坐标测量机机构,给出了其运动学正解模型,依据全微分理论,导出测头位置误差与结构参数误差及3个并联驱动杆长度误差之间的相互关系,从而建立起这种新型并联机构的误差模型;然后利用计算机仿真方法,验证了误差模型的准确性,分析了3个并联驱动杆长度变化以及结构参数误差变化对测头位置误差的影响,为该虚轴坐标测量机机构的加工制造及其误差补偿奠定了理论基础,该并联机构还可用于运动模拟器、并联机床等其它并联运动装备.     

An integrated error compensation method based on on-machine measurement for thin web parts machining

Thin webs are widely used in the aerospace industry for the advantages of compact structure, light weight and high strength-to-weight ratio. Due to its low rigidity, serious machining error may occur, therefore, Finite Element method and mechanism analysis are usually utilized to modeling its deformation. However, they are very time-consuming and only suitable for elastic deformation error. In this study, an integrated error compensation method is proposed based on on-machine measurement (OMM) inspection and error compensation. The OMM inspection is firstly applied to measure the comprehensive machining errors. The Hampel filtering is then used to eliminate outliers, followed by the triangulation-based cubic interpolation as well as a machine learning algorithm which are used to establish the compensation model. At last, the real time compensation of high-density cutting points is realized by developing the compensation system based on External Machine Zero Point Shift (EMZPS) function of machine tool. Three sets of machining experiment of a typical thin web part are conducted to validate the feasibility and efficiency of the proposed method. Experiment results revealed that after compensation, the comprehensive machining errors were controlled under different machining conditions and 58.1%, 68.4% and 62.6% of the machining error ranges were decreased, respectively. This method demonstrates immense potential for further applications in efficiency and accuracy improvement of thin-walled surface parts.     

Error budget and uncertainty analysis of portable machines by mixed experimental and virtual techniques

This paper analyzes the error sources of portable machines, which can move along large parts to perform machining operations and defines a mixed virtual-experimental model to quantify such errors. The method combines three different aspects of particular relevance in portable machines: a process force and machine stiffness model, a geometric error model and a machine and work piece inter-referencing error model. The combination of these models helps to control and define the effects of different errors in the virtual mobile machine, before a real prototype is built. An application to a particular portable machine is presented where error values are either simulated or experimentally obtained from a conventional three-axis milling machine where typical strategies of mobile machines are implemented and tested. The research shows that portable machines can be a solution for automatic and unattended machining operations with accuracy requirements below 0.1 mm.     

航空平显火控系统误差分析

讨论了航空平显火控系统的原理误差、测量参数误差和显示器误差,分析了原理误差在建立瞄准数学模型中产生的原因,测量误差在火控计算中所使用的参数通过传感器测量而造成的问题,以及显示误差和其他误差带来设备误差等的形成及结果,并对数学模型的简化引起的误差、显示器误差、瞄准误差和系统误差等几个主要误差提出了解决方法及补偿措施。     

全方位装配机器人的刚度误差分析

为了提高工作效率并节约劳动力,设计了一种可执行装配任务的全方位装配机器人,此机器人能在实际工程中执行一些简单的装配任务。为提高机器人在执行装配作业任务时的装配精度,对其刚度误差进行分析。根据机器人的结构特点并结合旋量理论对并联机构各支链进行建模,推导出机器人的刚度模型。通过仿真分析得出了支链长度以及载荷对系统刚度的理论影响。结合实验测试对刚度矩阵进行修正,得出不同姿态下系统刚度引起的误差。详细分析误差的产生的原因,提出了减小误差的改进方案。     

Elasto-geometrical error modeling and compensation of a five-axis parallel machining robot

Parallel manipulators have the potentials of high efficiency and high precision in the field of machining and manufacturing. However, accuracy improvement of the parallel manipulator is still an essential and challenging issue, encountering two important problems. Firstly, the ignorance of elastic deformation caused by gravity or deviations of static stiffness model restricts further improvement of accuracy. To solve this problem, an elasto-geometrical error modeling method is proposed. The comprehensive effects of structural errors, elastic deformation under gravity and compliance parameter errors on pose deviations are disclosed. On this basis, the identification equation of actual structural errors and compliance parameter errors can be established. Secondly, the ill-conditioned identification matrix and the identification equation with anisotropic residual error can lead to inaccurate identification results. To solve this problem, a weighted regularization method is proposed. The identification equation with isotropic residual error is built, and accurate identification can be realized with the regularization method. Based on the proposed methods, the error compensation experiment is conducted on the prototype of a five-axis parallel machining robot using a laser tracker. Experiment results show that the accuracy of the machining robot is significantly improved after compensation. An M1_160 test piece and an S-shaped test piece are machined and measured to further validate the effectiveness of the proposed methods. The elasto-geometrical error modeling method and the weighted regularization method can be applied to other parallel manipulators’ accuracy improvement.     

Error modeling and sensitivity analysis of a hybrid-driven based cable parallel manipulator

This paper deals with the error modeling and sensitivity analysis of a hybrid-driven based cable parallel manipulator (HDCPM). The HDCPM has the advantages of both cable parallel manipulator and hybrid-driven planar five-bar mechanism. Kinematics analysis and error modeling are performed based on closed loop vector conditions and direct differential method. The error model derived for the proposed HDCPM has the ability to account for the original errors from kinematics parameters. In addition, the sensitivity analysis is also carried out to investigate the effects of 36 error sources of kinematics parameters on the end-effector of the HDCPM. A detailed example of the sensitivity of the end-effector's position coordinates for the HDCPM is presented in order to demonstrate the validity of the error modeling and sensitivity analysis developed.     

并联运动模拟台几何误差的正交特性

分析了一台冗余电机驱动的新型六维正交并联运动模拟台,根据其位置反解的数学模型,导出了末端平台的位姿误差与机构各运动部件几何参数误差之间的函数关系,并基于模拟台的位置正解验证了误差模型的正确性.最后,以误差模型为基础,分析了运动模拟台六条支链几何误差的正交特性,为运动学标定和误差补偿提供了理论依据.     

Accuracy modeling,analysis and radical error distribution of 3-RPR planar parallel mechanism

Output accuracy performance is directly determined by geometric errors and working poses of a mechanism. Accuracy sensitivity as geometric error transmission coefficient, closely relates to pose configuration and geometric parameters. This research focuses on accuracy of a 3-RPR planar parallel mechanism: firstly, established 3 models in an analytic form, to describe relationship between output errors and geometric ones, then they are mutually verified statistically. Secondly, the anisotropy and periodic fluctuation of position errors, independently contributed by each category of geometric errors, are illustrated; and mirror symmetric trajectories and poses generating output errors with mirror symmetry, are also revealed by numerical simulation. Finally, the radical accuracy model in an analytic form, was established through variance and covariance analysis on output errors. We concluded that the radical error of the movable platform in central symmetric poses, follows Rayleigh distribution pattern. Through statistical comparison with Monte Carlo simulation, the radical error model was demonstrated, that provided a reference for accuracy design for other planar parallel mechanism.

     

3SPS+1PS并联仿生试验机误差建模与仿真

3SPS+1PS并联髋关节仿生试验机能否模拟人工髋关节的理想试验状态是正确评价关节材料特性的关键,因此,对此并联试验机整机误差建模及仿真成为必须。首先运用四元数法对其动平台位姿进行描述,建立了基于矩阵全微分理论的整机误差分析模型。通过计算机仿真,讨论了机构参数对位姿精度的影响,同时计算了单一结构或驱动参数误差变化时,输出位姿的变化趋势。由仿真结果知,输出误差中X轴误差和参数q误差较大,Z轴误差与参数n误差几乎为零。最后,对设计过程中机构参数的合理选取提出建议,为实际误差的补偿与控制提供了一定的理论基础。     

A method for assessing geometrical errors in layered manufacturing. Part 2: Mathematical modelling and numerical evaluation

Layered manufacturing based rapid prototyping processes are subjected to not only a staircase effect owing to the approximating process used, but also an accumulated error transfer between layers. Certain types of error such as surface tilting and layer thickness variations that occur in one layer can transfer to other layers above it. This paper describes a mathematical model based on the physical and geometrical models discussed in Part 1 of the paper. The model uses the matrix transformation method to analyse the effect of transformation of local errors to the multiple layer global errors. A data preparation error transformation matrix is used to describe the error interactions between layers during the data preparation stage. A disturbance error transformation matrix is used to describe the error interaction within each layer and error propagation between layers during the part building process. This model describes geometrical error analysis involving profiling error, layer inclination and layer thickness variations. Numerical evaluation of the model is carried out for a typical benchmark component.     

LOADS INFLUENCE ANALYSIS ON NOVEL HIGH PRECISION FLEXURE PARALLEL POSITIONER

A large workspace flexure parallel positioner system is developed, which can attain sub-micron scale accuracy over cubic centimeter motion range for utilizing novel wide-range flexure hinges instead of the conventional mechanism joints. Flexure hinges eliminate backlash and friction, but on the other hand their deformation caused by initial loads influences the positioning accuracy greatly, so discussions about loads' influence analysis on this flexure parallel positioner is very necessary. The stiffness model of the whole mechanism is presented via stiffness assembly method based on the stiffness model of individual flexure hinge. And the analysis results are validated by the finite element analysis (FEA) simulation and experiment tests, which provide essential data to the practical application of this positioner system.     

Kinematic calibration of gantry hybrid machine tool based on estimation error and local measurement information

This paper presents the kinematic calibration of a four degrees-of-freedom (DOF) hybrid machine tool based on a novel planar 3-DOFs parallel mechanism and a long movement of the worktable. Closed-form solutions are developed for both the inverse and direct kinematics about the parallel mechanism. The error model is built and the mechanism accuracy is investigated. Two types of kinematic calibration method are proposed by a simple measurement device. The first type of calibration method is based on estimation error, and can easy improve the machine tool accuracy quickly by estimating the error trends. The second type of kinematic calibration method is based on local measurement information, which includes the position errors and does not include the pose errors of the machine tool. The calibration tests showed the effectiveness of the calibration methods, which can be useful for the similar types of parallel machine tool.     

铣削加工过程中初始误差对薄壁零件的影响研究

薄壁零件的加工误差产生的机理相对复杂、而影响因素也较多,有效地控制或减小这些因素引起的加工误差对提高薄壁零件加工精度有着重要作用。主要讨论铣削加工过程中初始制造误差对零件综合误差的影响,分析了影响被加工零件的误差源,利用齐次坐标变换原理建立各种初始制造误差的数学模型,将被加工特征离散成点集,通过编译的Matlab程序进行各项误差的计算,得出铣削过程中各项误差对被加工零件的影响,并以实例进行了初始误差对综合误差影响的分析。     

The geometric dynamic errors of CMMs in fast scanning-probing

Quasi-stiffness model is effective for the compensation of the geometric errors of coordinates measuring machines (CMMs) in slow probing, but degrade the error compensation accuracy due to the generation of dynamic errors in fast probing. It is usually regarded that acceleration is the major origin of dynamic errors; and yet the dynamic effects that rise from the quick fluctuation of geometric errors in fast probing had attracted little attentions. This paper presents a model for the dynamic effects of the geometric errors of CMMs in fast probing, and investigates their properties with experiments. The error model is built with recursive least squares (RLS) identification technique by taking probing acceleration and the 6 geometric errors of X slideway for the inputs while the positioning error of probe tip for output. Then the positioning error of probe tip is decomposed into 7 components corresponding to the 7 inputs. Analyses on the experiments show that the angular errors around Y and Z axes, ε_Y(x) and ε_Z(x), can induce remarkable dynamic effects, especially in a CMM with low stiffness air bearing. Error compensation with RLS identification seems feasible theoretically, but it is not recommendable due to the veracity uncertainty of identification. Nevertheless smoothening the sharp corners of the curves of geometric errors, especially ε_Y ∼ x and ε_Z ∼ x, in terms of probing speed and Y coordinates of probe tip is considered as a simple but effective and reliable method to improve the accuracy of CMMs errors compensation in fast probing.     

交流伺服精密驱动系统机电耦合精度分析

对交流伺服精密驱动系统进行动力学分析时,必须考虑系统的机电耦合影响,将伺服精密驱动系统简化成三质量两轴系统．运用传递函数法建立系统模型,提取了伺服系统中精密传动装置的耦合因素,包括传动刚度、传动误差、传动回差,通过对系统的仿真,分析了传动刚度和传动误差对系统精度和振动特性的影响,为进一步优化系统参数提供了依据、利用该建模方法,能够实现多子系统、多能域的机电系统的建模,对其它复杂机电系统同样适用。     

可重构混联机械手--TriVariant的误差建模与灵敏度分析

针对少自由度并联构型装备,必须通过误差建模将影响末端可控和不可控误差的几何误差源进行分离,从而指导机构的精度设计和运动学标定的问题,以5自由度混联机械手TriVariant为对象,研究一种少自由度并联构型装备的误差建模方法。该方法可有效分离出影响末端不可控误差的几何误差源,得到由UP支链连架胡克铰的加工和装配误差,以及套筒导轨扭角误差引起的末端姿态误差为不可控误差,从而得到仅需控制恰约束支链的制造和装配误差,便可有效抑制末端的不可控姿态误差的重要结论。在此基础上,借助灵敏度分析方法,在统计意义下定量揭示出上述几何误差源对末端不可控姿态误差的影响。分析结果表明,胡克铰两轴线不相交误差对末端不可控误差的影响最大。     

Error analysis and auto-calibration for a Cartesian-guided tripod machine tool

This paper focuses on the error analysis and calibration methodologies for a parallel kinematic machine (PKM) called a Cartesian-guided tripod (CGT). The CGT volumetric error due to the geometric error, kinematic parameter error and nonlinear machine stiffness were studied. It is well known that the PKM nonlinear machine stiffness can produce significant volumetric errors from several tens to several hundreds of micrometres depending on the averaged value and deviation range for the machine stiffness. For most PKMs, joint level sensors are used to estimate the virtual Cartesian movements of the cutting tool. The nonlinear stiffness effect is not detected by this indirect metrology method and must be compensated for by a calibration methodology. A solution for the nonlinear stiffness effect implemented on the CGT involves using a passive Cartesian guiding/metrology leg that is independent of the driving legs to directly measure the Cartesian movement of the motion platform. Because the metrology loop of the Cartesian guiding/metrology leg is separated from the kinematic loops of the driving legs, the volumetric accuracy of the CGT is immunised against thermal errors and load deformations on the drive mechanisms. The passive Cartesian guiding/metrology leg is also used for the auto-calibration of the CGT kinematic parameters. The auto-calibration methodology and simulation results were studied and reported.     

NOVEL METHOD FOR ERROR ANALYSIS AND SELF-CALIBRATION OF LASER TRACKING MIRROR MECHANISM

Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the geometric errors of the tracking mirror mechanism. Proper calibration of LTS is essential prior to the use of it for metrology. A kinematics model that describes not only the motion but also the geometric variations of LTS is developed. Through error analysis of the proposed model, it is claimed that gimbals axis misalignments and tracking mirror center off-set are the key contributors to measuring errors of LTS. A self-calibration method is presented of calibrating LTS with planar constraints. Various calibration strategies utilizing single-plane and multiple-plane constraints are proposed for different situations. For each calibration strategy, issues about the error parameter estimation of LTS are exploded to find out in which conditions these parameters can be uniquely estimated. Moreover, these conditions reveal the applicability of the planar constraints to LTS self-calibration. Intensive studies have been made to check validity of the theoretical results. The results show that the measuring accuracy of LTS has increased by 5 times since this technique for calibration is used.     

3-RPS并联机构运动学标定方法的研究

针对六轴混联机床中因3-RPS并联机构结构参数误差引起的精度问题,分析了影响3-RPS并联机构几何精度的误差因素,给出了并联机构的误差模型;基于影响并联机构定平台运动精度较大的几何误差参数;建立了运动学标定模型.采用阻尼最小二乘法,经多次优化迭代实现了利用一组测量数据完成非线性超越矛盾标定方程组的求解.利用激光干涉仪完成了标定用数据的测量,通过3-RPS并联机构运动学逆解和各铰链的几何标定参数,得到动平台的实际位姿.通过对标定前后的Z轴定位精度的检测及实际零件加工试验,验证了3-RPS并联机构运动学标定模型和方法的正确性和有效性.