数控机床动态轨迹误差仿真与优化研究

在介绍数控机床加工轨迹运动控制原理的基础上,对数控机床动态轨迹误差进行了仿真研究,得出数控机床动态轨迹误差与拟加工曲线的曲率和机床进给速度相关的结论。在待加工的工件几何曲线曲率已定情况下,提出了变进给速度的数控机床动态轨迹误差优化策略,仿真结果表明:该控制策略能够有效地减少机床动态轨迹误差量,提高相关轨迹曲线的加工精度。     

Development of a multi-step measuring method for motion accuracy of NC machine tools based on cross grid encoder

Machining accuracy is directly influenced by the quasi-static errors of a machine tool. Since machine errors have a direct effect on both the surface finish and geometric shape of the finished work piece, it is imperative to measure the machine errors and to compensate for them. A revised geometric synthetic error modeling, measurement and identification method of 3-axis machine tool by using a cross grid encoder is proposed in this paper. Firstly a revised synthetic error model of 21 geometric error components of the 3-axis NC machine tools is developed. Also the mapping relationship between the error component and radial motion error of round work piece manufactured on the NC machine tools are deduced. Aiming to overcome the solution singularity shortcoming of traditional error component identification method, a new multi-step identification method of error component by using the cross grid encoder measurement technology is proposed based on the kinematic error model of NC machine tool. Finally the experimental validation of the above modeling and identification method is carried out in the 3-axis CNC vertical machining center Cincinnati 750 Arrow. The entire 21 error components have been successfully measured by the above method. The whole measuring time of 21 error components is cut down to 1–2 h because of easy installation, adjustment, operation and the characteristics of non-contact measurement. It usually takes days of machine down time and needs an experienced operator when using other measuring methods. Result shows that the modeling and the multi-step identification methods are very suitable for ‘on machine’ measurement.     

Virtual prediction and constraint of contour errors induced by cutting force disturbances on multi-axis CNC machine tools

This paper presents a strategy to virtually predict and constrain the contouring errors contributed by cutting force disturbances on feed drives. The tracking errors on each feed drive are predicted as a linear function of tangential feed by evaluating the product of estimated power spectrum of cutting forces and disturbance frequency response function along the tool path in virtual CAM environment. The corresponding tool tip contouring and tool axis orientation errors are estimated and constrained by scaling the feed along the tool path. The algorithm is experimentally illustrated to improve the machining accuracy on a 5 Axis CNC machine tool.     

提高轮廓加工误差联机检测精度的研究

在数控机床或加工中心上采用联机检测轮廓加工误差的方法，不用价格昂贵的坐标测量机，具有简单、省时、经济的特点。文章分析了数控机床或加工中心的直线运动误差对联机检测轮廓加工误差精度的影响，并测量出了加工中心的几何运动误差，提出了消除机床几何运动误差影响，提高轮廓加工误差联机检测精度的方法。实验结果表明，所采用的方法可以明显提高轮廓加工误差联机检测精度。     

Modeling and improvement of dynamic contour errors for five-axis machine tools under synchronous measuring paths

In this paper, a contour error model of the tool center point (TCP) for a five-axis machine tool is proposed to estimate dynamic contour errors on three types of measuring paths. A servo tuning approach to achieve five-axis dynamic matching is utilized to improve contouring performance of the cutting trajectory. The TCP control function is developed to generate measuring trajectories where five axes are controlled simultaneously to keep the TCP at a fixed point. The interpolation method of the rotary axes with S-shape acceleration/deceleration (ACC/DEC) is applied to plan smooth five-axis velocity profiles. The contour error model for five axes is derived by substituting five-axis motion commands into servo dynamics models. The steady state contour error (SSCE) model is demonstrated to illustrate three particular dynamic behaviors: the single-circle with amplitude modulation, double-circle effect and offset behavior. Furthermore, the model is also utilized to investigate the behaviors of dynamic contour errors change in 3D space. The factors that affect dynamic contour errors, including the initial setup position, feedrate and five-axis servo gains, are analyzed. With the developed servo tuning process under the measuring paths (CK1, CK2 and CK4), the contour errors caused by servo mismatch are reduced remarkably. Finally, experiments are conducted on a desktop five-axis engraving machine to verify the proposed methodology can improve dynamic contouring accuracy of the TCP significantly.     

Adaptronical compensation of geometrical machine errors

Static, quasi-static and dynamic displacements influence the accuracy of machine tool results. The low-frequency parts of these displacements can, on the one hand, be traced back to static stresses resulting from gravity as well as process loads and, on the other hand, to geometrical machine errors and the faulty positioning in the working area resulting from this. Dynamic loads, however, are characterised by the distribution of masses and stiffnesses. This paper aims to present an approach to adaptronically compensate for static and quasi-static displacements while, at the same time, showing how a component can fulfill the functions of a sensor and an actuator. In order to achieve this, an intelligent adaptronical strut was designed for which the piezoelectric transducer can fulfill actuated as well as sensoric tasks at the same time. Based on the principle of vibrating strings, a vibrating string is used to induce vibrations which allow for the static, quasi-static and dynamic machine displacements to be recorded using the developed integrated sensors and actuators. A first prototype was integrated into a machine tool to verify the concept. Static and dynamic measurements endorse the functionality of this approach. Machining trial runs show the effectiveness of this approach in a parallel kinematic machine tool with regards to adaptronically compensating for geometrical machine errors.     

基于敏感度分析的机床关键几何误差元素辨识与评定

为了正确识别和判定机床关键几何误差元素对机床精度设计的影响,以PCV-620立式加工中心为研究对象,采用多体系统理论建立机床空间误差模型,从而得到机床几何误差元素与机床精度之间的关联函数。对空间误差模型进行灵敏度分析,获得机床各运动方向的局部灵敏度系数,完成机床关键几何误差元素的初步辨识。以局部灵敏度系数为基础,提出一种与局部灵敏度系数和工作空间中任意位置处的几何误差元素值相关的全局灵敏度系数计算方法,将其作为机床关键几何误差元素的辨识和评定标准,分析得到PCV-620立式加工中心的关键几何误差元素包含3项定位误差、3项垂直度误差和5项直线度误差。     

Single setup estimation of a five-axis machine tool eight link errors by programmed end point constraint and on the fly measurement with Capball sensor

Five-axis machine tools can be programmed to keep a constant nominal tool end point position while exercising all five axes simultaneously. This kinematic capability allows the use of a 3D proximity sensing head mounted at the spindle to track the position changes of a precision steel ball mounted on the machine table effectively measuring the 3D Cartesian volumetric errors of the machine. The new sensing head uses capacitive sensors to gather data on the fly during a synchronized five-axis motion which lasts less than 2 min. Because the measured volumetric errors are strongly affected by the link geometric errors, they can be used to estimate the link errors through an iterative procedure based on an identification Jacobian matrix. The paper presents the new sensor, the identification model and the experimental validation. The approach allows all eight link errors i.e. the three squarenesses of linear axes and the four orientations and center lines offset of the rotary axes to be estimated with the proposed single setup test. The estimation approach is performed on a horizontal five-axis machine tool. Then, using the estimated link errors, the volumetric errors are predicted for axes combinations different from those used for the identification process. The estimated machine model correctly predicts 52–84% of the volumetric errors for the tested trajectories.     

五轴数控机床转动轴与平动轴联动的轮廓误差仿真分析

以主轴头两摆的五轴联动数控机床为研究对象,对转动轴与平动轴联动加工不同空间位置圆弧时的轮廓误差进行了分析。采用D-H(Denavit-Hartenberg)法对按不同圆弧路径加工时各轴的进给指令计算公式进行了推导,并将指令输入到动态仿真工具Simulink构建的进给系统仿真模型中,比较刀具理想位置与实际位置的偏差,从而得到轮廓误差曲线。通过仿真曲线分析了轮廓误差的分布特性,得到了各参数对轮廓误差影响的对应关系,利用这种关系检测机床,达到提高机床性能的目的,同时为机床的调整与维修提供一种便捷手段。     

Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

Pre-compensation of contour errors in five-axis CNC machine tools

This paper presents an analytical prediction and compensation of contouring errors in five-axis machining of splined tool paths. The position commands are first fitted to piecewise quintic splines while respecting velocity, acceleration and jerk continuity at the spline joints. The transfer function of each servo drive is kept linear by compensating the disturbance effect of friction with a feed-forward block. Using the analytically represented five-axis, splined tool path, splined tracking errors and kinematic model of the five-axis machine tool, contouring errors are predicted ahead of axis control loops. The contouring errors are decoupled into three linear and two rotary drives, and the position commands are modified before they are sent to servo drives for execution. The proposed method has been experimentally demonstrated to show significant improvement in the accuracy of contouring five-axis tool paths.     

A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools

Nonlinear and configuration-dependent five-axis kinematics make contouring errors difficult to estimate and control in real time. This paper proposes a generalized method for the on-line estimation and control of five-axis contouring errors. First, a generalized Jacobian function is derived based on screw theory in order to synchronize the motions of linear and rotary drives. The contouring error components contributed by all active drives are estimated through interpolated position commands and the generalized Jacobian function. The estimated axis components of contouring errors are fed back to the position commands of each closed loop servo drive with a proportional gain. The proposed contouring error estimation and control methods are general, and applicable to arbitrary five-axis tool paths and any kinematically admissible five-axis machine tools. The proposed algorithms are verified experimentally on a five-axis machine controlled by a modular research CNC system built in-house. The contouring errors are shown to be reduced by half with the proposed method, which is simple to implement in existing CNC systems.     

A decoupled path-following control algorithm based upon the decomposed trajectory error

This paper proposes a new path-following control algorithm for the machine tool servo systems. The control system first decomposes the contouring error into the normal tracking error and the advancing tangential error. A dynamic decoupling procedure is then applied to the system dynamics. Finally, a dynamic decoupled controller is proposed to compensate the decomposed tangential and the normal tracking errors. The normal control minimizes the perpendicular tracking error while the tangential control maintains a desired feed rate. The proposed method is applied to the control of an experimental x–y table. Experimental results show that the proposed control can achieve good tracking and trajectory following characteristics. The new algorithm also enables the design of a non-overshooting controller along the path. This will result in a no-overcutting process for the machine tool operation.     

立式加工中心关键几何误差判定与量化验证

针对现阶段机床空间误差模型不完整且传统灵敏度分析存在局限性,导致其关键几何误差溯源不准确,以及关键几何误差判定结果难以量化验证的问题,以某立式加工中心为研究对象,提出一种机床关键几何误差判定与量化验证方法。以旋量理论为基础,研究某立式加工中心空间误差建模,以输出机床完整空间误差模型;在此基础上,以基于传统局部灵敏度分析为基础,利用误差贡献度因子判定机床关键几何误差;借助数值模拟实验对判定结果进行量化验证。结果表明：相较于传统灵敏度分析结果,利用误差贡献度因子判定关键几何误差的结果更准确;基于误差贡献度因子的判定结果,不仅能量化几何误差相对机床空间误差的影响程度,同时可为机床部件制造精度设计提供理论参考。     

立式加工中心空间误差验证及补偿

为提高某立式加工中心整机加工精度,借助旋量理论建立完备立式加工中心空间误差模型,在此基础上实现机床空间误差有效补偿.以旋量理论为基础推导并建立机床刀具运动链与工件运动链运动学正解,分析机床21项几何误差原理,在考虑21项几何误差的基础上建立该立式加工中心完备空间误差模型;利用九线法完成各项几何误差辨识;基于旋量运动学正解求解机床运动学逆解后得出运动轴实际运动路径,并通过体对角线实验对比补偿前后的效果.结果表明:所提补偿方法补偿效果显著,验证了机床空间误差模型的准确性,实现了提高机床加工精度的目的.     

机床空间精度预测与NC代码补偿研究

以某立式加工中心为研究载体,提出一种空间精度补偿技术。以旋量理论为基础,在充分考虑机床切削点空间位置的基础上,建立包含全部几何误差的立式加工中心空间精度模型,同时输出空间精度显示预测模型。针对传统空间精度补偿不充分的局限性,将空间精度补偿思路转换为NC代码最优化问题,基于遗传算法求解该最优化问题,通过实验验证优化结果的有效性。结果表明：基于旋量理论的机床空间精度建模包含21项几何误差,空间精度预测结果较为准确;基于NC代码最优化的空间精度补偿技术使得机床空间定位精度最大补偿率为90.94%,验证了所提方法的有效性。     

Feed speed scheduling method for parts with rapidly varied geometric feature based on drive constraint of NC machine tool

As the existence of rapidly varied geometric feature and during the NC manufacturing process of this kind of parts, the actual moving speed of the workbench of the NC machine tool cannot reach the feed speed set in the NC program timely due to the drive constraint of NC machine tool. Furthermore, the machine tool would vibrate violently with the drive constraint when employing the constant machining parameter to process the parts with rapidly varied geometric feature, which seriously restricts the improvement of processing this kind of parts with high quality and high efficiency. In order to manufacture such parts with high quality and high efficiency, a sub-regional processing method with variable machining parameters is proposed. Firstly, the generation mechanism of the machining error is studied, and its mathematical model is built. Then the change rule of the machining error influenced by the curvature and the NC programmed feed speed is found out. Finally, taking the drive constraint and the machining error requirement into account, the relationship between the programmed feed speed and the curvature is established, and the corresponding programmed feed speeds to different curvatures are obtained. Taking the NC machining of the edge line of spiral microstrip antenna, which is an equiangular spiral, for example, the experiment results show that compared with the machining result with constant machining parameter, the maximum machining error of the sub-regional processing method with variable machining parameters decreases by 35.51% and the average value of the machining error decreases by 46.65%. For another example, the clover rose line is machined and the processing quality is also improved. This study proves that the method distributing the programmed feed speeds based on the curvature variation can improve the machining precision and ensure processing efficiency, and provides an effective method to manufacture parts with rapidly varied geometric feature.     

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

Contour error control of CNC machine tools with vibration avoidance

A vibration avoidance and contouring error compensation algorithm for feed drives is presented. The residual vibrations are avoided by applying input shaping filters on the reference axis commands. The input shaping filter avoids the excitation of the structural modes but at the expense of increasing tracking and contouring errors. The tracking errors are estimated from the closed loop transfer function of drives, and used to predict the contouring errors which are mapped to the each axis for pre-compensation. The integrated vibration avoidance and contouring error compensation is experimentally demonstrated to improve the damping and contouring accuracy on a two-axis table.     

Adaptive compensation of quasi-static errors for an intrinsic machine

An adaptive compensation strategy for quasi-static error correction in intrinsic machines is proposed and tested. The proposed methodology consists of systematic modelling of the machine forward kinematics, including quasi-static errors, as well as direct modelling of the inverse kinematics using nonlinear regression analysis. The result is a model which is a hybrid of physical modelling and regression analysis modelling. In addition, the methodology includes a compensation strategy of the machine contouring errors using the state observer technique for on-line adaptive compensation. A CMM is chosen as a test bed for validation of the proposed methodology. Systematic modelling is carried out in two stages for the forward and inverse kinematics. Regression based models are verified using two different tests. The statistical analysis of variance technique (ANOVA) is used to select the best model in addition to model testing using an independent set equal to approximately 10% of the fitting data. The obtained models are then employed in two compensation strategies; one for the measurement error correction, and another one for the contouring error correction by motion command modification in the forward control path. For contouring tests, the CMM behavior at different thermal states is estimated using experimentally obtained Effective Coefficient of Thermal Expansion (ECTE). Simulations of the machine in contouring selected trajectories are carried out over a range of thermal states. Results obtained show an improvement in the CMM performance to a level close to the machine resolution. The CMM performance is tested using the standard ASME B.89.1.12M-1990 evaluation test, as well as a novel modified version of the test accounting for a thermally varying environment. Machine errors are significantly reduced using the proposed methodology.