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.     

一种采用动态补偿的五轴机床铣削力预测方法

对五轴数控机床的铣削力进行精准预测,有利于提高工件的加工质量。因此,提出一种采用动态补偿的五轴机床铣削力预测方法。分析五轴数控加工中心结构,研究五轴数控铣削加工中心的进给传动动力学;通过测量切削扭矩,计算电机传递的总转矩,在冲击力激励的作用下,计算它与测量扰动频率响应间的传递函数。将实际切削扭矩分解成直流(静态)分量和交流(谐波)分量,在此基础上采用卡尔曼滤波器衰减噪声,并补偿结构动态模式对间隔采样的切削力矩的影响,从而减少结构动态模式引起的测量值失真。引入Denavit-Hartenberg方法,通过雅克比矩阵求取工件框架中刀具上的切削力和扭矩与驱动框架中驱动力和扭矩的转换关系,进而将刀尖力映射为驱动力矩,以实现对铣削力的预测。结果表明：所提方法预测的力信号与实测的力信号几乎一致,说明该方法能较精准地预测五轴机床的铣削力。     

考虑加工过程的复杂薄壁件加工综合误差补偿方法

针对机器人在空间曲面焊接过程中需要保持焊接速度和焊炬位姿恒定的工艺要求,提出了一种适用于复杂空间曲面焊接机器人的运动规划方法,该方法采用NURBS曲线对三维点云描述的空间轨迹进行光顺逼近,建立机器人配合变位机组成的多自由度焊接系统运动学模型并进行逆运动学求解. 开发了一套完整的复杂空间曲面焊接机器人自动编程系统. 以翻领成型器为例进行了复杂空间曲面焊接机器人的自动编程及焊接试验. 结果表明,文中提出的复杂空间曲面焊接机器人运动规划方法和自动编程系统能够顺利完成焊接任务,且运动平稳,具有良好的焊接轨迹精度.     

A novel spindle inclination error identification and compensation method in ultra-precision raster milling

In the ultra-precision raster milling (UPRM) process, the existence of spindle inclination error can directly affect the dimensional accuracy of machined components. This study developed a novel spindle inclination error identification and compensation method based on the groove cutting in UPRM. In this method, the tilt angle of the intersection curve of two toruses (ICTT) generated from two neighboring rotary cuts in UPRM was measured to identify the spindle inclination error. A mathematical model was developed to simulate the ICTT profile and present the relationship between the tilt angle of ICTTs and the spindle inclination error by solving the differential of the ICTT function, by which the spindle inclination error can be solved under the given cutting parameters and the tilt angle of ICTTs. The effects of cutting parameters on the tilt angle of ICTTs were explored. An error compensation procedure was designed and a group of groove cutting experiments was conducted to identify and compensate the spindle inclination error. The theoretical and experimental results show that the proposed method can compensate for the spindle inclination error effectively and accurately.     

参数曲线插补中一种截断误差补偿方法

参数曲线插补是高档CNC系统中的一项重要功能，针对目前参数曲线插补算法中截断误差的问题，本文从数据采样的插补原理出发，提出了一种截断误差补偿算法，有效地提高了插补精度，本算法对复杂曲面高精度加工具有十分重要的应用价值。     

Modeling system error in batch machining based on genetic algorithms

During batch machining under a static cutting-tool setting, machining errors of workpieces always have an ascending trend with the order of workpieces. Here the error trend is called the system error in batch machining. To compensate for the machining system error and enhance machining accuracy, modeling the system error is the key process. This paper first analyses several popular modeling methods and identifies their deficiencies when used in system error modeling. Subsequently, a new method of system error modeling based on Genetic Algorithms (GA) is introduced. Finally, a real-life application example using the new method and a comparison with other modeling methods are given, which indicate that the proposed GA based method is good. The paper also points out the essence that the proposed modeling method is a polynomial regression one in a broad sense, and is useful in the modeling of non-uniform error series.     

Study on the compensation of error by stick-slip for high-precision table

A simple approach of compensating friction error of high-precision tables is proposed in this paper. On the basis of accurate prediction of the magnitude of the friction error and the place where it occurs, a compensator is first constructed which consists of an online friction error prediction model and rectangular compensation curves regarded as compensation pulses. Then by carrying out optimal compensation experiments several times, the parameters describing the rectangular compensation curve at certain positions can be obtained. Finally, the optimal parameters of the rectangular compensation curve at any position can be determined by interpolation and approximation. It has been shown that, the method to compensate friction error proposed in this paper can be applied to effectively compensate the friction error for all circular motions of high-precision tables.     

精密立式加工中心运动轴的定位误差补偿研究

以某精密立式加工中心为对象,在西门子840D(Sinumerik 840D)数控系统平台下,基于分段补偿算法,利用Renishaw激光干涉仪对机床运动轴的位置精度进行定点测量,实现了对定位误差的补偿。实验结果表明了所述方法的有效性。     

Kinematic and geometric error compensation of a coordinate measuring machine

In this paper, kinematic modelling of a Coordinate Measuring Machine (CMM) is carried out and the methodology followed in modelling is explained in detail. The model is simplified by certain assumptions which may result in over-simplification of the model. Consequently, the model is investigated and enhanced by adding the relevant and suitable geometric error terms. Different approaches are employed to evaluate the model coefficients. In the first approach, a commercial ring gauge is measured in a structured lattice in the work volume of the CMM. Resulting errors in these measurements are used in conjunction with some statistical methods to arrive at sets of model coefficients values. The second approach is based on measurement of the individual 21 error terms in the CMM by means of laser interferometry. These measurements are used to evaluate another set of model coefficients. A compensation strategy is proposed and tested using the model and the sets of coefficients obtained. Volumetric Performance of the CMM is evaluated according to ASME standards, before and after compensation. Improvement in the CMM volumetric performance is demonstrated and compared.     

基于支持向量机的铣削力预测

针对小样本、低泛化、过拟合和局部极小等问题,建立基于支持向量机(SVM)的铣削力预测模型,对铣削力进行预测,将其预测结果与试验值、BP神经网络预测值进行对比分析。结果表明:在训练样本较小情况下,得到的预测值与试验值吻合较好,且相对于BP神经网络预测模型的预测精度高。     

高速铣削P20模具钢铣削力建模及试验研究

采用响应曲面试验法对P20模具钢进行高速铣削试验,建立了铣削力与铣削速度、每齿进给量、轴向切深和径向切深之间的预测模型并进行了显著性的检测,且对比预测结果与实测数据,验证了该模型的准确性.通过对响应曲面及其等高线图的分析,得出铣削用量对铣削力的影响规律.     

An advanced FEA based force induced error compensation strategy in milling

The study introduces a multi-level machining error compensation approach focused on force-induced errors in machining of thin-wall structures. The prediction algorithm takes into account the deflection of the part in different points of the tool path. The machining conditions are modified at each step when the cutting force and deflection achieve a local equilibrium. The machining errors are predicted using a theoretical flexible force-deflection model. The error compensation is based on optimising the tool path taking into account the predicted milling error. The error compensation scheme is simulated using NC simulation package and is experimentally verified.     

A method of tool path compensation for repeated machining process

This paper proposes a software method to compensate for the contour error in repeated machining process. In the proposed method, the profile of the first machined part is measured by a coordinate measuring machine. Based on the measured data, the tool path is modified by a compensation algorithm, and then, is represented by a series of linear segments. Finally, the compensated tool path is fed to the CNC machine tool for the machining of subsequent parts. Mathematical analysis and experimental evaluation are presented in this paper.     

Accuracy enhancement of five-axis CNC machines through real-time error compensation

Although error modeling and compensation have given significant results for three-axis CNC machine tools, a few barriers have prevented this promising technique from being applied in five-axis CNC machine tools. One crucial barrier is the difficulty of measuring or identifying link errors in the rotary block of five-axis CNC machine tools. The error model is thus not fully known. To overcome this, the 3D probe-ball and spherical test method are successfully developed to measure and estimate these unknown link errors. Based on the identified error model, real-time error compensation methods for the five-axis CNC machine tool are investigated. The proposed model-based error compensation method is simple enough to implement in real time. Problems associated with the error compensation in singular position of the five-axis machine tool are also discussed. Experimental results show that the overall position accuracy of the five-axis CNC machine tool can be improved dramatically.     

Deformation prediction and error compensation in multilayer milling processes for thin-walled parts

Deformation prediction and error compensation are effective approaches to improve machining accuracy in milling thin-walled parts. In this paper, it is considered that the machining deformation of the previous layer will influence the nominal cutting depth of the current layer. Therefore, a dynamical model is established to predict the deformation in multilayer machining a thin-walled part. The coupling relation between cutting force and machining deformation is taken into account using iterative computation. The dynamical model is validated by comparing the simulation result with the experimental one. A new approach of active error compensation is proposed, in which the machining error is compensated at each layer. By comparing the simulation results of compensation at the last layer with the results of compensation at per-layer, a conclusion is drawn that compensation at per-layer makes smaller machining errors and the errors are more uniform.     

能够进行热误差补偿的加工中心在线检测软件的研究

研究了加工中心在线检测软件误差补偿技术，基于Windows平台开发了误差补偿软件，并对软件开发中的关键技术：建立检测系统的几何误差与热误差综合模型，测头误差处理技术进行了研究。可以同时对测头误差、机床几何误差与热误差进行补偿，有效地提高了在线检测精度。软件系统在MAKINO立式加工中心上进行了实验验证。     

A unified framework of error evaluation and adjustment in machining

Errors of machine tool, fixture, and datum on workpiece to be machined influence the machining accuracy of the workpiece. The objective of this paper is to provide a framework for abstracting an error model that integrates three types of errors, i.e., machine tool, fixture, and datum errors, into a unified one. Differential motion theory is used to build the evaluation model of three types of errors. The resultant deviation model of the tool with respect to the workpiece is derived by using the model. For the purpose of eliminating the deviation, the resultant geometric variation is mapped into the locator errors on the fixture. Then the position and orientation errors of the tool with respect to the workpiece may be reduced by adjusting the length of locators. Finally, the effectiveness of the resultant deviation model is verified by examples.     

基于多体系统运动学的龙门铣床加工精度预测模型

五轴联动数控加工运动复杂,影响零件加工精度的误差因素很多,综合考虑多种误差因素,分析了各级工艺链系统的综合误差,提出了基于多体系统运动学理论建立工艺系统综合误差模型;在零件加工之前对零件的加工精度进行预测;通过切削试加工验证模型的可靠性。切削试加工实验证实了基于多体系统运动学的数学模型对零件加工精度预测的准确性和有效性,为今后进一步的研究及误差补偿提供了依据。     

Thermal error mode analysis and robust modeling for error compensation on a CNC turning center

In this paper a novel concept of thermal error mode analysis is proposed in order to develop a better understanding of the thermal deformation on a turning center. The thermal error of the machine can be treated as the superposition of a series of thermal error modes with corresponding mode shapes and time constants. The selection of sensor location can then be improved based on the thermal error mode analysis. A robust modeling approach is also proposed to minimize the errors due to temperature measuring noise and the adverse effect of environmental changes. Through the use of thermal error mode analysis and the robust modeling approach, the number of thermal sensors has been reduced from 16 to four. The thermal error compensation system has been applied to a turning center in daily production for more than two years and it has kept year-round accuracy. The thermal drift in workpiece diameter on the turning center has been reduced from 35 μm to 6 μm from its center of tolerance.