A Cutter Orientation Modification Method for the Reduction of Non-linearity Errors in Five-Axis CNC Machining

In the machining of sculptured surfaces, five-axis CNC machine tools provide more flexibility to realize the cutter position as its axis orientation spatially changes. Conventional five-axis machining uses straight line segments to connect consecutive machining data points, and uses linear interpolation to generate command signals for positions between end points. Due to five-axis simultaneous and coupled rotary and linear movements, the actual machining motion trajectory is a non-linear path. The non-linear curve segments deviate from the linearly interpolated straight line segments, resulting in a non-linearity machining error in each machining step. These non-linearity errors, in addition to the linearity error, commonly create obstacles to the assurance of high machining precision. In this paper, a novel methodology for solving the non-linearity errors problem in five-axis CNC machining is presented. The proposed method is based on the machine type-specific kinematics and the machining motion trajectory. Non-linearity errors are reduced by modifying the cutter orientations without inserting additional machining data points. An off-line processing of a set of tool path data for machining a sculptured surface illustrates that the proposed method increases machining precision.     

五轴数控加工中旋转轴运动引起的非线性误差分析及控制

五轴数控(Computer numerical control,CNC)加工中,刀具路径规划阶段与实际加工阶段对旋转轴运动采用的插补方式存在差异,其中刀具路径规划阶段是根据零件的几何信息进行插补,而实际加工中则根据机床信息进行插补,这种差异将引起原理性加工误差。针对五轴数控加工中旋转轴的运动,分析采用线性插补方式控制两个旋转轴进行加工时刀具姿态变化引起的原理性误差,进一步研究不同加工情况下由此产生的在垂直于走刀方向的平面内的非线性误差。通过分析旋转轴运动过程中线性插补引起的刀轴偏差角,证明刀具在相邻两刀位点运动过程的中间时刻处刀轴偏差角取得最大值,并得到由该最大值的显式表达式,在此基础上分析最大偏差角的影响因素。提出通过限制相邻两刀位点间刀轴夹角来控制此非线性误差的方法,并给出实例验证。     

五轴数控机床加工误差动态修正方法研究

为修正五轴数控机床加工误差,提高五轴数控机床加工质量,提出一种新的五轴数控机床加工误差动态修正方法.构建五轴数控机床加工误差计算模型,获取五轴数控机床加工的刀心方位、刀轴方位轮廓误差;锁定误差方位后,通过五轴数控机床误差的动态实时补偿方法,实现五轴数控机床加工误差动态修正.研究结果表明:所提方法可实现全方位、高效率的五...     

Tool path optimization in postprocessor of five-axis machine tools

Generally, tool path is generated in a computer-aided manufacturing software considering only the geometry of machining parts. It is converted into numerical control (NC) codes in the postprocessor based on the particular machine kinematics. For some special types of five-axis machine tools, e.g., non-orthogonal five-axis machine tools, the generated NC codes may produce unqualified parts because of the existence of the non-linear error. Conventional commercialized postprocessors usually do not have the function of non-linear error checking. Observing that the tool path is a non-smooth trajectory full of corners and a series of connected line segments, cubic spline interpolation is applied to smooth the tool path at regular points in this study. The cutter tip center points are computed by the cubic spine interpolation, while the cutter posture vectors are obtained via linear interpolation. At the splines (for regular points) and the line segments (feature points), more points are chosen to be converted into NC codes to reduce the non-linear error, which is called data densification. Using the cubic spline to smooth the tool path and the data densification to reduce the non-linear error, a novel tool path optimization algorithm in postprocessor is proposed. Experiments were carried out on an inclined rotary spindle axis non-orthogonal five-axis machine tool. It shows that the proposed tool path optimization provides improved accuracy and surface quality.     

A new accurate curvature matching and optimal tool based five-axis machining algorithm

Free-form surfaces are widely used in CAD systems to describe the part surface. Today, the most advanced machining of free from surfaces is done in five-axis machining using a flat end mill cutter. However, five-axis machining requires complex algorithms for gouging avoidance, collision detection and powerful computer-aided manufacturing (CAM) systems to support various operations. An accurate and efficient method is proposed for five-axis CNC machining of free-form surfaces. The proposed algorithm selects the best tool and plans the toolpath autonomously using curvature matching and integrated inverse kinematics of the machine tool. The new algorithm uses the real cutter contact toolpath generated by the inverse kinematics and not the linearized piecewise real cutter location toolpath.     

五轴微段平滑插补算法

在五轴加工编程中,计算机辅助制造系统对曲面加工通常采用以折代曲,采用大量的微小G01直线段来加工曲面,在曲率半径较大的工件表面会出现明显折痕,严重影响工件表面的加工质量。为提高五轴数控加工工件的表面质量,提出一种五轴微段平滑插补算法。该算法考虑五轴加工中刀位数据的量纲差异,根据相邻数据点间的线性轴长度、线性轴的夹角和旋转轴角度变化量识别五轴数控加工程序中非连续微段和连续微段加工区域。对非连续微段加工区域按照原始直线段和旋转轴直接插补,从而保证加工精度。对连续微段加工区域,先通过五维变量获取节点参数,采用最小二乘法对指令点在允许的精度范围内进行修正;对修正后的指令点采用4点构造法计算二阶切矢,根据连续微段的指令点修正值,节点参数值和对应的二阶切矢值获取二阶连续的三次样条曲线;在二阶连续平滑的曲线上进行实时插补计算,控制机床进行五轴加工。试验结果表明:通过提出的五轴微段平滑压缩算法拟合后的路径要更加接近原始的曲面模型,平滑处理过的实际工件加工表面也要优于未进行处理的工件加工表面,提高了五轴自由曲面的表面质量。     

An accurate surface error optimization for five-axis machining of freeform surfaces

This paper presents an accurate surface error interpolation algorithm for five-axis machining of freeform surfaces. One of the most important steps in the interpolation process is to calculate the next cutter contact (CC) point according to the present one. In this paper, the next CC point is calculated by an accurate chord evaluation method. This method is developed based on the cutting simulation process, which can be vividly described as firstly planting dense grasses on the tool path curve and then cutting them when the tool moves by. The left lengths of the grasses either positive or negative are considered to be the machining error. The method is accurate also because the tool geometry and the tool orientation changes during five-axis machining are taken into consideration. With this method, the chord errors between CC points are controlled uniform along the tool path. The proposed interpolation algorithm is compared with the commercial CAM systems like PowerMILL and UG. The results show that the proposed algorithm can significantly reduce the number of cutter locations meanwhile confine the chord error. A real cutting experiment is implemented, and the result indicates its promising value in industrial applications.     

An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.     

Optimal CNC plunge cutter selection and tool path generation for multi-axis roughing free-form surface impeller channel

Plunge milling is the most effective way for rough machining of impeller parts, but previous research had not considered the optimization of plunge cutter selection and tool path. In this paper, a new method for optimizing the plunge cutter selection and tool path generation in multi-axis plunge milling of free-form surface impeller channel is proposed in order to improve the efficiency in rough machining. Firstly, in the case of fixing a rotation axis at a certain angle in five-axis machine, a mathematical representation is formulated for the geometric model of the cutter interfering the impeller, and an optimization model of the cutter size is established at a cutter contact point on the impeller channel surface, so the largest tool could be determined. Secondly, by analyzing the machine tool movement characteristics, the geometric constraint model of the plunge tool path which relative to the largest tool, step distance, and row space is established, and a tool orientation calculation method of impeller channel machining is given, and then, the plunge tool path and tool orientation could be obtained. Finally, the generated tool path and tool orientation are simulated and verified in practical processing. Simulation and experimental result shows that the rough machining efficiency of the impeller part is improved up to 40 % with this method.     

汽车玻璃钢化风栅成形器五轴加工刀轴矢量插值

为了解决汽车玻璃钢化风栅成形器五轴加工时刀轴矢量频繁变换造成冲击或发生干涉等问题，提出一种刀轴矢量插值方法。根据被加工曲面的几何形状和误差要求确定刀触点，根据被加工曲面的微分几何性质确定刀轴矢量的后跟角和摆转角。在已确定刀触点处的刀轴矢量的基础上，采用空间矢量光滑插值方法获得一系列中间位置刀轴矢量使刀轴变化较均匀。以货车前挡风玻璃钢化风栅成形器的一个拼镶块工作表面和风栅孔五轴NC加工为例进行仿真。结果表明，该刀轴矢量光顺方法可以避免刀轴方向频繁变换，同时也可有效地提高加工精度。     

考虑热误差的双转台机床工艺误差谱预测方法

五轴数控机床的几何误差和热误差是影响工件加工精度的两个重要因素,对这些误差因素进行分析可以有效提高薄壁件工件的加工精度。本文首先基于齐次坐标变换法,建立了双转台五轴数控机床的旋转轴几何误差模型;然后基于对标准球进行在机接触测量,辩识得出两旋转轴的12项几何误差,这些误差考虑了两旋转轴之间的相互影响和其热误差的影响;最后分析五轴数控机床加工空间的几何误差场,在该加工空间内几何误差从中心到外侧逐渐增加,当A轴旋转角度增加时,误差的最大值也随之增加。与其它位置误差辨识方法相比,本方法的测量精度符合加工要求,测量时间只需要30 min。     

A postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation

Improvements in the machine tool and the machining process technologies increased the need for generic postprocessors in order to exploit the capabilities of the machine tools. Contrary to conventional machining approach, next-generation machining technologies such as force-based feedrate scheduling and toolpath optimization requires the implementation of the variable feedrate during toolpath which constitutes the aim of this article. Therefore, this paper introduces a postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation. Furthermore, a practical yet effective method for avoiding kinematic singularities by spherical interpolation and NC data correction is presented as well. Proposed approach is validated for various five-axis machine tools with different kinematic configurations via virtual machine simulation module. Results of the verification tests show that presented postprocessing approach can accurately convert the cutter location information into NC codes and it is demonstrated that integrated virtual simulation module can simulate toolpaths with large number of blocks.     

五轴数控刀具半径补偿算法研究与数控仿真

针对五轴数控机床中的刀具三维半径补偿,结合刀具二维半径补偿原理和空间坐标变换公式,推导出刀具三维半径补偿算法。利用UG获取人脸复杂曲面的刀路轨迹文件,根据补偿算法编制出后处理程序,通过转换刀路轨迹文件得到数控加工代码;对其进行加工仿真和精度分析,以验证该刀具半径补偿算法的实用性。结果表明,该算法简单、正确,能满足复杂曲面精密加工的要求。     

On the workpiece setup optimization for five-axis machining with RTCP function

Nonlinear errors in five-axis machining process are caused due to the nonlinear motions of the rotational axes, which are inevitable. For the RT-type machine tool, the workpiece setup location on the working table has a direct effect on the nonlinear errors, thus there must be an optimal setup position which can reduce the nonlinear errors. Today’s five-axis machine tools are mostly equipped the with the RTCP (rotational tool center point) function, with which the NC program becomes independent from the workpiece setup. In this paper, we have focused on finding the optimal workpiece setup for the RT-type machine tool with RTCP function, more specifically, the Mikron UCP 600 five-axis machine tool in our lab. The kinematics of the machine tool is briefly analyzed. Based on that, the nonlinear error evaluation method with RTCP interpolation is derived. With this method, nonlinear errors can actually be considered as a function of the workpiece setup position. Then, the particle swarm optimization (PSO) is applied to find the optimal workpiece setup, in which a mutation operation is used since PSO traps into local optimum easily. The proposed optimal workpiece setup method is implemented and tested. Example results show that the optimal setup with least nonlinear errors can be found. Some interesting results also show that the nonlinear errors are not sensitive with the z component of the workpiece setup vector. The proposed optimization is nearly zero-cost and easy to both understand and implement, yet has a potential to reduce the nonlinear errors and thus to improve the accuracy of five-axis machining.     

基于机床运动学约束球头刀多轴加工刀轴矢量优化方法

针对目前航空发动机叶片进排气边加工精度和表面质量较差的问题,提出了一种基于机床运动学约束球头刀多轴加工刀轴矢量优化方法。建立刀位优化变量与刀位数据之间的关系方程,同时建立刀位数据与机床回转轴角度之间的运动变换方程,从而推导出刀位优化变量与机床回转轴角度之间的关系方程。通过求解上述方程得到球头刀多轴加工复杂曲面的刀轴矢量计算公式。在此基础上,给出球头刀多轴加工刀轴矢量优化方法和刀轨生成方法。同时,以某航空发动机叶片为例,分析了本文算法和Sturz算法对机床回转轴角度的影响。分别利用本文算法和Sturz算法生成该叶片进气边加工的刀轨,并在五轴数控机床上进行加工试验。试验结果表明,该算法能够避免加工过程中机床回转轴的大幅波动,使机床轴运动更加平稳和光滑,从而提高曲面的加工质量和加工效率,具有一定的实际应用价值。     

A novel kinematic model for five-axis machine tools and its CNC applications

In conventional five-axis CNC machining, the machine structure is treated as a single kinematic chain just like a robotic manipulator while the cutter is treated as an end effector. In this paper, besides the machine kinematic chain, a cutter kinematic chain is introduced, and the two subkinematic chains are combined to form one machine–cutter kinematic chain. Forward, inverse kinematics and constrained inverse kinematics for the proposed machine–cutter kinematic chain are further put forward. Two applications are presented to demonstrate the advantages and effectiveness of the proposed kinematic model. The proposed kinematic model unifies the structure of the machine and cutter; therefore, the flexibility of the five-axis machine tool can be fully explored.     

直纹面叶轮插铣加工关键技术

为提高整体叶轮的粗加工效率,弥补目前商用计算机辅助制造软件在五坐标插铣加工能力方面的不足,研究了直纹面叶轮五坐标插铣加工的关键技术。根据直纹面叶片的偏移边界矢量,利用四元数插值方法计算插铣加工的刀轴矢量,提出并推导了五坐标插铣加工的行距和步距计算公式,保证了插铣加工的材料去除率和加工效率。依据上述算法自主开发了整体叶轮五坐标插铣加工专用计算机辅助制造软件,并对该软件生成的刀具轨迹进行了仿真和实际加工验证。结果证明,该方法在一定程度上提高了叶轮零件的粗加工效率。     

冗余轴解决五轴加工奇异问题的研究

为解决五轴加工在奇异点附近加工误差较大且易对工件和机床造成冲击的问题,对带有冗余ABC三转轴机床解决CA双摆头型五轴奇异问题进行了研究。建立了机床模型,依此得出了此冗余轴机床的运动关系,并根据加工刀位点特点对刀路进行初步研究。仿真结果表明,与其他解决奇异问题方法相比,该冗余轴机床可以有效克服五轴机床奇异问题,基本消除奇异区域的较大加工误差,并且各轴旋转角度得到了优化,从而使加工效率大大提高。     

Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors

Kinematic errors due to geometric inaccuracies in five-axis machining centers cause deviations in tool positions and orientation from commanded values, which consequently affect geometric accuracy of the machined surface. As is well known in the machine tool industry, machining of a cone frustum as specified in NAS979 standard is a widely accepted final performance test for five-axis machining centers. A critical issue with this machining test is, however, that the influence of the machine's error sources on the geometric accuracy of the machined cone frustum is not fully understood by machine tool builders and thus it is difficult to find causes of machining errors. To address this issue, this paper presents a simulator of machining geometric errors in five-axis machining by considering the effect of kinematic errors on the three-dimensional interference of the tool and the workpiece. Kinematic errors of a five-axis machining center with tilting rotary table type are first identified by a DBB method. Using an error model of the machining center with identified kinematic errors and considering location and geometry of the workpiece, machining geometric error with respect to the nominal geometry of the workpiece is predicted and evaluated. In an aim to improve geometric accuracy of the machined surface, an error compensation for tool position and orientation is also presented. Finally, as an example, the machining of a cone frustum by using a straight end mill, as described in the standard NAS979, is considered in case studies to experimentally verify the prediction and the compensation of machining geometric errors in five-axis machining.     

五轴数控空间刀具半径补偿的实现

深入分析了空间刀具半径补偿矢量的计算方法,对实现该空间刀补矢量到五轴联动数控系统中做了算法的准备和验证,并以UG NX6.0生成的刀位文件(CLSF)为坐标数据来源和五轴联动A/C双转台机床为例,开发了一个专用后置处理软件,并通过在Vericut7.0上模拟和五轴联动机床上实际加工叶片,加工结果说明了该算法的正确性和软件的实用性。