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。     

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.     

A methodology for systematic geometric error compensation in five-axis machine tools

To enhance the accuracy, an efficient methodology was developed and described for systematic geometric error correction and their compensation in five-axis machine tools. The methodology is capable of compensating the overall effect of all position-dependent and position-independent errors which contribute to volumetric workspace. It was implemented on a five-axis grinding machine for error compensation and for the check of its effectiveness. Error compensation algorithm was designed, and a routine was written in Matlab software. The developed technique and software are based on an error table which interprets the function of axis through cubic spline technique and synthesis modeling of a machine tool. Recursive compensation methodology was used to remove the machine errors from the actual tool path and inverse technique was implemented to find the corrected positions of prismatic and rotary joints. Moreover, it can convert the corrected tool paths into practical compensated NC codes. The generated, corrected and modified NC codes directly fed to the controller of a five-axis machine tool. Validation of the technique was preceded by repeated experimentation of measurement and through machining of typical standard workpieces with some additional specific features. Experimental results exhibit effective compensation and remarkable improvement in the parametric and volumetric-workspace accuracy of the five-axis machine tool.     

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.     

Postprocessor development of a five-axis machine tool with nutating head and table configuration

The postprocessor is an important interface that transforms cutter location data into machine control data, and in a five-axis machine tool is highly complex because the simultaneous linear and rotary motions occur. Since most works of the five-axis postprocessor method have dealt only with the orthogonal machine tool’s configuration, this study presents a postprocessor scheme for two types of five-axis machine tools, each with a nutating head and a table whose rotational axes are in an inclined plane. The benefit of such a configuration is that it allows switching from vertical to horizontal machining by a single machine. The general analytical equations of NC data are obtained from the forward and inverse kinematics and the homogeneous coordinate transformation matrix. The linearization algorithm for the postprocessor is developed to ensure the machining accuracy. The presented algorithm is implemented using a window-based five-axis postprocessor with nutating axes, and programmed in Borland C++ Builder and OpenGL. A simulation is performed using solid cutting software and a trial-cut experiment was conducted on a five-axis machine tool with a nutating table to elucidate the accuracy of the proposed scheme.     

Envelope surface formed by cutting edge under runout error in five-axis flank milling

This paper investigates the analytical envelope surface model formed by specially designed cutting edge under cutter runout error, including axis offset error and tilt error, in five-axis flank milling. This model, which is independent of the machine tool type, is determined by the tangency condition in envelope theory. First, the cutter runout is defined by four parameters, namely offset distance, offset direction angle, locating angle, and tilt angle. Then, the cutting edge represented by cubic B-spline curve is used as the generator of cutter rotation surface to formulate the closed-form envelope surface model. In particular, the runout error and feedrate are both integrated into the model. In addition, we study special cases of the analytical model and the runout effect on envelope surface. Finally, computer example validates the feasibility of the proposed model with runout. We find that envelope surface formed by cutter edge is different from each other at the existence of runout, and envelope surface dedicated to final machined surface is generated by the composition of some segments of cutter edges. The results can be applied to tool path optimization in five-axis flank milling and NC simulation with cutter runout.     

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。     

Developing a postprocessor for three types of five-axis machine tools

This paper presents a postprocessor capable of converting cutter location (CL) data to machine control data for three typical five-axis machine tools to establish an interface between computer-aided manufacturing (CAM) systems and numerically controlled (NC) machines. The analytical equations for NC data are obtained using the homogeneous coordinate transformation matrix and inverse kinematics. In addition, the developed postprocessor method is implemented through a trial-cut on a five-axis machine and verified on the coordinate measurement machine. Experimental results confirmed the effectiveness of the proposed postprocessor method which can be used to integrate the various five-axis machine tools employed in manufacturing systems.     

Reduction of geometry-based errors in five-axis machining through enhanced 5D interpolation

Geometry-based errors constitute a special category of CAM-originated machining inaccuracies that significantly influence the precision of five-axis surface machining operations. Geometry-based errors reflect the inability of the cutter to accurately trace a prescribed 3D tool path in five-axis machining. Their magnitude constitutes an overlapped effect of the adopted interpolation scheme, cutter, and surface geometries, as well as kinematics of the five-axis machine tool, assumed free of errors by the CAM software. Although the presence of these errors is inherent in the current configuration of five-axis computer numerically controlled machining systems, little efforts were made so far towards their reduction. In this regard, the present study has investigated the magnitude of geometry-based errors as generated by various 5D interpolation schemes. These enhanced interpolation functions were determined by enforcing better approximations of the ideal machine control coordinate (MCC) trajectory as calculated in five-axis machine tool’s joint space. By comparing the geometry-based errors generated by the enhanced 5D interpolation schemes with linear interpolation baseline, it was found that significant error reductions will be obtained when synchronized 5D quadratic functions are used to approximate the ideal MCC curve in joint space. Moreover, the parametric synchronization between rotational and translational machine tool motions represents an essential requirement for limitation of the amount of geometry-based errors.     

自由曲面五轴变步长数控加工刀轨生成方法

为了在满足逼近误差要求的同时最大程度减少冗余刀轨,对自由曲面提出了一种五轴变步长数控加工刀轨生成方法.首先对刀触点轨迹基于线性误差计算出初始刀触点点集,再以局部干涉调整前倾角的方式计算出无干涉刀位点和刀轴矢量;以最大非线性误差刀位处到刀触点轨迹的最小值作为相邻刀位点之间的逼近误差,并基于数据点自适应离散法计算逼近误差;...     

基于机床运动模型的走刀步长计算方法

为提高五坐标数控加工刀具轨迹生成的精度和切削效率,通过特定机床结构运动建模,对自由曲面刀具轨迹规划中的走刀步长计算方法进行研究。针对刀具摆动与工作台转动类型的非正交结构五坐标机床,在建立机床运动传递关系的基础上,实现任意刀轴方位的机床各轴运动坐标分解,构建机床运动模型。基于此,分析切削误差产生机理,推导出非正交结构的机床实际运动误差估计公式。利用切削误差对比关系,迭代计算满足精度要求的最大走刀步长。算例表明,在相同的允许误差条件下,本文算法较之传统变步长方法,最大误差降低了37.01%,而平均步长相对于等步长方法,增加了8.91%,说明基于机床运动模型的走刀步长计算方法能够有效控制切削误差,并提高自由曲面五坐标加工的刀具轨迹质量。     

An improved calculation method for cutting contact point and tool orientation analysis according to the CC points

Tool path generation is an important step of five-axis NC milling which plays an important role in parametric surfaces and free-form surfaces manufacturing. Cutter contacting (CC) point calculation is considered as a basic procedure of tool path generation. The step lengths formed by cutter contacting points have an effect on the chord error along feed direction. In traditional calculation method for CC point discretization, the segments connected by adjacent CC points distribute on both sides of the theoretical tool path curve. This situation magnifies the cutting error to some extent and enlarges the expected margin if the surface demands polishing or grinding. Aiming at this issue, this paper proposes an improved constant chord error method for CC point calculation. In the proposed method, the CC points lay on the theoretical tool path curve when the tool path curve is concave and lay on the chord error offset curve when is convex, which ensures the segments connected by the adjacent CC points distribute on one side of design surface, the side of the scallop height between tool paths. Therefore, the actual margin of polishing or grinding can be reduced. The influence of inflection points is also considered in this method to avoid accuracy deterioration caused by the long steps occurring near the inflection points. In part processing, local gouging and global collision must be avoided in tool orientation determination. This paper analyzes tool orientations with no rear gouging and no collision based on the calculated CC points. The novel discretization method for CC points is calculated on a single blade model, and the tool orientations are generated on an open integral impeller. A DMG DMU50 machine tool and a Hexagon three coordinates measuring machine are applied for experiments and measurements. The results show that, the CC point discretization method proposed in this paper offers many advantages over the traditional constant chord error method and commercial software, such as quantity of points, curve fitting, no overcut, and residual margin distributing. At last, blade and tunnel of the open integral impeller with safety tool orientation is machined and verified on the DMG DMU50 machine tool.     

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.     

Study of applying reverse engineering to turbine blade manufacture

A turbine blade has complex shaped free-form surfaces that can be modelled as surfaces with variable curvature by high-degree polynomials. Industry typically utilizes a turnkey system and special-purpose machine tool to manufacture turbine blades. A turkey system is a closed form design. Users need only input relevant data to this system to manufacture the product directly. However, users are unaware of the internal operation of the system. With rapidly advances in computing technology, commercial CAD/CAM systems can be utilized to design freeform surfaces and generate a tool path for the designed surfaces. This study uses a reverse engineering technology that is used to reconstruct the CAD model for a turbine blade. The prototype is measured by a coordinate measuring machine to obtain the geometrical control data points that are used to generate the CAD model in the UniGraphics (UG) CAD/CAM system. The UG/GRIP (GRaphics interactive Programming) language is used to generate the cutter location data rather than using the default UG CAM module. A five-axis NC code is acquired by the developed postprocessor and verified by the solid cutting simulation software VERICUT®. Real turbine blade machining is performed on a table/spindle tilting five-axis machine tool, demonstrating the effectiveness of the proposed approach.     

五轴加工奇异区域内的刀具路径优化

针对五轴加工在奇异区域内由于旋转轴运动的剧烈变化导致非线性误差过大并对工件、刀具和机床部件造成损害等问题,给出一种奇异区域内加工路径的优化方法。以AC双转台五轴联动数控机床为研究对象,在反向运动学变化中根据正弦、余弦三角函数的周期性对C轴转角进行初次优化;按照加工是否通过奇异点两种情况,采用设定奇异点处的C角值或者修改奇异点附近的刀轴方向两种方法,进一步降低C轴过大转角;以当前加工区间的非线性误差是否超过允许值为判断条件,对仍然不满足精度要求的区间进行递归插值处理。仿真试验和实际加工结果表明,与单纯采用线性插值方法相比,该方法在提高奇异区域内加工精度的同时,有效减少新插入点的数量,从而尽量降低加工速度的损失。     

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...     

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.     

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。     

AUTOMATIC PROGRAMMING SYSTEM WITH NURBS METHOD ON PC

ＡＵＴＯＭＡＴＩＣＰＲＯＧＲＡＭＭＩＮＧＳＹＳＴＥＭＷＩＴＨＮＵＲＢＳＭＥＴＨＯＤＯＮＰＣＤｕＪｕｎｗｅｎ；ＬａＹａｄｏｎｇ；ＫａｎｇＹｕ；ＬａｉＫｅｗｅｉ；ＺｈｕＭｅｎｇｚｈｏｕ（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐ...     

基于VERICUT的五轴数控加工仿真与优化

虚拟加工平台的构建、数控加工程序的正确性验证及加工过程的仿真与优化及是五轴数控机床实现高效加工的重要基础技术。基于VERICUT数控加工仿真与优化平台,以非正交五轴数控机床DMC70ev为研究对象,构建了数控加工仿真平台;以曲面加工为例,建立了基于恒定体积去除率和恒定切屑厚度的优化设计数学模型,进行了刀位轨迹的优化。应用表明:研究成果实现了五轴数控加工过程仿真及数控加工程序的正确性验证,减少了刀具磨损,提高了加工效率与加工质量,可以较好地提升企业数控加工技术的应用水平、应用质量,推动现代制造技术的发展。