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.     

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.     

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.     

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 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.     

Five-axis STEP-NC controller for machining of surfaces

Five-axis machining is more widely used in manufacturing of freeform surfaces. However, in five-axis machining of freeform surfaces, incomplete information exchange between computer numerical control (CNC) and computer-aided design/computer-aided manufacturing (CAM) results in many limitations need to be rectified. In the paper, a new structure of CNC based on STEP-NC standard is proposed, where tool path planning, tool offset, and inverse kinematics are transferred from CAM to CNC. In order to guarantee good openness, open platform and standard interface are applied in the development. Technology of module collaboration and design of data flow are studied. A five-axis real-time interpolator for non-uniform rational B-spline surfaces machining is realized. Based on these technologies, a five-axis CNC is developed in the manner of software realization, which consists of interpreter, task coordinator, axis group, softPLC, etc. The software CNC system has been applied on a tilt-rotary type five-axis machine tool, where the milling experiment has been performed successfully.     

Post-processor development for a turning and milling composite machine tool

The accomplishment of a turning and five-axis milling in only one setup is extremely useful and is possible on a turning and milling composite machine tool. In this work, we present a control algorithm and develop a post-processor for this machine, which has six linear and three rotary axes. To calculate a generalized kinematics model, coordinate systems are established by analyzing the basic kinematic chain relation of the turning and milling composite machine tool. The two vectors, which control the motions of the cutter contact workpiece, are simultaneously transformed to provide the algorithms of the rotary angles and motion coordinate. A special post-processor written in JAVA language is developed according to the proposed algorithm. To evaluate the effectiveness and accuracy of the developed post-processor, a specimen (blade) is used in the cutting simulation and real machining experiment. Experimental results showed the effectiveness and accuracy of the proposed algorithm. Furthermore, Compatibility is improved by adding new functions such as change of target machine, cutter location data change, workpiece origin offset, and cutting feed rate control.     

Generation of collision-free cutter location data in five-axis milling using the potential energy method

In five-axis milling, optimal cutter location data (CL-data) should be generated to have advantages over three-axis milling in terms of accuracy and efficiency. This paper presents an algorithm for generating collision-free CL-data for five-axis milling using the potential energy method. By virtually charging the cutter and part surfaces with static electricity, global collision as well as local interference is eliminated. Moreover, machining efficiency is simultaneously improved by minimising the curvature difference between the part surface and tool swept surface at a cutter contact point (CC-point).     

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...     

Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

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。     

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 cutter orientation modification method for five-axis ball-end machining with kinematic constraints

Cutter orientation modification with kinematic constraints is very necessary and effective for five-axis machining especially machining at high speed. It is very helpful for achieving a smooth cutter motion and keeping the process steady. Therefore, a cutter orientation adjustment method is proposed to obtain an optimized tool path which makes best use of the kinematic characteristics of angular feed for five-axis machining. For the given five-axis cutter location path and the feed profile of cutter tip point both expressed by b-spline formats with the same parameterization, the analytic relations of angular feed, angular feed acceleration, and jerk with respect to the geometric and tangential feed parameters of the cutter tip trajectory are first derived. Then, the conditional inequalities of these kinematic constraints used for orientation adjustment are built. Subsequently, the determination method of feasible cutter orientation and detailed algorithm of orientation adjustment are given. Finally, illustrated examples are conducted to validate the proposed orientation adjustment method. The results show that the developed method is effective and can be applied to optimize geometrically complex five-axis tool path by taking the angular feed, angular feed acceleration, and jerk into account.     

A study on the five-axis end milling for sculptured surfaces

The direction vector of milling cutter for CL-data of five-axis milling is obtained by the fact that the bottom part of the milling cutter rides on free-form surfaces using the z-map method. Since the direction vector is known, CL-data can be transformed to the NC-code with regard to the geometry of the five-axis machine and post-processing. For uniform surfaces, the tool path is created from the prediction of cusp heights. After generating the NC-code, a sculptured surface was machined by five-axis end milling and cusp heights on the machined surface were measured by a three-dimensional CMM with laser scanner. From this machining test, it was found that this machining method is effective.     

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.     

Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining

Reparameterization-based toolpath generation methods are usually adopted for machining triangular meshes, trimmed surfaces and compound surfaces. The quality of the reparameterization has an important effect on that of the surface. In this paper, a combined reparameterization procedure is introduced to generate an optimal mapping between the designed surface and a specified planar circular region with relatively less distortion both in length and in angle. Then, for five-axis sculptured surface machining the mathematical model of spiral guide path with maximum path interval is constructed in the circular region. Cutter contact paths are obtained by inversely mapping the guide path onto the designed surface. Under constraints of gouging and collision, continuous and optimal cutter orientations are subsequently calculated. Finally, the results of simulation and experiment of the machining process are given to illustrate the feasibility and applicability of the proposed method.     

An efficient five-axis machining method of centrifugal impeller based on regional milling

This paper presents an efficient five-axis machining method of centrifugal impeller based on regional milling. As the base of the machining method, geometry of the centrifugal impeller and blade surface is analyzed, and sub-machining regions are presented through the division of the double three-cubic d non-uniform rational B-spline (NURBS) surface. In rough milling, the cutter parameters, tool path interval, tool path curves, and the fixed tool axis vector are calculated by the novel algorithm based on regional milling; the biggest cutter and smaller tool path length are obtained. In finish milling, for the aerodynamic performance of the finished impeller, the tool path curves are modified and interlinked to make them uniform and orderly. A modified algorithm of the finish milling of the blade surface is proposed, and not only are the machining errors reduced; their reasonable distribution is also realized. Numerical simulation and a real test impeller are presented as the test of the proposed method.     

A comprehensive approach to determining minimum cutter lengths for five-axis milling

Interference detection and avoidance by the shortest cutter for the five-axis milling machining is a critical task. Short tool length increases the rigidity and chatter stability of the cutter. In this research, a new and efficient method of interference detection and avoidance by the shortest cutter is developed. For the specific five-axis machine configuration, first possible candidate parts for the collision are found, which are complete cutting system (spindle, tool holder, and cutter), the work in process model, and the fixture. Spindle, tool holder, and tool are represented by the solid geometry identity of the cylinder, truncated cone, and cylinder, respectively, with the length and diameter as parameters. The surfaces of the work in process model and the fixture model are represented as the point cloud data of the suitable density. The Kd-tree data structure is employed on point cloud data which gives an efficient searching of the potential candidate points for the interference detection with the complete cutting system. All existing methods are able to detect the collision, but they are not capable to remove it with the optimum cutter length. The proposed algorithm has not only the capability of collision detection; it can also remove the collision with the optimum tool length. Other scope of the proposed algorithm is the selection of the tool holder to minimize the overhang tool length.     

Local interference detection and avoidance in five-axis NC machining of sculptured surfaces

The tool interference problem is the most critical problem faced in sculptured surface machining. This paper presents a methodology for interference detection and avoidance in five-axis NC machining of sculptured surfaces with a filleted-end cutter. The surfaces to be machined are divided into convex and non-convex regions. There is no local interference inside the convex regions. For the non-convex regions, based on the analysis of the different local interference, local gouging is first detected and avoided by determining optimal cutter orientations. Rear gouging detection and avoidance algorithms are then proposed for simple smooth surfaces and complex shaped surfaces, respectively. The techniques presented in this paper can be used to generate interference-free tool paths. The realistic results indicate that the proposed method is feasible and reliable .     

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.