圆柱刀五轴数控侧铣直纹面的直线插补误差分析

在五轴联动数控系统中,相邻刀位点间的运动通过直线、圆弧或样条曲线进行插补运动,其中直线插补方法最具典型性。以圆柱刀侧铣加工直纹面时因线性插补引起的非线性误差为研究对象,首先,在被加工曲面上采用最佳一致逼近法规划圆柱刀侧铣直纹面的刀具位置;然后,利用包络原理建立刀具线性插补时所形成的包络面解析表达式;以理想曲面为基准面,利用牛顿迭代法求取点到曲面的最小距离,从而建立刀具包络面与理论曲面的误差模型,以此得到刀具线性插补时产生的非线性误差;最后,利用MATLAB软件通过数值算例对影响非线性误差的规律、大小以及其影响因素进行了分析。     

五轴联动数控加工中的刀具轨迹控制算法

已有的五轴联动数控加工系统往往忽略刀轴矢量插补问题,只是简单地通过对线性轴进行插补、对旋转轴进行跟随的方式来实现刀具轨迹的控制,导致产生非线性误差和刀具碰撞与干涉等问题。为此,提出一种基于刀轴矢量插补的刀具轨迹控制算法。该算法采用大圆弧插补法对加工过程中的刀轴矢量进行控制,同时采用NURBS曲线拟合方法对控制过程中产生的中间点进行处理,并通过对拟合而成的NURBS曲线进行插补来实时计算各运动轴的位置。该算法不仅能够有效地提高五轴联动数控加工的精度,而且可以有效减小数据存储量。仿真和实际加工验证了算法的有效性和实用性,证明算法具有轨迹过渡平稳、非线性误差小的特点。     

RTCP算法中无碰刀轴矢量的确定

针对五轴数控加工中主轴头中心角速度超限和非线性误差的问题,提出了基于旋转轴线性插补的RTCP算法,分析了插补过程中的全局干涉现象,推导了刀杆偏差系数公式,得到了RTCP模式下的无碰干涉区域,避免了干涉现象的发生。算法减小了非线性误差,保证了插补过程中机床旋转轴的运动平稳性,当刀具长度变化时无需重新通过后置处理生成数控程序,提高了加工效率。仿真结果证实了算法的可行性。     

五轴数控系统旋转轴快速平滑插补控制策略

在五轴联动加工中,刀轴矢量与旋转轴运动坐标之间存在非线性关系,刀轴矢量的平滑过渡不能保证旋转轴的平滑运动,尤其是当刀轴矢量接近机构奇异点时会引起旋转轴的剧烈震动,导致伺服报警,甚至损伤机床部件.通过分析旋转轴线性插补和矢量插补过程中刀具姿态的变化情况,抽象出刀具姿态误差模型.根据加工允许的刀具姿态误差,在矢量插值段中插入线性插值段,防止靠近奇异点处产生的旋转轴急速转动.结合指令行程和旋转轴性能进行旋转轴插补速度钳制,使用三次样条曲线对矢量插值段和线性插值段进行平滑连接,保证整个插补过程中速度的连续平滑.试验结果表明,本策略可以在满足刀姿误差要求的同时,实现旋转轴的快速平滑插补,并且已经应用于某航空结构件的批量加工生产中.     

五轴联动刀轴矢量平面插补算法

大多数数控系统仍默认以旋转轴角度线性插补插补方式进行铣削加工,实际刀轴矢量偏离理论刀轴矢量位置,产生极大的非线性误差。在五轴联动数控加工中心圆周铣削倾斜面时,表现为实际刀轴矢量偏离待加工平面,造成过切或欠切误差。而且,机床类型不同,铣削的误差表现形式也不同。经研究表明,此非线性误差完全来源于旋转轴角度的线性插补方式。从研究分析运动学坐标转换开始,从理论上研究旋转轴角度线性插补的原理和产生非线性加工误差的根源,提出刀轴矢量平面插补具体算法,并针对CA型双摆头类型机床进行仿真验证,新算法从根本上解决了该问题。     

双转台五轴数控机床的非线性误差补偿

针对双转台五轴数控机床因旋转轴与平移轴联动而产生的非线性误差,提出一种解析模型对非线性误差进行实时预测和补偿。选取刀位文件中的相邻点作为建立模型的刀位点,然后根据经典后置处理中的误差分布建立谐波函数解析的非线性误差模型;用该模型的解析表达式快速预测两刀位点之间的非线性误差,实现了对中间插补点的实时误差补偿。最后对一叶轮零件加工的刀位文件进行MALTLAB仿真分析,验证了所提算法的有效性。     

非可展直纹面侧铣刀具插补轨迹优化方法

针对圆柱刀侧铣加工非可展直纹面的刀路规划问题，将刀具线性插补轨迹与理论轨迹面之间的几何偏差考虑到刀位优化中。首先从设计曲面的两条引导线偏置并离散成初始刀位，提出网格法构建刀位点处的误差函数，运用动点寻优的方法优化初始刀位的刀轴矢量。在此基础上，构建了插补轨迹面与理论刀具轨迹面之间的几何偏差分布模型，调整刀位点以减小相邻刀位间的几何偏差，在无需增加刀位点的情况下使刀具插补轨迹面逼近理论刀轴面。实验结果表明，优化后的加工曲面误差波动范围减小，最大误差值降低了35.78%。     

五轴加工奇异问题分析与非线性误差控制

在计算机辅助制造软件中进行五轴加工编程时,后置处理反求旋转轴角度存在无解,即五轴加工的奇异问题,具体表现为旋转轴运动产生突变、非线性误差增大、加工质量下降。以A-C型五轴机床为例,通过研究刀轴的运动过程,证明C轴的转角是奇异问题产生的原因。基于该结论提出一种新的检测奇异刀位点的刀轴分量k值遍历法和基于刀轴矢量插值与样条曲线拟合的非线性误差控制方案。通过S样件的五轴加工实验表明,相比于线性插值,所提方案在奇异区域内误差显著减小,曲面更加光滑,加工效率有所提高。     

双转台五坐标机床RTCP功能的研究

五轴加工中由于旋转运动的影响,会产生非线性误差.RTCP(绕刀具中心点旋转)功能可使数控系统自动对旋转轴的运动进行实时线性补偿,从而保证插补点始终位于编程轨迹上.在深入分析双转台五坐标机床运动原理的基础上,介绍了一种集成RTCP功能的插补算法,并在MATLAB中做了仿真计算.计算结果表明该算法可以有效减小非线性误差.     

双转台五轴机床运动学分析及非线性误差研究

建立正确的A-C型五轴联动机床的WCS(工件坐标)和MCS(机床坐标)之间的矩阵转换关系,从而得出刀轴矢量和机床两个转轴的转角之间的映射方程,对于理解机床运动和CAM系统是至关重要的。由于旋转轴运动及CNC的平动轴线性插补、旋转轴跟随插补,导致五轴铣削过程会不可避免地产生非线性误差,详细分析了非线性误差产生的原因,舍弃线性插补而采用刀轴矢量平面插补,通过机床的逆运动学方程计算刀位的插补点和新的插补矢量,经CAM后处理系统转换成NC数控程序。最后给出一个实例进行分析和MATLAB仿真,验证了运动学推论和减小非线性误差策略的正确性。     

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 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.     

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。     

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 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.     

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.     

Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools

A machining test of cone frustum, described in NAS (National Aerospace Standard) 979, is widely accepted by machine tool builders to evaluate the machining performance of five-axis machine tools. This paper discusses the influence of various error motions of rotary axes on a five-axis machine tool on the machining geometric accuracy of cone frustum machined by this test. Position-independent geometric errors, or location errors, associated with rotary axes, such as the squareness error of a rotary axis and a linear axis, can be seen as the most fundamental errors in five-axis kinematics. More complex errors, such as the deformation caused by the gravity, the pure radial error motion of a rotary axis, the angular positioning error of a rotary axis, can be modeled as position-dependent geometric errors of a rotary axis. This paper first describes a kinematic model of a five-axis machine tool under position-independent and position-dependent geometric errors associated with rotary axes. The influence of each error on machining geometric accuracy of a cone frustum is simulated by using this model. From these simulations, we show that some critical errors associated with a rotary axis impose no or negligibly small effect on the machining error. An experimental case study is presented to demonstrate the application of R-test to measure the enlargement of a periodic radial error motion of C-axis with B-axis rotation, which is shown by present numerical simulations to be among potentially critical error factors for cone frustum machining test.     

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.     

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.