Using rotary contact method for 5-axis convex sculptured surfaces machining

The 5-axis tool positioning strategy named rotary contact method (RCM) for sculptured surfaces machining has been developed in our previous paper (Wengang Fan et al., J Manuf Sci E-T ASME 134(2):021004.1-021004.6, 2012). The RCM finds the optimal tool positions by rotating the tool backward based on the offset surface instead of the design surface, and can generate big machined strip width without gouging. However, the RCM only deals with concave sculptured surfaces machining well at present, and the special property of convex sculptured surfaces machining has not been fully exploited. To resolve this problem, the general convex sculptured surfaces machining using the RCM is implemented in this paper. Firstly, the tool position error distribution for different tool feed directions is deeply investigated. It is concluded that the best tool feed direction is collinear with the maximum direction of curvature, which is completely opposite to the case for concave sculptured surfaces machining. Then the relationship between the key parameters in the RCM and the tool position error distribution as well as the tool path generation is totally discussed. Finally, machining simulation and cutting experiment of a convex sculptured surface example are performed. The results show that the RCM can apparently raise the efficiency of manufacturing process by contrast with the algorithm in the software UG for convex sculptured surfaces machining.     

轴交角误差对内齿轮刮齿加工精度的影响分析

针对内齿轮刮齿加工过程中,由于轴交角误差的存在而影响齿轮加工精度的问题,为了提高刮齿机的加工精度,首先建立了无进给、刀具进给和工件进给三种运动方式下刀具与工件之间的运动学模型;其次,通过分析不同轴交角误差方向下刀具和工件之间的相对运动关系,研究了内齿轮齿廓加工误差的产生机理;然后,通过建立多因素耦合关系模型,分析了不同轴交角误差方向对刮齿加工误差的影响程度,获得了最佳的轴向进给方式和轴交角误差方向;最后,通过样机试切实验验证了理论分析的有效性,样机满足6级加工精度要求。     

基于SVR-GA算法的广义加工空间机床切削稳定性预测与优化研究

针对机床零件加工位置和进给方向不确定造成刀尖频响函数变化,导致切削稳定性叶瓣图与无颤振工艺参数预测具有不确定性问题,提出一种耦合支持向量回归机(SVR)与遗传算法(GA)的切削稳定性预测与优化方法。该方法采用锤击法模态实验和空间坐标变换,获取样本空间不同加工位置与进给方向的刀尖频响函数;进而结合传统切削稳定性预测方法构建以各向运动部件位移、进给角度、主轴转速、切削宽度、每齿进给量为输入的极限切削深度SVR预测模型;采用该SVR模型作为切削稳定性约束建立材料切除率优化模型,通过遗传算法求解各运动轴位移、进给角度与切削参数的最优配置。以某型加工中心展开实例研究,实验结果表明获取的优化配置能实现稳定切削,验证了该方法的有效性。     

Adaptive feedrate interpolation with multiconstraints for five-axis parametric toolpath

A good adaptive feedrate will be helpful for improving machining accuracy and efficiency, as well as avoiding the excess of the machine’s physical capabilities and feed fluctuations during machining. Therefore, it is highly desirable to consider the constraints of geometric error, cutting performance, and drive constraints in the feedrate scheduling of the parametric curve interpolator for five-axis computer numerical control machining. In this paper, a novel multiconstraints feedrate scheduling method is proposed for the parametric curve interpolator in five-axis machining. In the method, the feed optimization model is first built with the constraints of geometric error, the maximum feedrate and acceleration of cutter tip, and the maximum feedrate and acceleration of five-drive axes. Then, the relations between each constraint and the cutter tip feedrate are derived by means of near arc length parameterization. After that, a linear programming algorithm is applied to obtain the optimal feed profile on the sampling positions of the given tool path. Finally, illustrated examples are given to validate the feasibility and applicability of the proposed feedrate scheduling method. The comparison results show that the proposed method has an ability of the simultaneous guarantees of geometric accuracy, cutting performance, and drive characters of machine tools.     

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。     

Form error estimation in ball-end milling of sculptured surface with z-level contouring tool path

This paper presents a flexible model for estimating the form error in three-axis ball-end milling of sculptured surface with z-level contouring tool path. At an interval of feed per tooth, the whole process of sculptured surface machining is treated as a combination of sequential small inclined surface milling. For ball-end milling of the inclined surface with z-level contouring tool path, at surface generation position, an analytical model is proposed to identify the feedback effect of tool deflection on cutting edge engagement. The deflection-dependent cutting edge engagement is determined by using an iterative procedure. And ultimately, the form error is obtained from the balanced tool deflection and associated surface inclination angle. In a validation experiment, the estimated form errors are compared with both the measurements and the predictions of a rigid model. It is shown that the proposed flexible model gives significant better predictions of the form error than rigid model. Good agreement between the predicted and measured form errors is demonstrated for the ball-end milling of sculptured surface with z-level contouring tool path.     

基于UG的螺旋叶片数控五轴加工

为提高螺旋叶片的加工效率和质量,提出了一种新的综合优化方法.以螺旋叶片高效率、高质量、无干涉五轴加工刀具轨迹为目标,采用UG CAM可变轴曲面轮廓铣的曲面区域驱动方法,选择合适的投影矢量方向和刀轴方向,采用合理的加工工艺、切削用量和优化进退刀,采用自定义的后处理文件生成了相应数控系统的数控代码实验结果表明该零件的加工质...     

基于误差模型的三轴联动加工轨迹预补偿方法

为了减小由于进给系统动态特性造成的多轴联动加工轮廓误差,提出了一种基于轮廓误差模型的三轴联动加工轨迹预补偿方法。首先建立了关于轨迹曲率、加工速率及进给系统动态特性参数的轮廓误差模型;然后根据读取的插补数据,利用轮廓误差模型实时预测三轴联动加工过程中的轮廓误差补偿向量并对加工轨迹指令进行补偿;最后通过对圆、变曲率和螺旋线轨迹的MATLAB仿真和机床加工实验,证明该补偿方法将轮廓误差减小了85%以上,可显著提高数控机床加工精度。     

Optimal five-axis tool path generation algorithm based on double scalar fields for freeform surfaces

In order to generate efficient tool path with given precision requirements, scallop height should be kept under a given limit, while the tool path should be as short as possible to reduce machining time. Traditional methods generate CC curves one by one, which makes the final tool path far from being globally optimal. This paper presents an optimal tool path generation model for a ball-end tool which strives to globally optimize a tool path with various objectives and constraints. Two scalar functions are constructed over the part surface to represent the path intervals and the feedrate (with directions). Using the finite element method (FEM), the tool path length minimization model and the machining time minimization model are solved numerically. The proposed method is also suitable for tool path generation on mesh surfaces. Simulation results show that the generated tool path can be direction parallel or contour parallel with different boundary conditions. Compared to most of the conventional tool path generation methods, the proposed method is able to generate more effective tool paths due to the global optimization strategy.     

Theoretical and experimental analysis of the effect of error motions on surface generation in fast tool servo machining

The fast tool servo (FTS) machining process provides an indispensable solution for machining optical microstructures with sub-micrometer form accuracy and a nanometric surface finish without the need for any subsequent post processing. The error motions in the FTS machining play an important role in the material removal process and surface generation. However, these issues have received relatively little attention. This paper presents a theoretical and experimental analysis of the effect of error motions on surface generation in FTS machining. This is accomplished by the establishment of a model-based simulation system for FTS machining, which is composed of a surface generation model, a tool path generator, and an error model. The major components of the error model include the stroke error of the FTS, the error motion of the machine slide in the feed direction, and the axial motion error of the main spindle. The form error due to the stroke error can be extracted empirically by regional analysis, the slide motion error and the axial motion error of the spindle are obtained by a kinematic model and the analysis of the profile in the circumferential direction in single point diamond turning (SPDT) of a flat surface, respectively. After incorporating the error model in the surface generation model, the model-based simulation system is capable of predicting the surface generation in FTS machining. A series of cutting tests were conducted. The predicted results were compared with the measured results, and hence the performance of the model-based simulation system was verified. The proposed research is helpful for the analysis and diagnosis of motion errors on the surface generation in the FTS machining process, and throws some light on the corresponding compensation and optimization solutions to improve the machining quality.     

Five-axis tool path and feed rate optimization based on the cutting force–area quotient potential field

Feed rate assignment in five-axis surface machining is constrained by many factors, among which a particularly critical one is the deflection cutting force on the tool: while a larger feed rate increases the machining productivity by shortening the total machining time, it nevertheless inevitably enlarges the deflection cutting force as well, which will cause the tool to be more prone to bending and the machine more prone to vibration, thus adversely degrading the surface finish quality. In this paper, we present a new five-axis tool path generation algorithm that strives to globally maximize feed rate for an arbitrary free-form surface while respecting a given deflection cutting force threshold. The crux of the algorithm is a new concept of the (cutting) force–area quotient function—at any cutter contact point on the surface, the maximal effective material removal rate (with respect to the deflection cutting force threshold) is a continuous function of the feed direction. This function induces a potential field on the surface and based on which an efficient tool path generation algorithm is designed. Preliminary experiments show that substantial reduction in total machining time can often be achieved by the proposed algorithm.     

交叉耦合算法的超精密数控机床伺服控制

超精密加工的轮廓精度控制直接影响到工件的加工精度,交叉耦合控制算法通过对两轴进行协调而影响轮廓控制精度。文章在分析超精密数控机床误差模型的基础上,将变增益交叉耦合控制算法引入超精密空机床的伺服控制,实验结果表明：变增益交叉耦合控制算法可以在不改变位置环的情况下,有效地提高系统的轮廓精度。     

Optimization of rotations for six-axis machining

Five-axis machines with three translational and two rotation axes are becoming increasingly popular in serving the needs of the mass production industry due to their ability to handle geometrically complex workpieces using the rotational axes. Theoretically, the combination of the five axes offers a minimal number of the degrees of freedom required to transport the tool into a prescribed spatial position and establish a required orientation. However, the rotation axes lead to an inevitable nonlinearity of the tool tip trajectory and the so-called kinematics errors appearing due to the specific kinematics of the machine. Eventually, one arrives at an interesting question. Is it possible to compensate this error by introducing an additional rotation axis? In other words, ??does an additional rotation axis offer any optimization benefits in the sense of the above mentioned error??? In this paper, we answer this question positively by analyzing a hypothetical six-axis milling machine with two rotation axes on the table and one additional rotation axis on the tool. The sixth axis is build on the top of the existing five-axis machine MAHO600E by Deckel Gildemeister. We present an extension of an optimization algorithm developed earlier by the authors for five-axis machining based on an optimal angle sequencing (the shortest path optimization). The extension is a combination of the shortest path strategy and the use of the additional axis. The algorithm leads to an increase in the machining accuracy, in particular, for rough milling. Numerical experiments and cutting by a virtual six-axis machine built in Vericut 5.0 validates the results of the optimization. The proposed optimization procedure is capable of upgrading the existing five-axis G-codes to the case of six-axis machine.     

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。     

自由曲面五轴加工刀具轨迹规划技术的研究进展

利用五坐标设备进行自由曲面的数控加工是提高加工质量和加工效率的有效途径,自由曲面形状和五坐标机床运动的复杂性导致其刀具轨迹规划技术十分困难。针对自由曲面五坐标端铣加工、侧铣加工以及碰撞干涉分析中的关键技术,综述了近年来自由曲面五坐标数控加工领域刀具轨迹规划技术的研究进展和现状。结合自由曲面数控加工的工程实用性要求,分析了当前研究中存在的不足,指出目前的研究成果在通用性、稳定性和有效性方面尚不能完全满足工程应用,认为自由曲面五坐标数控加工刀具轨迹规划技术的研究应从三维的角度出发,在更为广域的刀具影响空间研究刀具同自由曲面之间的几何啮合关系,同时需要考虑机床的运动学和动力学特性以实现五坐标机床的高速和高效运行。     

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。     

ENHANCEMENT OF PRODUCTIVITY BY INTELLIGENT PROGRAMMING OF FEED RATE IN 3-AXIS MILLING

An optimized feed scheduling strategy (OFSS) is proposed in this paper to maximize the metal removal rate in 3-axis milling while guaranteeing the machining accuracy. This strategy integrates the feed drive dynamics, described by the acceleration/deceleration (Acc/Dec) profile, with the minimum-time trajectory planning in order to achieve the desired feed rate at the appropriate position. An optimum use of the feed drive capabilities is considered to track the changes in the cutting geometry along the tool path. Therefore, this strategy combines different constraints and various criteria in modifying the feed rate to maintain near-constant cutting force resulting in highly non-linear problem. The constraints include the cutting force, the feed rate boundaries, the contour error and the characteristics of the (Acc/Dec) profile. The criteria are the maximum production rate, the machining accuracy and safety. The performance of the OFSS in terms of these criteria, is compared to two end milling operations where the trajectory planning disregards the feed drive dynamics. The first is based on a feed scheduling strategy using control points (FSCP). The second is a milling operation with nominal feed rate. By increasing the feed rates, the OFSS improves the machining accuracy, reduces the machining time, and allows a better regulation of the cutting force.     

Machining simulation and system integration combining FE analysis and cutting mechanics modelling

This work presents a method for machining complex three-dimensional surfaces using only one axis of controlled motion for positioning a cutting tool on a specially designed numerically controlled (NC) machine. This single controlled axis lathe is configured like a lathe, but is used to produce complex sculptured surfaces out of wood. This is accomplished by mechanically linking two axes of motion to produce a fixed helical footprint of a tool path with constant step-over distance. As the linked axes are rotated, their location is measured by an encoder and passed directly to a personal computer (PC). Software running on the PC determines the depth of the computer-controlled axis. The depth information is used to control the depth axis. Several test pieces have been machined out of cedar for evaluating the method.     

ENHANCEMENT OF PRODUCTIVITY BY INTELLIGENT PROGRAMMING OF FEED RATE IN 3-AXIS MILLING

An optimized feed scheduling strategy (OFSS) is proposed in this paper to maximize the metal removal rate in 3-axis milling while guaranteeing the machining accuracy. This strategy integrates the feed drive dynamics, described by the acceleration/deceleration (Acc/Dec) profile, with the minimum-time trajectory planning in order to achieve the desired feed rate at the appropriate position. An optimum use of the feed drive capabilities is considered to track the changes in the cutting geometry along the tool path. Therefore, this strategy combines different constraints and various criteria in modifying the feed rate to maintain near-constant cutting force resulting in highly non-linear problem. The constraints include the cutting force, the feed rate boundaries, the contour error and the characteristics of the (Acc/Dec) profile. The criteria are the maximum production rate, the machining accuracy and safety. The performance of the OFSS in terms of these criteria, is compared to two end milling operations where the trajectory planning disregards the feed drive dynamics. The first is based on a feed scheduling strategy using control points (FSCP). The second is a milling operation with nominal feed rate. By increasing the feed rates, the OFSS improves the machining accuracy, reduces the machining time, and allows a better regulation of the cutting force.     

Dynamic contour error compensation in micro/nano machining of hardened steel by applying elliptical vibration sculpturing method

In this study, a novel dynamic contour error compensation technique has been proposed for the elliptical vibration cutting process achieved through the ultra-precision amplitude control. The influence of the contour error, triggered due to the inertial vibrations of the friction-less feed drive system, on the machining accuracy deterioration has been experimentally investigated. In order to reduce the contour error, a compensation method utilizing a real-time amplitude control in the elliptical vibration cutting process has been applied. In the proposed method, the dynamic motion error along the depth of cut direction is detected by utilizing the precise linear encoders installed on the feed drive system. The motion error in real-time is subsequently converted into cancelling amplitude command for the vibration control system of the ultrasonic vibrator, thus, guaranteeing that the envelope of the vibration amplitudes auto-tracks the dynamic reference position of the motion axis in the depth of cut direction. Due to this, a constant nominal depth of cut can be obtained even though the inertial vibrations disturb the feed drive control during machining. A series of experimental investigations have been conducted in order to analyze the machining performance by employing the proposed method. The maximum machining error is observed to significantly decrease from 0.6 to 0.04 μm by applying the proposed compensation method. Finally, the micro dimple array with a structural height from about 200 to 600 nm could be accurately fabricated with a maximum machining error of 36.8 nm, which verified the feasibility of the proposed amplitude control compensation method.