自由曲面的五坐标端铣加工研究

针对自由曲面的五坐标端铣加工，建立了平底刀有效切削轮廓的数学模型，分析了刀具姿态对有效切削轮廓及加工效率的影响。沿行距方向，通过对被加工曲面法截线的偏置曲线与有效切削轮廓求交，得到一种走刀行距的计算方法。探讨了影响走刀行距的因素，在不发生干涉的前提下，小的后跟角和侧偏角有利于加工行距的提高。结合平底刀加工不发生过切的充要条件和被加工曲面沿行距方向的法曲率，给出了后跟角的自动计算方法。算例表明，所提出的走刀行距及刀具倾角的计算方法合理可行，能够有效提高计算精度和加工效率。     

Optimising tool positioning for achieving multi-point contact based on symmetrical error distribution curve in sculptured surface machining

The multi-point tool positioning algorithms produce much larger machining strip width than the single-point algorithms and apparently reduce the actual machining time. This paper presents a tool positioning algorithm for multi-point machining of sculptured surface, which is excellent at dealing with both of concave and convex surfaces. The proposed method is based on the middle-point error control (MPEC) method, which means the connection point between cutter and surface corresponds to the middle point of error distribution curve. Usually, only one cut contact (CC) point can be obtained with this method. Thus, the proposed method improved the MPEC method for achieving two CC points. At first, the shape of error distribution curve is investigated, and its asymmetry is evaluated. Secondly, the error distribution curve becomes symmetrical after the cutter is rotated with a roll angle, and the cutter is separated with surface at the same time. Finally, the minimum tilt angle is found, and two CC points are obtained without gouging. Machining experiment is conducted to verify the proposed method, and the result reveals that the machining strip width is increased apparently and the tool position is almost unchanged after the adjustment with proposed method. Simulation, measurement, and analysis are also given in the part of the experiment.     

Face-milling spiral bevel gear tooth surfaces by application of 5-axis CNC machine tool

In order to solve some common problems of CNC-machined spiral bevel gears such as small cutting strip width and poor surface quality, while milled by the ball-end, a machining method of face milling using a disk cutter with a concave end is presented. The research theories are based on the foundation of spiral bevel gears’ geometry structure. Firstly, a bigger diameter disk cutter with a concave end is selected. Then, change the setting order of cutter orientation angles. The functions of cutter tilt and yaw angle are separated, and tooth surfaces machined with big cutting strip width and no bottom land gouge can be expected. Since the cutter yaw angle, determined firstly by cutting contact point, positions in the tooth surface machine, the bottom land gouge interference can be avoided effectively. Then, the tilt angles of the gear pair, both side tooth surfaces, are determined by the theory of sculptured surfaces machined by the flat-end cutter, respectively. As a result, the improved cutting strip width and machining efficiency can be realized. Finally, feasibility of this method is verified through machining experiment and measurement of a spiral bevel gear pair.     

复杂曲面五坐标数控加工刀具轨迹的规划算法

提出了复杂曲面五坐标数控加工刀具轨迹的规划算法。该算法在保证刀具不与被加工曲面发生干涉的基础上 ,使得刀具扫描面与被加工曲面在刀触点处切平面上每个方向的曲率相匹配 ,由此规划的等残留高度刀具轨迹能改善曲面加工精度和加工效率     

圆环面刀具五坐标数控加工旋转切触刀位算法

针对圆环面刀具加工开阔自由凹曲面,提出一种新的五坐标旋转切触刀位算法。算法来自于传统多点切触加工的逆向思考,首先确定刀具在工件曲面等距面上局部坐标系中的初始位置,然后优化调整刀具的后跟角和侧偏角,使刀具表面和工件曲面在不发生局部过切的前提下在最小主曲率方向两侧实现两点切触。与传统的多点刀位算法根据两个切触点来计算刀位不同,旋转切触刀位算法通过刀具的后跟角和侧偏角来确定最优刀位,而刀具表面和工件曲面之间的两个切触点则不需要求出。实例计算和加工仿真表明,旋转切触刀位算法不仅能够有效地产生无局部过切的多点刀位,从而不需要额外的局部过切检测及修正过程,而且在相同的加工误差下其产生的加工带宽约为UG算法的两倍,加工效率得到明显提高。     

类回转体曲面数控加工刀位轨迹规划

针对类回转体曲面高速进给数控加工,提出螺旋线驱动方式下圆环刀具加工轨迹的规划方法。构造螺旋线作为类回转体曲面的导动线,根据曲面上已知接触点轨迹的切线方向估算后续导动点对应的初始接触点。计算初始接触点处圆环刀具的刀心位置,再计算初始刀心位置与后续导动点对应的目标刀位点分别在圆周方向以及轴向的距离差值,利用相邻刀位点与相邻接触点存在的准相似关系,得到接近目标接触点的搜索方向和步长,经过迭代得到目标接触点和刀位点。在分析接触点处曲面曲率和圆环刀曲率的基础上,给出圆环刀加工误差计算方法。将所提出的算法用于鞋楦的五轴数控轨迹规划中,计算结果表明,该算法搜索效率较高,具有理论和实际应用价值,并通过鞋楦的五轴数控加工试验验证了算法的有效性。     

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.     

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。     

平底刀最优刀轴矢量规划算法

在进行自由曲面平底刀五轴数控加工刀轴矢量规划时,现有算法多以材料去除率最大作为优化目标,然而加工效率最高的刀轴矢量不一定是刀具最优姿态,还需要综合考虑加工质量、刀轴光顺等因素。从这几个方面建立单个刀轴矢量和相邻刀轴矢量光顺性的度量指标,并以归一化度量指标加权和最小作为优化目标建立刀轴矢量优化模型,经理论分析将多目标规划问题转化为力学平衡问题,弹簧模型中高斯球面上运动节点的平衡位置就是最优刀轴矢量。仿真结果表明SE权因子影响加工效率,DW、DM权因子影响机床运动平稳性,DF权因子影响切削条件,选择合适的权因子可以获得材料去除率大、加工效率高以及在工件坐标系、机床坐标系和进给坐标系下光顺的刀轴矢量。     

基于定向距离理论的五轴加工刀具轨迹规划算法

针对环形刀五轴加工自由曲面的残留误差问题,在传统等残留高度算法的基础上,提出了一种基于定向距离理论的等最大残留高度刀具轨迹规划算法。首先根据微分几何理论计算已知刀触点的初始侧向行距,并在侧向行距方向进行偏置得到相邻刀触点;然后以基于定向距离理论的残高误差计算模型对相邻刀触点间的实际残高值进行计算;最后通过迭代计算规划出等最大残留高度的相邻刀具轨迹。如此循环,从而获得整个曲面的刀具轨迹。实验结果表明,相对于商用软件MasterCAM9.0,该算法在充分保证曲面加工质量的同时最大限度地减小了刀具轨迹的总长度,从而提高了加工效率。     

复杂自由曲面曲率分布特征对数控铣削性能的影响

针对复杂自由曲面的数控铣削性能难预测的问题,提出曲面曲率分布特征值,用于评价数控加工效率和加工精度。在构建的刀位面上策划等间距行走的刀位轨迹,建立刀位轨迹长度和刀具间的最大残余高度作为加工效率和加工精度的评价指标,分析曲面曲率分布特征值对加工效率和加工精度的影响。试验结果证明该自由曲面数控加工模式的有效性。分析发现,随着曲面曲率分布特征值增大,刀位轨迹长度和最大残余高度同时增加,导致加工效率和加工精度同时下降。此外,在曲面曲率分布特征值小于0.5 mm–1时,加工效率降低幅度不超过7 %,但加工精度却下降6～7倍。因此,曲面曲率分布特征值可用于评价和预测复杂自由曲面的数控铣削性能。     

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.     

Optimising Tool Positioning for End-Mill Machining of Free-Form Surfaces on 5-Axis Machines for both Semi-Finishing and Finishing

End-milling of free-form surfaces on 5-axis NC machine tools is a complex problem which has been studied by a large number of research scientists. When end-milling non-convex surfaces there is a risk of interference between the tool and the surface. Using a 5-axis NC machine tool enables the tool to be oriented in any spatial direction to access a given point. This means interference can be avoided and the position of the tool can be optimised so as to minimise residual material. Here, a new method is presented for tool positioning in end-milling of free-form surfaces based on evaluating the interference for a set of test points distributed around the circumference of the tip of the tool. Distinction is made between the cases of semi-finishing and finishing which can be performed using a large diameter flat-end tool and a toroidal tool, respectively. Further, all developments are implemented for interactive use in a CAD/CAM software environment.     

鼓形砂轮周磨自由曲面刀位算法

对采用鼓形砂轮周磨自由曲面的刀位计算进行了研究。为了提高加工效率，提出了一种基于避免加工中砂轮和工件曲面局部干涉的鼓形砂轮几何参数的优化方法。在刀位计算中，砂轮被限定在摆刀平面中旋转；离散鼓形砂轮表面，计算采样点到工件曲面的有向距离，获得当前刀位的加工误差分布和加工带宽；以砂轮轴和工件曲面最小法曲率方向的夹角为优化变量，以当前刀位的加工带宽的最大化为优化目标，用格点法进行了鼓形砂轮周磨自由曲面的刀位优化。利用UG二次开发技术编程，生成了Bezier曲面的加工轨迹的计算实例，验证了所提出的砂轮几何参数和刀位的优化算法。     

Near net-shape five-axis face milling of marine propellers

We present an optimal cutter location (CL) data computation for face-milling of large marine propellers composed of CL point optimization and CL path optimization on a given tool path. The CL point optimization at a single cutter contact (CC) point is conducted by maximizing the effective radius of the face milling cutter, while the CL path optimization on a series of CC points is performed by conforming deviation of the tool-swept surface from the design surface between consecutive CL data to a given machining tolerance. The proposed algorithm was implemented and applied to the machining of a large marine propeller which proved effective from a quantitative point of view, and is used on the shop floor in a Korean ship building company.     

五坐标端铣数控加工计算理论分析

本文介绍了五坐标端铣数控加工中的后跟角计算方法及刀位计算方法,分析了加工误差,包括直线逼近误差和刀轴摆动误差,提出了刀轴摆动误差补偿方法——刀具切触点偏置法,给出了走刀步长、走刀步距及刀具半径计算公式。     

Correcting and compressing interpolation algorithm for free-form surface machining

The existing interpolation algorithm cannot meet the need of high-speed and high-accuracy machining of a free-form surface. So this paper proposed a correcting and compressing interpolation algorithm. Depending on the distance and angle evaluated from the adjacent command points, the machining path of free form can be divided into two machining types. For those regions where the accurate figure is critical such as corners, the convention linear interpolation is performed exactly between the adjacent command points. For those regions having a large radius of curvature where the smooth figure is critical, firstly, the interior point selection method based on circle transition is derived to reduce the tolerance between the machining path and the original surface; secondly, the interior point correction method based on the least-square method is proposed to reduce the calculation error and round-off error in the interior point and estimate the first- and second-order derivative vectors of the interior point; thirdly, the shape-defining point is selected by the bend direction of the machining path and fitted to a quintic spline curve which has the C2 continuity; fourthly, the fitting accuracy controlling method is proposed to ensure the machining accuracy; lastly, the curve interpolation is performed on the fitted smooth curve. Machining tests carried out on a vertical machining center show that the proposed algorithm can improve the machining efficiency and machining quality of a free-form surface.     

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact(CC) point,while not considering the smoothness and continuity of a whole tool path.When the surface curvature varies significantly,a local abrupt change of tool paths will happen.The abrupt change has a great influence on surface machining quality.In order to keep generated tool paths smooth and continuous,a five-axis tool positioning algorithm based on smooth tool paths is presented.Firstly,the inclination angle,the tilt angle and offset distance of the tool at a CC point are used as design variables,and the machining strip width is used as an objective function,an optimization model of a local tool positioning algorithm is thus established.Then,a vector equation of tool path is derived by using the above optimization model.By analyzing the equation,the main factors affecting the tool path quality are obtained.Finally,a new tool position optimization model is established,and the detailed process of tool position optimization is also given.An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine,and the machined blade surface is measured with a coordinate measuring machine(CMM).Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous,improve the tool path quality,avoid the local abrupt change of tool paths,and enhance machining quality and machining efficiency of sculptured surfaces.     

自由曲面数控加工刀具轨迹生成的约束条件分析

在提出自由曲面数控加工过程和刀具轨迹的规划原则情况下,分析无干涉控制、恒表面速度进给、伺服能力控制和相邻加工曲线影响等轨迹控制的约束条件,实时对轨迹的生成进行系统优化控制。通过系统分析刀具轨迹生成的约束条件,为刀具轨迹优化控制提供决策,对提高自由曲面的切削质量和加工效率具有重要意义。