Elliptical model for surface topography prediction in five-axis flank milling

In five-axis flank milling operations,the intersecting surfaces of different cutting edges create roughness on the milled surfaces that cannot be ignored in situations with strict requirements,especially in aeronautical manufacturing.To focus on motion problems in milling operations,this paper presents a new model that utilizes elliptical paths as cutting edge trajectories on 3D surface topography machined by peripheral milling.First,the cutter parallel axis offset and location angle are considered,which change the location of the ellipse center and intersection point of the cutting edges.Then,through the proposed model,the predicted surface topography is obtained,and the factors that affect the development tendency of roughness are analyzed.Next,the effects of the cutter location position(CLP)geometric parameters,cutter parallel axis offset and curvature on the roughness are evaluated by a numerical simulation.Finally,machining tests are carried out to validate the model predictions,and the results show that the surface topography predictions correspond well with the experimental results.

Global optimization of tool path for five-axis flank milling with a cylindrical cutter

In this paper, optimum positioning of cylindrical cutter for five-axis flank milling of non-developable ruled surface is addressed from the perspective of surface approximation. Based on the developed interchangeability principle, global optimization of the five-axis tool path is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation. By using the signed point-to-surface distance function, tool path plannings for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework. Based on the second order Taylor approximation of the distance function, a sequential approximation algorithm along with a hierarchical algorithmic structure is developed for the optimization. Numerical examples are presented to confirm the validity of the proposed approach.

Five-axis flank milling tool path generation with curvature continuity and smooth cutting force for pockets

In order to ensure machining stability,curvature continuity and smooth cutting force are very important so as to meet the constraints of both cutting force and kinematics of machine tools.For five-axis flank milling,it is difficult to meet both of the constraints because tool path points and tool axis vectors interact with each other.In this paper,multiple relationships between tool path points and tool axis vectors with cutting force and kinematics of machine tools are established,and the strategies of corner-looping milling and clothoidal spirals are combined so as to find feasible solutions under both of the constraints.Tool path parameters are iterated by considering the maximum cutting force and the feasible range of the tool axis vector,and eventually a curvature continuity five-axis flank milling tool path with smooth cutting force is generated.Machining experimental results show that the conditions of cutting force are satisfied,vibration during the process of machining is reduced,and the machining quality of the surface is improved.

A New Dynamics Analysis Model for Five-Axis Machining of Curved Surface Based on Dimension Reduction and Mapping

The equipment used in various fields contains an increasing number of parts with curved surfaces of increasing size.Five-axis computer numerical control(CNC)milling is the main parts machining method,while dynamics analysis has always been a research hotspot.The cutting conditions determined by the cutter axis,tool path,and workpiece geometry are complex and changeable,which has made dynamics research a major challenge.For this reason,this paper introduces the innovative idea of applying dimension reduction and mapping to the five-axis machining of curved surfaces,and proposes an efficient dynamics analysis model.To simplify the research object,the cutter position points along the tool path were discretized into inclined plane five-axis machining.The cutter dip angle and feed deflection angle were used to define the spatial position relationship in five-axis machining.These were then taken as the new base variables to construct an abstract two-dimensional space and establish the mapping relationship between the cutter position point and space point sets to further simplify the dimensions of the research object.Based on the in-cut cutting edge solved by the space limitation method,the dynamics of the inclined plane five-axis machining unit were studied,and the results were uniformly stored in the abstract space to produce a database.Finally,the prediction of the milling force and vibration state along the tool path became a data extraction process that significantly improved efficiency.Two experiments were also conducted which proved the accuracy and efficiency of the proposed dynamics analysis model.This study has great potential for the online synchronization of intelligent machining of large surfaces.

Generation of tool path for flank milling in divided areas

Presents the division of non developable ruled surface into divided small areas and flank milling in these divided areas to improve machining efficiency and machined surface quality by controlling the machining error for each area, and the algorithms developed for generation of tool path and calculation of errors, and concludes from computer simulation results that the algorithms are correct.

New Mathematical Method for the Determination of Cutter Runout Parameters in Flat-end Milling

The cutting force prediction is essential to optimize the process parameters of machining such as feed rate optimization, etc. Due to the significant influences of the runout effect on cutting force variation in milling process, it is necessary to incorporate the cutter runout parameters into the prediction model of cutting forces. However, the determination of cutter runout parameters is still a challenge task until now. In this paper, cutting process geometry models, such as uncut chip thickness and pitch angle, are established based on the true trajectory of the cutting edge considering the cutter runout effect. A new algorithm is then presented to compute the cutter runout parameters for flat-end mill utilizing the sampled data of cutting forces and derived process geometry parameters. Further, three-axis and five-axis milling experiments were conducted on a machining centre, and resulting cutting forces were sampled by a three-component dynamometer. After computing the corresponding cutter runout parameters, cutter forces are simulated embracing the cutter runout parameters obtained from the proposed algorithm. The predicted cutting forces show good agreements with the sampled data both in magnitude and shape, which validates the feasibility and effectivity of the proposed new algorithm of determining cutter runout parameters and the new way to accurately predict cutting forces. The proposed method for computing the cutter runout parameters provides the significant references for the cutting force prediction in the cutting process.

Investigation on tool wear and tool life prediction in micro-milling of Ti-6Al-4V

Short tool life and rapid tool wear in micromachining of hard-to-machine materials remain a barrier to the process being economically viable. In this study, standard procedures and conditions set by the ISO for tool life testing in milling were used to analyze the wear of tungsten carbide micro-end-milling tools through slot milling conducted on titanium alloy Ti-6 Al-4 V. Tool wear was characterized by flank wear rate,cutting-edge radius change, and tool volumetric change. The effect of machining parameters, such as cutting speed and feedrate, on tool wear was investigated with reference to surface roughness and geometric accuracy of the finished workpiece. Experimental data indicate different modes of tool wear throughout machining, where nonuniform flank wear and abrasive wear are the dominant wear modes. High cutting speed and low feedrate can reduce the tool wear rate and improve the tool life during micromachining.However, the low feedrate enhances the plowing effect on the cutting zone, resulting in reduced surface quality and leading to burr formation and premature tool failure. This study concludes with a proposal of tool rejection criteria for micro-milling of Ti-6 Al-4 V.

Dynamic synchronous motion accuracy measurement and estimation for a five-axis mirror milling system

A mirror milling system(MMS)comprises two face-to-face five-axis machine tools,one for the cutting spindle and the other for the support tool.Since it is essential to maintain the cutter and support coaxial during the cutting process,synchronous motion accuracy is the key index of the MMS.This paper proposed a novel method for measuring and estimating the synchronous motion accuracy of the dual five-axis machine tools.The method simultaneously detects errors in the tool center point(TCP)and tool axis direction(TAD)during synchronous motion.To implement the suggested method,a measurement device,with five high-precision displacement sensors was developed.A kinematic model was then developed to estimate the synchronous motion accuracy from the displacement sensor output.The screw theory was used to obtain the analytical expression of the inverse kinematic model,and the synchronous motion error was compensated and adjusted based on the inverse kinematic model of the dual five-axis machine tools.TCP and TAD quasi-static errors,such as geometric and backlash errors,were first compensated.By adjusting the servo parameters,the dynamic TCP and TAD errors,such as gain mismatch and reversal spike,were also reduced.The proposed method and device were tested in a large MMS,and the measured quasi-static and dynamic errors were all reduced when the compensation and adjustment method was used.Monte Carlo simulations were also used to estimate the uncertainty of the proposed scheme.

基于刀齿轨迹模型的五轴侧铣加工铣削力预测

在五轴侧铣加工过程中刀具的刀轴姿态变化复杂,导致瞬时切屑厚度计算困难。为提高切削力的预测精度,首先通过五轴侧铣几何模型描述了圆柱铣刀的刀齿运动轨迹,在建立微元切削力模型后,提出了一种瞬时切屑厚度的计算方法,计算当前切削刃上切削点到前几个刀齿回转圆柱面的映射距离,并在齐次坐标变换下,将空间中的线面求交计算转换成二维平面的线与圆弧的求交运算,在考虑刀具跳动对圆弧轨迹的影响后,求解方程组获得瞬时切屑厚度值。最后在五轴机床上进行了切削力试验,对比测量的力数据发现,仿真结果无论趋势还是大小都和实测值较好地吻合,验证了所建立的切削力预测模型的有效性。

基于接触区域自适应调整的圆弧头立铣刀后刀面磨削轨迹精确计算方法

为保证圆弧头立铣刀后刀面的加工精度,提出一种基于接触区域自适应调整的圆弧头立铣刀后刀面磨削轨迹精确计算方法。通过圆弧头立铣刀结构特征分解构建了后刀面的数学模型;通过计算砂轮和后刀面之间的磨削接触区域,自适应修正砂轮姿态,避免磨削干涉,实现了后刀面几何参数控制的准确性和一致性,并保证了曲面的光滑连接。最后,在VC++平台算法模块开发的基础上,通过加工仿真和磨削试验验证了该算法的有效性。

五轴侧铣加工铣削接触区域建模

五轴侧铣加工时,刀具姿态的时变性使得加工过程中的刀具和工件接触区域复杂多变,提取铣削接触区域对研究多轴铣削中的切削力、加工误差和颤振稳定性至关重要,对此提出一种无需提取待加工表面信息的瞬时接触轮廓解析法。使用一系列离散切削微元表示刀具,根据刀具位置和铣削参数获得各切削微元特征点集,并使用样条曲线对其拟合。综合距离和进给方向条件限制筛选出每段切削微元的切入/切出点,同时表示在工件坐标系中获得瞬时接触轮廓。仿真和试验结果表明,最大切入/切出角误差均在3%以内,且计算效率约为实体建模法的9.5倍,证明了本方法的准确性和高效性。

Tool path generation for 5-axis flank milling of ruled surfaces with optimal cutter locations considering multiple geometric constraints

Ruled surfaces found in engineering parts are often blended with a constraint surface,like the blade surface and hub surface of a centrifugal impeller.It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path,while current models in fulfilling these goals are complex and rare.In this paper,a tool path planning method with optimal cutter locations(CLs)is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints.To be specific,a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter.Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm.Fairing angular curves are derived from candidates in this pool,and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness.On this basis,an adaptive interval determination model is developed for deviation control of interpolated cutter locations.This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique.Finally,tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time,and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.

高效铣刀后刀面摩擦应力波传播与衰减特性

高效铣削加工过程中,受高频、断续切削载荷作用,铣刀与工件接触角度、姿态频繁变动,使得刀工界面相对摩擦力及其引起的应力波传播、衰减过程动态变化,导致高效铣削过程摩擦磨损、磨损寿命难以准确识别及预测。构建刀齿误差和铣削振动影响下的铣刀-工件动态接触关系模型,解算铣刀刀齿后刀面摩擦力,根据一维弦线理论,提出刀齿后刀面摩擦应力波传播距离、变化速率与衰减率的解算方法。结果表明,靠近刀尖处应力波峰值和变化速率更大,高效铣刀摩擦应力波衰减过程呈偏态指数型衰减。应力波解算方法的关联度验证结果表明,刀齿后刀面特征点能量与试验累积磨损深度的关联度大于0.8,验证了模型的准确性。

基于螺旋接触线的五轴侧铣刀具定位方法

针对五轴侧铣加工非可展直纹面时刀具与设计曲面相互干涉的问题,提出了一种基于螺旋接触线的刀具定位方法。首先,基于Z-buffer法建立单个刀位下的误差解析模型,以评估刀具定位方法的优劣。其次,根据非可展直纹面的扭转特性,构造刀轴矢量的数学模型,同时分析刀具-工件接触线的性质及参数表达式。再次,考虑实际加工中的非线性加工误差,通过运动学变换对全局刀位进行路径插补优化。最后,基于改进两点偏置法、最小二乘法及所提出的方法进行仿真分析并对比3种方法所产生的误差,同时基于后2种方法进行实验验证。仿真和实验结果表明,所提出的方法能够有效减小侧铣加工中的原理误差,可为非可展直纹面的五轴侧铣加工提供一定的参考依据。

IMPROVING THE SIMULATION EFFICIENCY IN FIVE-AXIS MILLING BY USING AN ADVANCED OCTREE AND AN IMPLICIT FORMULA OF A GENERALIZED CUTTER

This paper presents an advanced octree(AO-rep) model and an implicit formula of a generalized cutter model for five-axis milling simulation.First,the main ideal of the AO-rep model is building a hierarchical structure and representing solid volumes.The AO-rep model utilizes an octree to cull unrelated voxels,and generates a small-scale voxel model in grey octants when a cutter intersects these octants.Using a simplified intersection computation between a cube and triangles in E^3,an STL model can be converted into its AO-rep model at a preprocessing stage.Second,the authors formulate an implicit function of a generalized cutter in moving cutter frame,and determine the function in fixed workpiece frame using the theory of a rigid body motion.Finally,the authors make a simulation of machining an impeller.The result shows that the proposed approach has a high performance of time and space.

Online tool-wear measurement of small-diameter end mills based on machine vision

The objective of this study was to develop an online tool-wear-measurement scheme for small diameter end-mills based on machine vision to increase tool life and the production efficiency. The geometrical features of wear zone of each end mill were analyzed, and three tool wear criterions of small-diameter end mills were defined. With the uEye camera, macro lens and 3-axis micro milling machine, it was proved the feasibility of measuring flank wear with the milling tests on a 45# steel workpiece. The design of experiment （DOE） showed that Vc was the most remarkable effect factor for the flank wear of small-diameter end mill. The wear curve of the experiments of milling was very similar to the Taylor curve.

基于铣削力参数化模型的铣刀非均匀磨损状态监测方法研究

在航空结构件钛合金零件数控加工中,刀具非均匀磨损状态对工件的最终质量影响很大。为了及时发现并控制因刀具非均匀磨损导致的异常加工状态,对钛合金加工刀具非均匀磨损状态监测方法进行了研究。建立了基于刀具刃线参数化模型的铣削力参数化模型,实现了对钛合金加工刀具非均匀磨损状态的监测,解决了零件单件或首件加工中样本数据缺失条件下的钛合金加工刀具非均匀磨损状态准确监测难题。

Prediction of cutting forces in flank milling of parts with non-developable ruled surfaces

Predicting the cutting forces required for five-axis flank milling is a challenging task due to the difficulties involved in determining the Undeformed Chip Thickness(UCT) and CutterWorkpiece Engagement(CWE). To solve these problems, this paper presents a new mechanistic cutting force model based on the geometrical analysis of a flank milling process. In the model,the part feature and corresponding cutting location data are taken as input information. The UCT considering cutter runout is calculated according to the instantaneous feed rate of the element cutting edges. A solid-discrete-based method is used to precisely and efficiently identify the CWE between the end mill and the surface being machined. Then, after calibrating the specific force coef-ficients, the mechanistic milling force can be obtained. During the validation process, two practical operations, three-axis flank milling of a vertical surface and five-axis flank milling of a nondevelopable ruled surface, are conducted. Comparisons between predicted and measured cutting forces demonstrate the reliability of the proposed cutting force model.

基于三点偏置刀位偏差补偿的五轴侧铣加工路径优化方法

直母线刀具在五轴侧铣加工非可展直纹面过程中难与曲面准确贴合,为解决此问题,提出通用的三点偏置方法完成刀具初始定位,沿刀轴计算刀具与被加工曲面之间的几何偏差,基于偏差补偿思想偏置得到轴迹面采样点在空间中的理想分布,据此建立轴迹面拟合模型,通过奇异值分解(SVD)算法求解该模型,以加工偏差绝对值之和最小为目标,求解得到最优加工路径。仿真算例表明,与基于智能算法的侧铣路径优化方法相比,所提方法在提升加工精度方面优势明显。

平行砂轮磨削球头立铣刀后刀面的轨迹算法研究

针对磨削球头立铣刀周刃偏心型后刀面的工艺参数化定义不完善,由砂轮姿态突变导致的后刀面磨削宽度不均匀等问题,提出了一种球头立铣刀后刀面采用平行砂轮加工的磨削轨迹算法。该算法首先建立了一种具有齿偏中心量的球头立铣刀刀刃曲线模型,根据模型结构对相关坐标系及其转换关系进行了定义。随后,在描述砂轮姿态的坐标系下构建了砂轮初始磨削姿态模型以及对其工艺参数进行了定义,并根据转换关系对砂轮磨削姿态进行了统一表达。最终,算法的验证通过仿真及实际加工环境进行,并通过测量仪器对后刀面相关参数进行了测量,算法的可行性及准确性得到了进一步验证。