复杂曲面的数控加工误差分析

针对复杂曲面的多轴数控加工,应用数学知识建模,从理论上分析了平底铣刀刀具加工复杂曲面时的误差,得出了影响数控加工精度的主要因素并提出了误差补偿方法,为控制多轴数控加工的误差提供了理论依据与补偿算法,对高精度复杂曲面的数控加工具有借鉴意义。     

复杂曲面几何仿真与误差分析

针对复杂曲面数控加工中加工误差进行了研究,分析了各种铣刀的几何特征,归纳出一种用参数表示的通用铣刀模型,并以通用铣刀模型为基础,结合复杂曲面的包络法数控加工原理,给出了一种基于啮合基本定理的点接触包络加工表面的几何仿真算法.利用几何仿真的计算结果,分析复杂曲面加工中的法向误差,该仿真算法把复杂的仿真问题转化成了非线性方程组的求解问题,从而使仿真过程得到简化,对于提高数控编程精度具有重要意义.还以截面包络法数控加工螺旋面为例,验证了该仿真算法,并分析了螺杆加工精度.     

仿真加工编程误差分析算法

对于复杂曲面来说,要分析实际加工曲面与理论曲面之间的误差情况,应该分析曲面上各点处的法向误差,这是由于复杂曲面的特殊性所决定的。复杂曲面在空间上具有复杂形状,如果单一分析某一方向上的误差,不足以说明实际曲面与理论曲面的误差情况,但只要求出曲面上各点处的法向误差,就可以真正确定实际曲面与理论曲面之间的差异程度。在此背景下,该文提出了一种新的算法,将解决如何分析实际加工曲面与理论曲面之间的法向误差的问题。     

基于三角网格模型的自由曲面自适应测点规划

测点自适应规划是复杂曲面类零件在加工质量数字化测量环节的关键。针对自由曲面自适应测点规划问题,开展曲面自适应布点研究。设置给定条件下的测点密度判定方法,生成样本集,再训练神经网络组合模型,构建测点密度预测模型,用于精简测点数量;按照给定的测点密度阈值自适应获取聚类中心,并采用区域生长算法将曲面划分为测点密度大致相等的子曲面;以子曲面为基础,根据其测点密度进行局部均匀布点,提出一种基于曲面划分的自适应测点规划算法。实验结果表明,在该算法的误差结果接近样本组的情况下,所需测点数量较迭代重构算法明显减少;在相同测点数量下,该算法的误差比均匀布点算法更接近样本组。根据测点密度,将曲面由一个复杂、非规则的模型分成若干测点密度相近的子曲面可以减少测点数量;所规划的测点能较好地描述自由曲面的加工质量。     

复杂曲面误差评估的最小区域包容配准算法

鉴于复杂曲面误差评估问题中,不同配准方法往往导致不同的评估结果,在精度要求较高或误差形势较严峻时,恰当的配准位姿具有重要意义,提出一种面向复杂曲面误差评估的最小区域包容配准算法。为解决计算复杂性,采用凝聚函数一致光滑逼近不连续的极差函数,并利用高效有限存储拟牛顿算法求解大规模无约束非线性问题。最近点迭代算法为最小区域包容配准方法提供了收敛条件,同时加快了收敛速度,而且算法容易实施,对复杂曲面扫描数据点云有效。通过仿真平面和实测钣金件的误差评估配准实验说明了所提算法的有效性。     

复杂参数曲面高精度刀具轨迹规划算法

在对等残余高度刀具轨迹规划算法加工参数曲面研究的基础上,提出带有误差补偿值的复杂参数曲面高精度刀具轨迹规划算法——高精度刀轨误差补偿算法。通过分析刀触点及与之相应的相邻路径上的粗、精刀位对应点间的关系,引入误差补偿值以提高精对应刀位点的求解精度,得到经过合理简化的误差补偿值表达式,并得出粗、精对应刀位点与理论刀位点的距离误差表达式。高精度刀轨误差补偿算法可以在满足插补运算实时性要求的前提下,使相邻轨迹上与刀触点相对应的刀位点的参数值计算精度得到极大提高,进而提高复杂参数曲面的加工刀具轨迹精度。以使用平底铣刀为例进行仿真加工,结果表明高精度刀轨误差补偿算法适合进行对复杂参数曲面的高精度加工。     

复杂曲面高效铣削加工的刀具尺寸优选

刀具尺寸是影响复杂曲面数控加工质量和效率的重要因素,基于刀具尺寸与曲面加工质量和效率的函数关系,给出了保证加工曲面精确性的最优小刀具选择方法,建立了以效率最高为目标的合理大刀具尺寸优选算法,并针对几何特征复杂的曲面,提出了以刀具加工有效面积比值为参考的刀具组合选择方法。应用实例表明:该刀具尺寸优选策略在充分保证复杂曲面加工质量的前提下,能有效提高其整体加工效率。     

基于遗传算法和分割逼近法精确计算复杂曲面轮廓度误差

在超精密复杂零件加工与检测技术中,高精度轮廓度误差的评估方法一直是一个研究重点。在分析研究现状基础上,阐明精确计算复杂曲面轮廓度误差需要解决的关键问题,阐述复杂曲面轮廓度误差定义,建立复杂曲面轮廓度误差的数学模型。在分析基于NURBS描述复杂曲面特点基础上,提出分割逼近法计算测点到曲面的最小距离快速简便算法。分析传统遗传算法存在计算精度与编码长度、计算工作量之间的矛盾,提出改进型归一化实数编码的遗传算法,建立相应的交叉算子和变异算子,确立分割逼近法和归一化实数值编码遗传算法相结合计算复杂曲面轮廓度误差的具体步骤。该算法易于计算机实现,且计算精确度高,可以达到任意给定的精度,非常适用于三坐标测量机。     

复杂曲面零件加工精度原位检测系统的残余误差补偿

复杂曲面零件数控加工后直接进行原位加工精度检测和误差补偿,是实现精密产品闭环制造模式的有效途径。原位检测系统的误差来源于测量系统误差和机床运动系统误差,经相关的误差分离与误差补偿后,仍存在较大的残余误差,影响检测精度及其推广应用。针对原位检测系统的检测精度问题,开展检测系统残余误差的回归建模与补偿研究,在机床几何误差、测头半径误差以及预行程等基本误差补偿的基础上,建立基于偏最小二乘回归分析算法的误差回归模型,实现曲面零件测点法矢方向的检测数据二次补偿。在算法实现的基础上,列举复杂曲面零件进行数控加工与在线检测的试验研究。试验结果表明,二次误差补偿方法可以进一步提高原位检测系统的检测精度。     

自适应变步长算法(ABPM)在复杂曲面零件数控加工中的应用

分析传统的固定步长插补算法在复杂曲面零件加工中的缺点,提出自适应变步跃算法,该方法按照曲线的曲率变化而采用相应的步长,算法简单,插补误差小,达到快速、高效的加工效果。     

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.     

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.     

Geometrical Error Analysis and Control for 5-axis Machining of Large sculptured surfaces

One of the important tasks in five-axis machining of large sculptured surfaces is to control and reduce the machined errors. This paper presents the methods to control geometrical errors based on the establishment of the link between geometrical errors and the parameters of tool path planning. Nonlinear errors, which are the majority of geometrical errors during five-axis machining, are is strictly analysed and formulated. An adaptive step length method is proposed to control effectively the cutter contact path error. The measures to reduce the scallop error in machining of the large sculptured surfaces are discussed also. With the combination of this research with CAM software, both large Kaplan and Francis hydroturbine blades have been successfully machined. It shows that the machined errors can be controlled effectively and the machining efficiency can be improved in the machining of the large sculptured surfaces by the proposed methods.     

虚拟制造中基于刀具变形的复杂曲面加工误差预报

复杂曲面加工过程中刀具的弹性变形是产生曲面加工误差的重要原始误差。着重研究了虚拟制造环境下基于球面铣刀弹性变形的曲面加工误差预报模型。研究并建立了球面铣刀加工复杂曲面的切削力模型和刀具弹性变形模型,在此基础上,分析了曲面生成机理,提出了利用曲面变形敏感系数建立刀具弹性变形对法向加工误差的影响关系。利用该模型可以在实际切削加工前对曲面加工误差进行预报,用以进行误差补偿或切削参数优化。最后,以二维半圆形拉伸曲面为例通过切削实验对本文提出的模型进行了验证。     

A unified localization approach for machining allowance optimization of complex curved surfaces

The goal of workpiece localization is of interest to find the optimal Euclidean transformation that aligns the sampled points to the nominal CAD model to ensure sufficient stock allowance during the machining process. In this paper, a unified localization technique is developed for sculptured surface machining. This technique concerns an alignment process to satisfy a user-defined set of constraints for some specific surfaces where the machining allowance is preferentially guaranteed. The mathematical model of the constrained optimization alignment is firstly established, and is efficiently solved by a combination of the multipliers method and the BFGS algorithm to handle the large number of constraints in allowance optimization. To efficiently calculate the Euclidean oriented distance, a novel approach, which combines the robust arithmetic for multivariate Bernstein-form polynomials and Bezier surface segmentation algorithm, is presented based on recursive quadtree decomposition. Two typical sculptured surfaces are used to test the developed algorithm and comparisons between the proposed algorithm and the existing algorithms are given. Experiment results show that the proposed method is appropriate and feasible to distribute the stock allowance for proper sculptured surface machining.     

Complexity analysis and calculation for sculptured surface in multi-axis CNC machining based on surface subdivision

Complexity of sculptured surfaces has a great influence on multi-axis computer numerical control (CNC) machining performances such as processing efficiency, surface quality, and energy consumption. A term called surface machining complexity (SMC) is first presented to describe the complexity level of surface geometrical shape features, and its influence on CNC machining performance. Shape features of sculptured surfaces are classified into seven categories based on surface curvature. An innovative method for quantifying SMC using surface subdivision is proposed. Firstly, representation of sculptured surfaces is introduced. Then, three processes of surface subdivision are presented, which are surface discretization based on iso-parameter line sampling, rough partitioning based on surface shape categories, and region grouping based on two criteria. After that calculation, formulas of SMC including formulas of local SMC and global SMC are developed. The proposed formulas utilize three correction factors to describe the influences of surface size, cutter diameter, grouping order, and mode of different surface shape categories. Finally, the proposed method is applied to calculate SMC for a typical sculptured surface and multi-axis CNC machining experiments to demonstrate the ability of our method, which can form a foundation for further research.     

Influence of the phase composition and microstructure of plasma cladding Fe-Cr-Ni-C alloy coating on residual stress and crack formation

Tool path generation is one of the key challenges in multi-axis sculptured surface machining. Besides geometry accuracy, machining processes have been considered in tool path generation in order to improve machining quality and efficiency as far as possible. However, so far, the machine tool accuracies have not been yet fully taken into account during tool path generation. Contour accuracy is one of the most important precision indexes to guarantee the machining quality of sculptured surfaces. One of the major reasons causing contour error is the dynamic mismatch between feed axes of machine tools. In this study, the mathematic relationship between the cutting direction, dynamic mismatch of feed axes and contour error is theoretically established. The mathematic relationship can be used to calculate the optimal cutting directions which minimize the contour error caused by dynamic mismatch between feed axes during machining a sculptured surface by a three-axis machine tool. A machining experiment is carried out to verify the mathematic relationship. In the experiment, the tool paths are generated along the optimal cutting direction and other cutting directions for comparison. The results show that the contour error under the case of the optimal cutting direction is much smaller than that under the other cases.     

复杂曲面加工干涉避免及轨迹的规划

对复杂曲面进行分析,通过调节后跟角和摆动角来避免刀具与被加工曲面发生干涉,并提出了复杂曲面五坐标数控加工刀具轨迹的规划算法,以改善曲面加工精度和加工效率。     

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.     

基于正向杜邦指标线的五坐标侧铣加工

为实现叶轮类零件的多坐标侧铣加工,通过引入正向杜邦指标线,利用鼓锥形刀对自由曲面的五坐标侧铣加工进行研究。针对具有严格凸切削刃的侧铣加工刀具,提出不发生局部干涉的充要条件是切触点处刀具曲面的正向杜邦指标线位于被加工曲面的正向杜邦指标线之内。给出利用鼓锥形刀侧铣加工自由曲面时实施干涉检查的判断准则以及消除干涉的修正方法,推导出具有严格凸切削刃的刀具在给定的残留高度下侧铣加工带宽的计算方法。在此基础上,利用等残留高度法实现鼓锥形刀侧铣加工自由曲面无干涉刀具轨迹的生成。算例表明,在相同残留高度下,鼓锥形刀侧铣较之球头刀加工效率提高37.44%,说明侧铣加工是提高切削效率和加工质量的一种有效途径。