Optimized tool path generation based on dynamic programming for five-axis flank milling of rule surface

This paper presents a computation scheme that generates optimized tool path for five-axis flank milling of ruled surface. Tool path planning is transformed into a matching problem between two point sets in 3D space, sampled from the boundary curves of the machined surface. Each connection in the matching corresponds to a possible tool position. Dynamic programming techniques are applied to obtain the optimal combination of tool positions with the objective function as machining error. The error estimation considers both the deviation induced by the cutter at discrete positions and the one between them. The path planning problem is thus solved in a systematic manner by formulizing it as a mathematical programming task. In addition, the scheme incorporates several optimization parameters that allow generating new patterns of tool motion. Implementation results obtained from simulation and experiment indicate that our method produces better machining quality. This work provides a concise but effective approach for machining error control in five-axis flank milling.     

Improved positioning for side milling of ruled surfaces: Analysis of the rotation axis's influence on machining error

This article covers side milling of ruled surfaces using a milling cutter. Flank milling is useful for machining objects such as impellers, turbine blades, fan vanes and all workpieces defined by non-developable, ruled surfaces. In the present article, the influence of parameters defining improved positioning described in a previous study will be appraised. The general idea with improved positioning is to position the milling cutter at a tangent to the 2 directrices of the ruled surface while keeping a point of contact between the milling cutter and the rule considered. This is obtained by a rotation at a point about an imposed axis. Having defined calculation of error between the milled surface and the nominal surface, the influence of the point and the axis of rotation of improved positioning on error will be studied. From this, optimum improved positioning parameters allowing minimisation of error between the ruled surface and the milling cutter will be deduced.     

Removing tool marks of blade surfaces by smoothing five-axis point milling cutter paths

Focused on the reverse movements of moving axes along five-axis tool paths, this study presents a procedure of removing a gouge phenomenon on impeller surfaces in five-axis machining. That is, when an impeller of a centrifugal compressor is being cut in finish milling, reverse movements and/or other linearization problems of moving axes along a five-axis interference-free tool path may make a cutter leave tool marks on the impeller surfaces. For generating interference-free cutter location (CL) data needed in rough, semi-finish and finish five-axis cutting processes, first, a simple yet useful approach is proposed. To identify the potential gouge area and to solve the problem for a tool path having reverse motion directions with its moving axes in finish milling, the CL data are further smoothed to remove the reverse movements about its rotating and tilting axes. The effectiveness of this procedure has been experimentally confirmed by successful five-axis finish milling of an impeller without leaving tool marks on its surfaces. In addition, with the spline tool paths, the machining time can be saved up to 23.57%.     

An investigation of workpiece temperature variation in end milling considering flank rubbing effect

Better prediction about the magnitude and distribution of workpiece temperatures has a great significance for improving performance of metal cutting process, especially in the aviation industry. A thermal model is presented to describe the cyclic temperature variation in the workpiece for end milling. Owing to rapid tool wear in the machining of aeronautical components, flank rubbing effect is considered. In the proposed heat source method for milling, both the cutting edge and time history of process are discretized into elements to tackle geometrical and kinematical complexities. Based on this concept, a technique to calculate the workpiece temperature in stable state, which supposes the tool makes reverse movement, is developed. And a practicable solution is provided by constructing a periodic temperature rise function series. This investigation indicates theoretically and experimentally the impact of different machining conditions, flank wear widths and cutter locations on the variation of workpiece temperature. The model results have been compared with the experimental data obtained by machining 300M steel under different flank wear widths and cutting conditions. The comparison indicates a good agreement both in trends and values. With the alternative method, an accurate simulation of workpiece temperature variation can be achieved and computational time of the algorithm is obviously shorter than that of finite element method. This work can be further employed to optimize cutting conditions for controlling the machined surface integrity.     

Quadric method for cutter orientation in five-axis sculptured surface machining

Existing orientation strategies in 5-axis sculptured surface machining mostly limit the cutter to incline in one direction and lack an effective approach to assess the orientation. This paper presents the quadric method (QM) that exploits fully the two orientation angles to maximise the machining efficiency at a cutter contact point. The geometric construction assumes that the local shape of a sculptured surface can be suitably approximated by two quadrics. An upper quadric lying above the surface is used to orient the cutter, and a lower quadric lying below the surface is used to evaluate machined strip width. Then, the cutter orientation is optimised with respect to the width and is guaranteed to give no gouging. Both flat-end cutter and fillet-end cutter are considered. Simulated examples demonstrate the improved machining efficiency of the QM over current published methods.     

Time domain prediction of milling stability according to cross edge radiuses and flank edge profiles

This article proposes a time domain model for predicting an end milling stability considering process damping caused by a variety of cross edge radiuses and flank profiles. The time domain model of calculating indentation areas, as well as regenerative dynamic uncut chips, is formulated for the prediction of the stabilizing effect induced by interference areas between the edge profiles and undulation left on a workpiece. The interference area generates forces against the vibration motion, which acts as a damping effect. In the model, the present and previous angular position of cross radiuses and flank edge profiles are located to calculate the dynamic uncut chip as well as indentation area based on a time history of the dynamic cutter center position. The phenomenon that chatter is damped according to cross edge radiuses and flank edge profiles is successfully simulated with the proposed dynamic model and validated through the extensive experimental tests.     

5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement

Deformation of the part and cutter caused by cutting forces immediately affects the dimensional accuracy of manufactured parts. This paper presents an integrated machining deviation compensation strategy based on on-machine measurement (OMM) inspection system. Previous research attempts on this topic deal with deformation compensation in machining of geometries in 3-axis machine tools only. This paper is the first time that concerned with 5-axis flank milling of flexible thin-walled parts. To capture the machined surface precision dimensions, OMM with a touch-trigger probe installed on machine׳s spindle is utilized. Probe path is planned to obtain the coordinate of the sampling points on machined surface. The machined surface can then be reconstructed. Meanwhile, the cutter׳s envelope surface is calculated based on nominal cutter location source file (CLSF). Subsequently, the machining error caused by part and cutter deflection is calibrated by comparing the deviation between the machined surface and the envelope surface. An iteration toolpath compensation algorithm is designed to decrease machining errors and avoid unwanted interference by modifying the toolpath. Experiment of machining the impeller blade is carried out to validate the methodology developed in this paper. The results demonstrate the effectiveness of the proposed method in machining error compensation.     

An accurate,efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool

Geometric deviation, defined as the difference between the nominal surface and the simulation model of the machined surface, is the fundamental concern of five-axis tool path planning. Since the machined surface is part of the cutter envelope surface generated by the cutter motion, it is necessary to calculate the envelope surface in order to obtain the geometric deviation. In the stage of tool path planning, current approaches calculate the cutter envelope surface by using the cutter motion along the given tool path. However, the cutter motion of practical machining on a specific five-axis CNC machine tool is different from the given tool path. Moreover, the computation is very challenging when the accurate cutter motion of practical machining is applied to calculate the envelope surface. To overcome these two problems, a geometric envelope approach with two major distinctions is proposed in this paper. First, the envelope surface of the cutter undergoing a general motion is efficiently obtained as a closed-form vector expression. Second, the accurate cutter motion, which is determined by machine kinematic and interpolation scheme in practical machining, can be easily applied to calculate the accurate envelope surface. With the envelope surface, the geometric deviation is calculated to estimate the overcut or undercut in five-axis milling. An example is given to demonstrate the validity of the proposed method.     

Machining performance of silicon carbide ceramic in end electric discharge milling

A new process of machining silicon carbide (SiC) ceramic using end electrical discharge milling is proposed in this paper. The process is able to effectively machine a large surface area on SiC ceramic with good surface quality and low cost. The effects of machining conditions on the material removal rate, electrode wear ratio, and surface roughness have been investigated. The surface microstructures machined by the new process are examined with a scanning electron microscope (SEM), an energy dispersive spectrometer (EDS), and an X-ray diffraction (XRD). The results show that the SiC ceramic is removed by melting, evaporation and thermal spalling, the material from the tool electrode can transfer to the workpiece, and a combination reaction takes place during end electric discharge milling of the SiC ceramic.     

Development of freeform grinding methods for complex drill flank surfaces and cutting edge contours

This paper details the development of an innovative freeform grinding method that enables the generation of complex drill flank surfaces and cutting edge contours that are non-quadratic model based. This method allows a direct and independent design of drill cutting angle distributions—normal rake angle (γ_n) and relief angle (α_f). Mathematical formulations were first developed for γ_n and α_f in terms of drill geometric parameters such as helix angle, flute contour, and cutting edge contour. The developed freeform grinding methods enhance the flexibility of the grinding process by enabling the production of drills with convex and concave flank surfaces and complex cutting edge contours with standard wheel sets, eliminating the need to manufacture specially designed form grinding wheels.     

Prediction of cutting force distribution and its influence on dimensional accuracy in peripheral milling

Cutting force has a significant influence on the dimensional accuracy due to tool and workpiece deflection in peripheral milling. In this paper, the authors present an improved theoretical dynamic cutting force model for peripheral milling, which includes the size effect of undeformed chip thickness, the influence of the effective rake angle and the chip flow angle. The cutting force coefficients in the model were calibrated with the cutting forces measured by Yucesan [18] in tests on a titanium alloy, and the model was proved to be more accurate than the previous models. Based on the model, a few case studies are presented to investigate the cutting force distribution in cutting tests of the titanium alloy. The simulation results indicate that the cutting force distribution in the cut-in process has a significant influence on the dimensional accuracy of the finished part. Suggestions about how to select the cutter and the cutting parameters were given to get an ideal cutting force distribution, so as to reduce the machining error, meanwhile keeping a high productivity.     

Deviation of a machined surface in flank milling

The flatness defects observed in flank milling with cutters of long series are mainly due to the tool deflections during the machining process. This article present the results of an identification procedure of the coefficients of a force model for a given tool workpiece couple for the prediction of the defects of the tool during the cutting. The calibration method proposed meets a double aim: to define an experimental protocol that takes the industrial constraints of time and cost into account and to work out a protocol which minimizes uncertainties likely to alter the interpretation of the results (environmental, software or mechanical uncertainties). For that, the procedure envisages the machining of a simple plane starting from a raw part formed by a tilted plane, allowing for the variation of the tool engagement conditions. The tool deviation during the cutting process is indirectly identified by measuring the machined surface. The observed straightness defect conditions can be explained by the evolution of the cutting pressures applied to the cutting edges in catch during the cutter rotation. The precision was considerably improved by the taking into account of the cutter slope defect in the calculation of the load applied to the tool. After identification of the tool-workpiece couple, the prediction model was applied to some examples and allowed to determine the variations of form and position of the surface points with a margin of 5%.     

Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining

Motivated by the excellent performance of three-axis NURBS interpolation, this paper presents a numerically efficient and accuracy controllable five-axis sculptured surface machining method with dual NURBS curve. Unlike the traditional three-axis NURBS interpolation, a dual NURBS format of the five-axis toolpath is developed to accurately and smoothly describe the tool movement in the part coordinate system. Different from the subdivision methods using the Taylor series expansion or inverse function, a piece-wise Bézier curve method is implemented to fast subdivide the NURBS curve within the user-defined tolerance. A generic rotation tool center point management module is also designed to realize the coordinate transformation and adaptive nonlinear error control for major five-axis machine tools. The overall effectiveness of the proposed five-axis NURBS machining scheme is demonstrated by the five-axis machining of an impeller’s flow channel.     

CNC machine tool surface interpolator for ball-end milling of free-form surfaces

This paper presents a new type of CNC machine tool interpolator that is capable of generating the cutter path for ball-end milling of a free-form surface. The surface interpolator comprises on-line algorithms for cutter-contact (CC) path scheduling, CC path interpolation, and tool offsetting. The interpolator algorithms for iso-parametric, iso-scallop and iso-planar machining methods are developed, respectively. The proposed surface interpolator method gains the advantages for minimizing the data loaded to the CNC machine tool and maintaining the desired feedrate and position accuracy along the CC path.     

The analysis of correlative error in principal axis method for five-axis machining of sculptured surfaces

Correlative error is a kind of error between the cutter locations. This text presents a detailed analysis about correlative error in the principal axis method (PAM) that is a strategy of tool positioning for five-axis machining. It points out all the strategies based on linear projection cannot avoid this interference and cannot be disregarded especially in the strategies with large stepover. Accurate calculating is made individually on linear and curve feed and formulae are developed. The author also gave the available application range of PAM and the algorithm for estimating correlative error.     

Feed rate optimization for 3-axis ball-end milling of sculptured surfaces

The aim of this research is to improve the productivity of CNC machine tools by optimizing feed rate. To optimize feed rate two programs were used: “ACIS” (with scheme language) and “Visual Basic”. The scheme program for modeling the work piece, tool, cutting edge, and calculating maximum cutting force and the Visual Basic program to control all the activities linked to the ACIS program for estimating optimized feed values. Laboratory tests were conducted to verify the results from the modeling, using an insert-type one-flute ball-end cutter on a CK45 carbon steel work piece. No coolant was used throughout the experimental works. Comparisons were made between the maximum cutting forces, in the “fix” feed rate tests. The results indicate significant increases in productivity, which can be achieved, by using the optimized feed rate method.     

数控加工中发挥五轴设备优势的分析

分析五轴数控机床的特点和五轴加工中的各种误差,提出在使用五轴数控机床中应注重一些问题,以合理利用五轴设备,发挥其优势。     

Machining accuracy for shearing process of thin-sheet metals—Development of initial tool position adjustment system

In the shearing process, clearance has a significant effect on machining accuracy. However, the relationship between uneven clearance caused by misalignment of tool position and machining accuracy remains unclear. This is attributed to the fact that, previously, the effect was small because the thickness of the workpiece was not so thin, and a method for precisely measuring and adjusting the tool position had not been established. Therefore, in the present study, a new method of adjusting the initial tool position is developed. In addition, punching experiments are conducted under the condition that the initial tool position is adjusted to an accuracy of 2 μm or better, and the effects of clearance on machining accuracy, shape of cross-section, and diameter of hole, are investigated in three types of materials. From these results, the importance of adjusting the initial tool position is clarified.     

基于误差分析的复杂曲面可侧铣判定方法研究

基于复杂曲面侧铣加工误差计算,提出了一种曲面能否通过侧铣实现高精度加工的判定方法,该方法适用于任意直纹和非直纹曲面。侧铣加工误差为待加工理论曲面与刀具运动包络曲面之间的距离,在此基础上,应用整体最优刀具路径下的最大几何偏差进行曲面可侧铣判定依据。数值仿真算例表明:该方法不仅能够有效地判定曲面能否侧铣,同时能够输出满足误差要求的最优刀具路径,加工实验也表明该方法能够极大地提高加工效率。