Incomplete mesh-based tool path generation for optimum zigzag milling

The majority of mechanical parts are manufactured by milling machines. Hence, geometrically efficient algorithms for tool path generation and physical considerations for better machining productivity with guarantee of machining safety are the most important issues in milling tasks. In this paper, we present an optimized path-generation algorithm for zigzag milling, which is commonly used in the roughing stage as well as in the finishing stage, based on an incomplete two-manifold mesh model, namely, an inexact polyhedron that is widely used in recent commercialized CAM software systems. First of all, a geometrically efficient tool path generation algorithm using an intersection points-graph is introduced. Although the tool path obtained from geometric information has been successful to make a desirable shape, it seldom considers physical process concerns like cutting forces and chatter. In order to cope with these problems, an optimized tool path that maintains constant MRR in order to achieve constant cutting forces and to avoid chatter vibrations at all times is introduced and the result is verified. Additional tool path segments are appended to the basic tool path by using a pixel-based simulation technique. The algorithm was implemented for two-dimensional contiguous end-milling operations with flat end mills and cutting tests were conducted by measuring the spindle current, (which reflect machining situations) to verify the significance of the proposed method.     

Tool path generation and modification for constant cutting forces in direction parallel milling

This paper presents an optimized path generation algorithm for direction parallel milling, which is commonly used in the roughing and finishing stages. First, a geometrically efficient tool path generation algorithm using an intersection points graph is introduced. Second, the generated tool path is modified as an optimized tool path that maintains a constant material removal rate to achieve a constant cutting force and avoid chatter vibration, and the results are verified. Additional tool path segments are appended to the basic tool path through a pixel-based simulation technique. The algorithm is implemented for two-dimensional contiguous end milling operations with flat end mills, and cutting tests are conducted by measuring the spindle current, which reflects the changing machining situations, to verify the performance of the proposed method.     

An optimized contour parallel tool path for 2D milling with flat endmill

Although the conventional contour parallel tool path obtained from geometric information has been successful in making desirable shapes, it seldom considers the physical process concerns like cutting forces and chatters. In this paper, an optimized contour parallel path, which maintains constant MRR (material removal rates) at all times, is introduced and the results are verified. The optimized tool path is based on a conventional contour parallel tool path. Additional tool path segments are appended to the basic tool path in order to achieve constant cutting forces and to avoid chatter vibrations in the entire machining area. The algorithm has been implemented for two dimensional contiguous end milling operations with flat end mills, and cutting tests were conducted to verify the significance of the proposed method.     

Optimization of machining parameters using genetic algorithm and experimental validation for end-milling operations

Optimization of cutting parameters is valuable in terms of providing high precision and efficient machining. Optimization of machining parameters for milling is an important step to minimize the machining time and cutting force, increase productivity and tool life and obtain better surface finish. In this work a mathematical model has been developed based on both the material behavior and the machine dynamics to determine cutting force for milling operations. The system used for optimization is based on powerful artificial intelligence called genetic algorithms (GA). The machining time is considered as the objective function and constraints are tool life, limits of feed rate, depth of cut, cutting speed, surface roughness, cutting force and amplitude of vibrations while maintaining a constant material removal rate. The result of the work shows how a complex optimization problem is handled by a genetic algorithm and converges very quickly. Experimental end milling tests have been performed on mild steel to measure surface roughness, cutting force using milling tool dynamometer and vibration using a FFT (fast Fourier transform) analyzer for the optimized cutting parameters in a Universal milling machine using an HSS cutter. From the estimated surface roughness value of 0.71 μm, the optimal cutting parameters that have given a maximum material removal rate of 6.0×10³ mm³/min with less amplitude of vibration at the work piece support 1.66 μm maximum displacement. The good agreement between the GA cutting forces and measured cutting forces clearly demonstrates the accuracy and effectiveness of the model presented and program developed. The obtained results indicate that the optimized parameters are capable of machining the work piece more efficiently with better surface finish.     

复杂曲面环形刀五轴端铣加工的刀具轨迹规划方法

为了降低复杂曲面类零部件加工的刀具路径,减小刀具路径条数,提高加工效率,提出了一种新的复杂曲面环形刀五轴端铣加工刀具轨迹优化方法。在局部可铣性基础上对刀轴矢量角进行自适应优化,采用新型加工带宽计算方法——等残留高度算法,给出了等残留高度算法的刀具轨迹生成具体步骤。仿真结果表明:与传统等残留高速算法相比,刀具轨迹优化算法的刀具路径更短、条数更少,能够有效提高复杂曲面加工效率。     

Development of an automatic arc welding system using SMAW process

In end milling of pockets, variable radial depth of cut is generally encountered as the end mill enters and exits the corner, which has a significant influence on the cutting forces and further affects the contour accuracy of the milled pockets. This paper proposes an approach for predicting the cutting forces in end milling of pockets. A mathematical model is presented to describe the geometric relationship between an end mill and the corner profile. The milling process of corners is discretized into a series of steady-state cutting processes, each with different radial depth of cut determined by the instantaneous position of the end mill relative to the workpiece. For the cutting force prediction, an analytical model of cutting forces for the steady-state machining conditions is introduced for each segmented process with given radial depth of cut. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpiece material properties, as well as the relative position of the tool to workpiece. Experiments of pocket milling are conducted for the verification of the proposed method.     

Feedrate scheduling strategy for free-form surface machining through an integrated geometric and mechanistic model

In free-form surface machining, it is essential to optimize the feedrate in order to improve the machining efficiency. Conservative constant feedrate values have been mostly used up to now since there was a lack of physical models and optimization tools for the machining processes. The overall goal of this research is the integration of geometric and mechanistic milling models for force prediction and feedrate scheduling in five-axis CNC free-form surface machining. For each tool move, the geometric model calculates the cut geometry, and a mechanistic model is used along with a maximum allowable cutting force to determine a desired feedrate. The results are written into the part NC program with optimized feedrates. When the integrated modeling approach based feedrate scheduling strategy introduced in this paper was used, it was shown that the machining time can be decreased significantly along the tool path.     

END MILLING SYSTEM COMPLIANCE AND MACHINING ERROR

Tool deflection resulting from cutting forces places a constraint on the achievable precision and productivity in machining. This paper presents an analytical model of machining error, in terms of part form deviation in end milling due to the elastic compliance of cutting tool. Based on the relationship of local cutting forces and chip thickness, the shear loading and bending moment on the tool cross section are presented in terms of cutter angular position. The tool deflection resulting from the bending moment is then established from the principle of virtual work. The resulting deflection of workpiece and machine tool structure is also considered through shear loading analysis. The expression for machining error is derived as a closed-form function of the machining parameters, cutting configuration, material characteristics, and machine receptance. End milling experiments were conducted to verify the analytical model under various cutting conditions. Error maps are presented to illustrate the effects of process conditions on the achievable part accuracy.     

Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

A mapping-based spiral cutting strategy for pocket machining

Almost 80 % of the milling operations to produce mechanical parts are produced by NC pocket milling, especially in aerospace and automobile industry. At present, for 2.5D pocket machining, direction-parallel and contour-parallel machining strategies have gained nearly universal acceptance. However, in such tool path, abrupt change of path direction, frequent acceleration and deceleration, and sharp velocity discontinuous are found to significantly limit the machining efficiency of pockets. To address these problems, this paper introduces a method for generating a spiral tool path that maintains a steady-state cutting process by as smoothly as possible curvature evolution of the tool path for pocket machining. First, the machined region of a layer of a pocket is mapped onto a circular domain by means of mesh mapping, which reduces the task of tool path generation from the geometrically complex pocket region to a topologically simple disk. On this disk, a guide spiral is constructed according to a mathematical function constrained by the calculated path interval map. Using the mapping from the pocket to the disk as a guide, the guide spiral is inversely mapped into the interior of the pocket and then a smooth low-curvature spiral path is derived. The generated tool paths are guaranteed to not inherit any corners in the subsequent interior tool paths and allows cutting of the pocket without tool retractions during the cutting operations. Finally, the proposed method is implemented and tested on several typical sample pockets to demonstrate its validity and significance.     

Grind-free tool path generation for five-axis surface machining

This paper discusses automatic tool path generation for five-axis filleted end mill finish-surface machining. A new method of automatic five-axis tool path generation is introduced called Grind-Free (GF) tool path generation. GF surfaces result from tool paths that avoid gouging and have scallops that are within the surface profile or waviness tolerances. New algorithms are presented for determining tool forward step and tool path step-over that produce a GF surface. Gouge-free tool paths can be generated directly from CAD data based solely on local and global machining constraints. The proposed methodology for GF tool path generation has been implemented in the C language using the CODE/Robline system. Surfaces were machined on a Boston Digital 505 five-axis milling machine to confirm this method.     

Surface generation modeling of micro milling process with stochastic tool wear

Micro milling is widely used to manufacture miniature parts and features at high quality with low set-up cost. To achieve a higher quality of existing micro products and improve the milling performance, a reliable analytical model of surface generation is the prerequisite as it offers the foundation for surface topography and surface roughness optimization. In the micro milling process, the stochastic tool wear is inevitable, but the deep influence of tool wear hasn't been considered in the micro milling process operation and modeling. Therefore, an improved analytical surface generation model with stochastic tool wear is presented for the micro milling process. A probabilistic approach based on the particle filter algorithm is used to predict the stochastic tool wear progression, linking online measurement data of cutting forces and tool vibrations with the state of tool wear. Meanwhile, the influence of tool run-out is also considered since the uncut chip thickness can be comparable to feed per tooth compared with that in conventional milling. Based on the process kinematics, tool run-out and stochastic tool wear, the cutting edge trajectory for micro milling can be determined by a theoretical and empirical coupled method. At last, the analytical surface generation model is employed to predict the surface topography and surface roughness, along with the concept of the minimum chip thickness and elastic recovery. The micro milling experiment results validate the effectiveness of the presented analytical surface generation model under different machining conditions. The model can be a significant supplement for predicting machined surface prior to the costly micro milling operations, and provide a basis for machining parameters optimization.     

An efficient five-axis machining method of centrifugal impeller based on regional milling

This paper presents an efficient five-axis machining method of centrifugal impeller based on regional milling. As the base of the machining method, geometry of the centrifugal impeller and blade surface is analyzed, and sub-machining regions are presented through the division of the double three-cubic d non-uniform rational B-spline (NURBS) surface. In rough milling, the cutter parameters, tool path interval, tool path curves, and the fixed tool axis vector are calculated by the novel algorithm based on regional milling; the biggest cutter and smaller tool path length are obtained. In finish milling, for the aerodynamic performance of the finished impeller, the tool path curves are modified and interlinked to make them uniform and orderly. A modified algorithm of the finish milling of the blade surface is proposed, and not only are the machining errors reduced; their reasonable distribution is also realized. Numerical simulation and a real test impeller are presented as the test of the proposed method.     

END MILLING SYSTEM COMPLIANCE AND MACHINING ERROR

Abstract

Tool deflection resulting from cutting forces places a constraint on the achievable precision and productivity in machining. This paper presents an analytical model of machining error, in terms of part form deviation in end milling due to the elastic compliance of cutting tool. Based on the relationship of local cutting forces and chip thickness, the shear loading and bending moment on the tool cross section are presented in terms of cutter angular position. The tool deflection resulting from the bending moment is then established from the principle of virtual work. The resulting deflection of workpiece and machine tool structure is also considered through shear loading analysis. The expression for machining error is derived as a closed-form function of the machining parameters, cutting configuration, material characteristics, and machine receptance. End milling experiments were conducted to verify the analytical model under various cutting conditions. Error maps are presented to illustrate the effects of process conditions on the achievable part accuracy.     

Cutting parameter and tool path style effects on cutting force and tool deflection in machining of convex and concave inclined surfaces

Convex and concave inclined surfaces are frequently encountered in the machining of components in industries such as aerospace, aircraft, automotive, biomedical, and precision machinery manufacturing and mold industries. Tool path styles, generated by different cutting strategies, result in various cutting forces and tool deflection values that might lead to poor surface integrities. In cost-effective manufacturing, it is helpful to make known their effects on machinability. Thus, the first aim of this study is to investigate optimum cutting parameter values in ball end milling of EN X40CrMoV5-1 tool steel with three coated cutters. The parameters taken into consideration are cutting speed, feed rate, step over, and tool path style. The second aim of the study is to determine the effects of tool path styles in ball end milling of inclined surfaces. As a result, the most effective parameter within the selected cutting parameters and cutting styles for both inclined surfaces and different coatings was step over. In terms of tool coatings, the most rapidly deteriorating coating was TiC coating for cutting forces in both inclined surfaces and for tool deflection in convex inclined surface. In addition, the response surface methodology is employed to predict surface roughness values, depending on the cutting forces obtained. The model generated gives highly accurate results.     

型腔边界拐角精加工刀轨生成算法的研究

在识别粗加工余料区域的基础上,从均匀径向切削深度、平滑刀轨路径等方面考虑,研究并实现了型腔边界拐角处的精加工刀轨生成算法。采用将拐角区域加工分为多个循环进行渐进切削的策略,可减小径向切深。同时,每一切削循环内切削段和空程刀轨段、各循环之间均采用圆弧过渡,刀轨路径满足一阶连续,从而可减小切削力的变化幅度和方向突变,提高加工精度。     

Research on tool path planning method of four-axis high-efficiency slot plunge milling for open blisk

The great mass of machining allowance for blisk is removed in the rough milling, so improving the rough machining efficiency for the blisk’s tunnel is the key of realizing high-efficiency machining of blisk. According to the structure characteristic of open blisk’s tunnel, a four-axis plunge slot rough milling with high-efficiency and low machining cost is advanced. First, the plunge slot process for blisk and the generation process of the ruled enveloping surface for the freeform surface of the blisk’s blade are put forward. Then, the generating method of the ruled enveloping surface for the blade’s freeform surface and the tool path generation method of four-axis plunge slot milling for blisk are studied. The rough milling region of open blisk’s tunnel is determined by generating the ruled enveloping surface of blade’s offset surface, and the algorithm of tool path for four-axis plunge milling is given. When using a ruled surface to approach a freeform surface, the problem of getting boundary is solved, and the error from the calculation of tool path is avoided by the algorithm. At last, the experiment shows that comparing to the traditional side slot milling, the cutting force of four-axis plunge milling can be reduced by 60% and even the rough machining efficiency can be increased to more than double.     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

Theoretical modelling of cutting forces in helical end milling with cutter runout

A theoretical cutting force model for helical end milling with cutter runout is developed using a predictive machining theory, which predicts cutting forces from the input data of workpiece material properties, tool geometry and cutting conditions. In the model, a helical end milling cutter is discretized into a number of slices along the cutter axis to account for the helix angle effect. The cutting action for a tooth segment in the first slice is modelled as oblique cutting with end cutting edge effect and tool nose radius effect, whereas the cutting actions of other slices are modelled as oblique cutting without end cutting edge effect and tool nose radius effect. The influence of cutter runout on chip load is considered based on the true tooth trajectories. The total cutting force is the sum of the forces at all the cutting slices of the cutter. The model is verified with experimental milling tests.     

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。