Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

A coupled dynamics,multiple degree of freedom process damping model,Part 2: Milling

Self-excited vibration, or chatter, is an important consideration in machining operations due to its direct influence on part quality, tool life, and machining cost. At low machining speeds, a phenomenon referred to as process damping enables stable cutting at higher depths of cut than predicted with traditional analytical models. This paper describes an analytical stability model for milling operations which includes a process damping force that depends on the surface normal velocity, depth of cut, cutting speed, and an empirical process damping coefficient. Model validation is completed using time domain simulation and milling experiments. The results indicate that the multiple degree of freedom model is able to predict the stability boundary using a single process damping coefficient.     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.     

A 3D Predictive Cutting-Force Model for End Milling of Parts Having Sculptured Surfaces

A comprehensive, 3D mathematical model of desired/optimal cutting force for end milling of freeform surfaces is proposed in this paper. A closed-form predictive model is developed, based on a perceptive cutting approach, resulting in a cutting force model having a comprehensive set of essential cutting parameters. In particular, the normal rake angle, usually missing in most existing models of the same sort, is included in the developed model. The model also permits quantitative analyses of the effect of any parameters on the cutting performance of the tool, providing a guideline to improving the tool performance. Since the axial depth of cut varies with time when milling sculptured surface parts, an innovative axial depth of cut estimation scheme is proposed for the generation of 3D cutting forces. This estimation scheme improves on the practicality of most existing predictive cutting-force models for milling, in which the major attention has been focused on planar milling surface generation. In addition, the proposed model takes the rake surface on the flute of mills as an osculating plane to yield 3D cutting force expressions in only two steps. This approach greatly reduces the time-consuming mathematical work normally required for obtaining the cutting-force expressions. A series of milling simulations for machining freeform parts under specific cutting conditions have been performed to verify the effectiveness of the proposed cutting-force model. The simulation results demonstrate the accurate estimating capability of the proposed method for axial depth of cut estimation. The cutting force responses from the simulation exhibit the same trends as can be obtained using the empirical mechanic’s model referenced in the literature. Finally, from the simulation results it is also shown that designing a tool with a combination of different helix angles, having cutting force signatures similar to those of the single helix angle counterparts, is particularly advantageous.     

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.     

基于动力学不确定性的重型切削工艺参数优化

针对数控重型切削加工过程的切削稳定性具有不确定性的特点,提出了在切削稳定性和机床工作能力的约束下,获得最大材料去除率的工艺参数优化方法。根据重型切削加工的工艺特点建立三维动力学模型,以机床的固有频率、阻尼比、刚度和切削力系数作为不确定因素,结合排零定理和边理论对其进行不确定性分析,获得稳健的切削稳定性叶瓣图,结合切削深度、刀具直径和刀具齿数的关系,为加工过程选择能获得最大切削深度的刀具。在此基础上,建立工艺参数优化模型,选择最佳的轴向切削深度、径向切削深度和主轴转速的组合,最后以一台加工中心上某型号发动机缸体表面的粗加工过程为例进行了验证。     

A composite fitting model of discrete handbook data for peripheral end milling

Machining data handbooks are important reference books in the machining industry, as they provide recommended process parameter values for common machining operations. The machining data, although covering a wide range of relevant cutting conditions, are only listed under discrete cutting conditions. Rough interpolation-based calculations are often needed in order to estimate the process parameter values at the desired cutting condition. In this work, a composite fitting model is presented to fit a composite functional curve through the discrete handbook data of recommended cutting speeds and feeds with respect to the cutting condition of radial depth of cut for peripheral end milling. The objective is to establish a functional relationship from the handbook data such that recommended cutting speed and feed can be obtained for any given radial depth of cut. According to the tabulated layout of the machining data, the entire range of the radial depth of cut is divided into three segments having distinctive formulations and trends. Constraints are then imposed to preserve the trends and smoothly connect the adjacent segments. As a possible application of the presented model, a case study of machining a rectangular pocket is provided. Machining time of a potential process plan is readily evaluated based on the cutting speeds and feeds obtained from the composite model.     

Milling Force Model for Aviation Aluminum Alloy:Academic Insight and Perspective Analysis

Aluminum alloy is the main structural material of aircraft,launch vehicle,spaceship,and space station and is pro-cessed by milling.However,tool wear and vibration are the bottlenecks in the milling process of aviation aluminum alloy.The machining accuracy and surface quality of aluminum alloy milling depend on the cutting parameters,material mechanical properties,machine tools,and other parameters.In particular,milling force is the crucial factor to determine material removal and workpiece surface integrity.However,establishing the prediction model of milling force is important and difficult because milling force is the result of multiparameter coupling of process system.The research progress of cutting force model is reviewed from three modeling methods:empirical model,finite element simulation,and instantaneous milling force model.The problems of cutting force modeling are also determined.In view of these problems,the future work direction is proposed in the following four aspects:(1)high-speed milling is adopted for the thin-walled structure of large aviation with large cutting depth,which easily produces high residual stress.The residual stress should be analyzed under this particular condition.(2)Multiple factors(e.g.,eccentric swing milling parameters,lubrication conditions,tools,tool and workpiece deformation,and size effect)should be consid-ered comprehensively when modeling instantaneous milling forces,especially for micro milling and complex surface machining.(3)The database of milling force model,including the corresponding workpiece materials,working condi-tion,cutting tools(geometric figures and coatings),and other parameters,should be established.(4)The effect of chatter on the prediction accuracy of milling force cannot be ignored in thin-walled workpiece milling.(5)The cutting force of aviation aluminum alloy milling under the condition of minimum quantity lubrication(mql)and nanofluid mql should be predicted.     

Prediction of cutting force, tool wear and surface roughness of Al6061/SiC composite for end milling operations using RSM

The results of mathematical modeling and the experimental investigation on the machinability of aluminium (Al6061) silicon carbide particulate (SiCp) metal matrix composite (MMC) during end milling process is analyzed. The machining was difficult to cut the material because of its hardness and wear resistance due to its abrasive nature of reinforcement element. The influence of machining parameters such as spindle speed, feed rate, depth of cut and nose radius on the cutting force has been investigated. The influence of the length of machining on the tool wear and the machining parameters on the surface finish criteria have been determined through the response surface methodology (RSM) prediction model. The prediction model is also used to determine the combined effect of machining parameters on the cutting force, tool wear and surface roughness. The results of the model were compared with the experimental results and found to be good agreement with them. The results of prediction model help in the selection of process parameters to reduce the cutting force, tool wear and surface roughness, which ensures quality of milling processes.     

基于有限元数值模型和进给速度优化的薄壁件侧铣变形在线控制

为实现在加工过程中对薄壁件侧铣产生的较大切削变形进行在线控制,提出基于有限元数值模型和进给速度优化的在线控制策略。根据薄壁件切削过程的有限元仿真结果,建立数控机床进给速度、切削力、工件切削变形间的数值模型,进而确定用于控制变形的最优目标切削力。在具有开放式模块化的数控系统平台上开发了切削力信号实时采集、滤波功能和基于Brent-Dekker算法的进给速度在线优化策略,并根据滤波后的切削力及相应算法在加工过程中实时调整机床进给速度,保证切削力逐渐接近最优控制目标而实现切削变形的在线控制。试验结果表明,经过进给速度在线优化后的切削过程可将薄壁件侧铣变形控制在规定范围内,同时提高了切削效率。     

Effect of machining parameters on the milling process of 2.5D C/SiC ceramic matrix composites

Abstract

The C/SiC ceramic matrix composites are widely used for high-value components in the nuclear, aerospace and aircraft industries. The cutting mechanism of machining C/SiC ceramic matrix composites is one of the most challenging problems in composites application. Therefore, the effects of machining parameters on the machinability of milling 2.5D C/SiC ceramic matrix composites is are investigated in this article. The related milling experiments has been carried out based on the C/SiC ceramic matrix composites fixed in two different machining directions. For two different machining directions, the influences of spindle speed, feed rate and depth of cut on cutting forces and surface roughness are studied, and the chip formation mechanism is discussed further. It can be seen from the experiment results that the measured cutting forces of the machining direction B are greater than those of the in machining direction A under the same machining conditions. The machining parameters, which include spindle speed, feed rate, depth of cut and machining direction, have an important influence on the cutting force and surface roughness. This research provides an important guidance for improving the machining efficiency, controlling and optimizing the machined surface quality of C/SiC ceramic matrix composites in the milling process.     

Cutter workpiece engagement region and surface topography prediction in five-axis ball-end milling

Based on the machining tool path and the true trajectory equation of the cutting edge relative to the workpiece, the engagement region between the cutter and workpiece is analyzed and a new model is developed for the numerical simulation of the machined surface topography in a multiaxis ball-end milling process. The influence of machining parameters such as the feed per tooth, the radial depth of cut, the angle orientation tool, the cutter runout, and the tool deflection upon the topography are taken into account in the model. Based on the cutter workpiece engagement, the cutting force model is established. The tool deflections are extracted and used in the surface topography model for simulation. The predicted force profiles were compared to the measured ones. A reasonable agreement between the experimental and the predicted results was found.     

基于铣削均匀性的切削参数优化

分析了高速铣削加工切屑形成过程中刀具—工件的接触行为,提出了考虑轴向切削深度和径向切削深度的铣削均匀性模型。在此基础上,以恒定的金属去除率为约束条件、铣削均匀性系数为优化目标,建立了切削参数的优化模型。通过对航空铝合金进行高速铣削试验,验证了铣削均匀性理论及优化模型的合理性。结果表明,对于航空铝合金的高速铣削加工,采用大径向切深—小轴向切深有利于提高铣削均匀性,减小切削力。     

基于UG的小直径立铣刀应力场有限元分析

为了提高加工精度,对小直径立铣刀的应力场进行了有限元分析。通过铣削力试验,对不同切削参数下立铣刀的铣削力进行动态采集,利用UG建模模块进行立铣刀实体建模,根据铣削力试验结果给出边界条件,在立铣刀有限元模型上加载载荷,利用UG有限元分析模块获得了立铣刀切削过程中切入、切出的瞬时应力场云图,显示了切削中立铣刀应力场的变化规律。     

An experimental investigation on micro machining of fine-grained graphite

Industrial applications of the micro milling process require sufficient experimental data from various micro tools. Research has been carried out on micro milling of various engineering materials in the past two decades. However, there is no report in the literature on micro milling of graphite. This paper presents an experimental investigation on micro machinability of micro milling of moulded fine-grained graphite. Full immersion slot milling was conducted using diamond-coated, TiAlN-coated and uncoated tungsten carbide micro end mills with a uniform tool diameter of 0.5 mm. The experiments were carried out on a standard industrial precision machining centre with a high-speed micro machining spindle. Design of experiments (DoE) techniques were applied to design and analysis of the machining process. Surface roughness, surface topography and burrs formation under varying machining conditions were characterized using white light interferometry, SEM and a precision surface profiler. Influence of variation of cutting parameters including cutting speeds, feedrate and axial depth of cut on surface roughness and surface damage was analysed using ANOVA method. The experimental results show that feedrate has the most significant influence on surface roughness for all types of tools, and diamond tools are not sensitive to cutting speed and depth of cut. Surface damage and burrs analysis show that the primary material removal mode is still brittle fracture or partial ductile in the experimental cutting conditions. 3D intricate micro EDM electrodes were fabricated with good dimensional accuracy and surface finishes using optimized machining conditions to demonstrate that micro milling is an ideal process for graphite machining.     

Feedrate optimisation/scheduling on sculptured surface machining: a comprehensive review, applications and future directions

Free-form or sculptured surface milling is one of the continually used manufacturing processes for die/mould, aerospace (especially turbine blades), precision machine design, bio-medical devices and automotive industries. Developments of machining technologies for quality enhancement of machining results have become a very important fact in current real industry. Therefore, reducing milling time, tool wear, cutter deflection and improving surface texture quality and machining operations through adaptation and optimisation of tool feedrates based on changing surface geometry in sculptured surface machining is a great step in this direction. Various feedrate optimisation strategies have different feedrate rescheduling control parameters such as chip thickness, material removal rate (MRR), min(mrr,chip,force), max(expo.Acc/dec) and resultant forces. Some commercial CAM softwares come with MRR-based feedrate optimisation algorithms which have a very short calculation time. However, commercial feedrate scheduling systems have some limitations in generating the scheduled feedrates because they use the MRR or the cutting force model which is dependent on milling conditions. However, for the processes in which machining precision/accuracy is very important, it is inevitable that mechanistic force-based feedrate optimisation approaches, for which the calculation time is improved, will be integrated into commercial CAM software packages. Here, developing only the mechanistic cutting force-based algorithm is not enough. In this paper, improvement and optimisation of machining feedrate value, which is one of the cutting parameters which has a tremendous effect on the precise machining of free-form surfaces, was discussed by using the virtual machining framework. For this purpose, the boundary representation solid modelling technique-based free-form milling simulation and feedrate optimisation system integrated with commercial CAD/CAM software is developed for three-axis ball-end milling. This review study includes the information regarding the following topics: The algorithms developed for the feedrate value optimisation, MRR calculation approaches, cutting force computation methods, details of algorithms, the effects on the surface accuracy, the effects on the machining time, the capabilities of the present commercial CAM software packages, the encountered difficulties and overcoming those difficulties, recent developments and future research directions.     

模具钢Cr12MoV硬态铣削过程切削力的研究

切削力是铣削机理研究的重要对象,与刀具磨损和已加工表面质量等指标关系密切。本文通过软件ThirdWave建立了球头铣刀高速铣削模具钢Cr12MoV的仿真模型。该模型采用了网格自适应技术和删除技术。成功实现了切削力的高精度仿真,并对仿真模型进行了实验验证。模型分析了切入切出过程切削力的变化特性,同时也揭示了切削条件对切削力变化的影响规律。本研究成果可对切削工艺条件的合理选择提供借鉴。     

MAXIMIZATION OF CHATTER-FREE MATERIAL REMOVAL RATE IN END MILLING USING ANALYTICAL METHODS

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Various numerical and analytical stability models have been considered in the previous publications, where mostly the stability limit of axial depth of cut is emphasized for chatter-free cutting. In this paper an analytical stability model is used, and a simple algorithm to determine the stability limit of radial depth of cut is presented. It is shown that, for the maximization of chatter-free material removal rate, radial depth of cut is of equal importance with the former. A method is proposed to determine the optimal combination of depths of cut, so that chatter-free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal parameters. The procedure can easily be integrated to a CAD/CAM or virtual machining environment in order to identify the optimal milling conditions automatically.     

MAXIMIZATION OF CHATTER-FREE MATERIAL REMOVAL RATE IN END MILLING USING ANALYTICAL METHODS

ABSTRACT

Chatter vibrations in milling, which develop due to dynamic interactions between the cutting tool and the workpiece, result in reduced productivity and part quality. Various numerical and analytical stability models have been considered in the previous publications, where mostly the stability limit of axial depth of cut is emphasized for chatter-free cutting. In this paper an analytical stability model is used, and a simple algorithm to determine the stability limit of radial depth of cut is presented. It is shown that, for the maximization of chatter-free material removal rate, radial depth of cut is of equal importance with the former. A method is proposed to determine the optimal combination of depths of cut, so that chatter-free material removal rate is maximized. The application of the method is demonstrated on a pocketing example where significant reduction in the machining time is obtained using the optimal parameters. The procedure can easily be integrated to a CAD/CAM or virtual machining environment in order to identify the optimal milling conditions automatically.     

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.