Prediction of cutting forces and machining error in ball end milling of curved surfaces -I theoretical analysis

This paper presents a theoretical model by which cutting forces and machining error in ball end milling of curved surfaces can be predicted. The actual trochoidal paths of the cutting edges are considered in the evaluation of the chip geometry. The cutting forces are evaluated based on the theory of oblique cutting. The machining errors resulting from force induced tool deflections are calculated at various parts of the machined surface. The influences of various cutting conditions, cutting styles and cutting modes on cutting forces and machining error are investigated. The results of this study show that in contouring, the cutting force component which influences the machining error decreases with increase in milling position angle; while in ramping, the two force components which influence machining error are hardly affected by the milling position angle. It is further seen that in contouring, down cross-feed yields higher accuracy than up cross-feed, while in ramping, right cross-feed yields higher accuracy than left cross-feed. The machining error generally decreases with increase in milling position angle.     

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。     

Form error estimation in ball-end milling of sculptured surface with z-level contouring tool path

This paper presents a flexible model for estimating the form error in three-axis ball-end milling of sculptured surface with z-level contouring tool path. At an interval of feed per tooth, the whole process of sculptured surface machining is treated as a combination of sequential small inclined surface milling. For ball-end milling of the inclined surface with z-level contouring tool path, at surface generation position, an analytical model is proposed to identify the feedback effect of tool deflection on cutting edge engagement. The deflection-dependent cutting edge engagement is determined by using an iterative procedure. And ultimately, the form error is obtained from the balanced tool deflection and associated surface inclination angle. In a validation experiment, the estimated form errors are compared with both the measurements and the predictions of a rigid model. It is shown that the proposed flexible model gives significant better predictions of the form error than rigid model. Good agreement between the predicted and measured form errors is demonstrated for the ball-end milling of sculptured surface with z-level contouring tool path.     

Investigate on milling force of cryogenic cooling processing aluminum honeycomb treated by ice fixation

Aerospace metal honeycomb materials with low stiffness had often the deformation, burr, collapse, and other defects in the mechanical processing. They were attributed to poor fixation method and inapposite cutting force. This paper presented the improvement of fixation way. The hexagonal aluminum honeycomb core material was treated by ice fixation, and the NC milling machine was used for a series of cryogenic machining. Considering the similar structure of fiber-reinforced composite materials, the milling force prediction model of ice fixation aluminum honeycomb was established, considering tool geometry parameters and cutting parameters. Meanwhile, the influence rule on milling force was deduced. The results show that compared with the conventional fixation milling method, the honeycomb processing effect is improved greatly. The machining parameters affect order on milling forces: the cutting depth is the most important, followed by the cutting width, then the spindle speed and the feed. Moreover, too small cutting depth (a_p?=?0.5 mm) will cause insufficient cutting force, while a_p?>?2 mm with higher force will reduce the processing quality of honeycomb. Simultaneously, the honeycomb orientation (θ) has a great influence on processing quality. Using the model, the predicted and measured error values of the feed and main cutting force are all small in θ?<?90°. But, the rate is 33 and 26% for the main cutting force and feed force error in θ?>?90°, respectively, while they all exhibit the smallest error in θ?=?60°. This bigger error mainly is due to unstable cutting force with obtuse angle. In addition, the tool rake angle has little influence on cutting quality in θ?<?90°, but bigger on that in θ?>?90°. Furthermore, the calculation model successfully conforms to the main deformation mechanism and influences parameters of the cutting force in the milling process, and it can accurately predict the cutting force in θ?<?90° and guide the milling process.     

高硅铝合金的金刚石涂层刀具铣削损伤机理研究

高硅铝合金由于硅含量很高,故切削加工性较差,切削刀具极易磨损且已加工表面存在大量缺陷.为进一步研究材料加工损伤,采用化学气相沉积法制备了金刚石涂层铣刀,开展70％Si/Al(70％指质量分数)合金材料铣削试验.试验研究了铣削力、刀具磨损及加工损伤机理,并与常用TiN涂层铣刀进行了对比.结果 表明:铣削过程中由于初晶硅硬...     

Development of a finite element analysis tool for fixture design integrity verification and optimisation

Machining fixtures are used to locate and constrain a workpiece during a machining operation. To ensure that the workpiece is manufactured according to specified dimensions and tolerances, it must be appropriately located and clamped. Minimising workpiece and fixture tooling deflections due to clamping and cutting forces in machining is critical to machining accuracy. An ideal fixture design maximises locating accuracy and workpiece stability, while minimising displacements.The purpose of this research is to develop a method for modelling workpiece boundary conditions and applied loads during a machining process, analyse modular fixture tool contact area deformation and optimise support locations, using finite element analysis (FEA). The workpiece boundary conditions are defined by locators and clamps. The locators are placed in a 3-2-1 fixture configuration, constraining all degrees of freedom of the workpiece and are modelled using linear spring-gap elements. The clamps are modelled as point loads. The workpiece is loaded to model cutting forces during drilling and milling machining operations. Fixture design integrity is verified. ANSYS parametric design language code is used to develop an algorithm to automatically optimise fixture support and clamp locations, and clamping forces, to minimise workpiece deformation, subsequently increasing machining accuracy. By implementing FEA in a computer-aided-fixture-design environment, unnecessary and uneconomical “trial and error” experimentation on the shop floor is eliminated.     

球头铣刀高速铣削斜面的三维数值模拟研究

用球头铣刀高速铣削斜面是在三轴加工中心上加工模具时的一种走刀方式。根据球头铣刀高速铣削斜面的特点,建立了在垂直向上和向下、水平向上和向下四种走刀方式下高速铣削45°斜面,以及在垂直向下走刀方式下高速铣削30°、60°、75°斜面的三维有限元模型,以分析不同走刀方式下铣削斜面以及铣削不同角度斜面时切削力和切削温度的变化规律。模拟结果表明,在铣削45°斜面时,采用向上走刀方式较向下走刀方式的切削力幅值小、波动大,且切削温度高;采用垂直向下走刀方式铣削大角度斜面时也出现类似情况。对切削力的实测结果验证了该模型的可靠性。     

Examination of surface location error due to phasing of cutter vibrations

The purpose of this research is to investigate the relative importance of spindle speed, system dynamics, and cutting conditions on the accuracy of surface location in computer numerical-control (CNC) finish machining operations. The relationship between the spindle speed, the most flexible modes of the machine/cutting tool system and the final part dimensions is rather complex. The underlying theory, based on the situation of forced vibrations, is outlined. It is shown that the critical factor is the ratio of the tooth passing frequency to the system most flexible mode and corresponding natural frequency. Simple analytical calculations are carried out to illustrate the overcut/undercut surface error phenomenon. A simple simulation for end milling operations is also described which calculates the force on the cutter, the resulting cutter deflection, and the final error of surface. A comparison between the simulated and experimental results is presented. From experimental data, it shown that a change in surface location (and part dimension) of up to 50 μm is seen for a set of given conditions (i.e., cutter, material, chip load) simply by changing spindle speeds. Furthermore, it is seen that certain spindle speeds produce surfaces with no error introduced by the machining process.     

基于斜角切削理论的钛合金螺旋铣孔切削力建模

通过分析螺旋铣孔的加工原理和计算加工过程中的运动向量,结合侧刃和底刃对切削力的影响,建立了螺旋铣孔过程的切削力解析模型。提出了基于斜角切削的切削力系数辨识方法,并根据斜角切削过程几何关系推导出摩擦角、剪切角、剪切应力的约束方程。开展切削力系数辨识试验和钛合金螺旋铣孔试验对仿真值进行验证,结果表明,切削力的仿真值与试验值误差较小,平均误差为9.55%,从而验证了斜角切削系数辨识方法的有效性和切削力模型的正确性。     

In-process estimation of radial immersion angle using cutting force in face milling

In this paper, a on-line estimation method of the radial immersion angle using cutting force is presented. The ratio of cutting forces in feed and cross-feed directions acting on the single tooth at the immersion angle is a function of the immersion angle and the ratio of radial to tangential cutting force. It is found that the ratio of radial to tangential cutting force is not affected by cutting conditions and axial rake angle, which implies that the ratio determined by one preliminary experiment can be used regardless of the cutting conditions for a given tool and workpiece material. Using the measured cutting force during machining and predetermined ratio, the radial immersion ratio is estimated in process. Various experimental results show that the proposed method works within5% error range.     

Testing the diagonal measuring technique

This paper describes the results of a set of linear displacement accuracy measurements performed on two vertical CNC machining centers. The main scope of the work is to verify or disprove some of the recently claimed limitations of the conventional diagonal measurement method and of the “laser vector” or “sequential diagonal” method. Basically, we tested the effect of a large linear error deliberately introduced into one of the machine tool's axes. It is concluded that the laser vector method has not correctly identified this error and distributed the error into the remaining axes of the machine tool.     

Closed-form solution for wedge cutting force through thin metal sheets

A simple kinematic model is developed which describes the main features of the process of the cutting of a plate by a rigid wedge. It is assumed in this model that the plate material curls up into two inclined cylinders as the wedge advances into the plate. This results in membrane stretching up to fracture of the material near the wedge tip, while the “flaps” in the wake of the cut undergo cylindrical bending. Self-consistent, single-term formulas for the indentation force and the energy absorption are arrived at by relating the “far-field” and “near-tip” deformation events through a single geometric parameter, the instantaneous rolling radius. Further analysis of this solution reveals a weak dependence on the wedge angle and a strong dependence on friction coefficient. The final equation for the approximate cutting force over a range of wedge semiangles 10° ≤ θ ≤ 30° and friction coefficients 0.1 ≤ μ ≤ 0.4 is: F = 3.28σ₀(δ_t)^0.2l^0.4t^1.6μ^0.4, which is identical in form and characteristics to the empirical results recently reported by Lu and Calladine [Int. J. Mech. Sci.32, 295–313 (1990)].This analysis is believed to resolve a controversy recently developed in the literature over the interpretation of plate cutting experiments.     

虚拟加工中的加工误差分析与预测

分析了影响虚拟环境下复杂曲面产品数字化端铣加工误差产生的主要因素,综合考虑刀具和工件的柔度,同时考虑加工表面的变形敏感度,讨论面向虚拟制造的加工尺寸误差预测模型总体框架,提出了一个端铣加工过程表面加工尺寸误差预测模型。所给出的表面误差预测模型较全面地考虑了端铣加工过程,适于多种加工条件,能够反映端铣加工过程由切削力导致的系统变形对加工误差所造成的影响。最后给出了一个仿真实例。     

超声纵扭辅助铣削高强铝合金表面润湿性能研究

针对超声辅助加工在工件表面形成微刻划表面可以提高高强铝合金表面的微结构性能的现象,进行了单激励旋转超声纵扭复合铣削表面微观结构的试验,基于水接触角理论和纵扭铣削运动学理论分析了加工参数对水接触角的影响;搭建了单激励超声纵扭铣削试验平台,采用正交试验法研究了不同加工参数对表面粗糙度、铣削力以及表面润湿性能的影响。结果表明：超声振幅为4μm时表面质量最佳,切削速度和进给量与表面粗糙度和水接触角呈正相关的关系;超声加工方式下的表面水接触角较普通方式更大,而在超声加工时低振幅加工比高振幅加工的表面水接触角大,当转速达到一定值时,高振幅和低振幅所加工的表面水接触角差别不大。合适的加工参数条件下超声纵扭加工方式可以降低加工表面的粗糙度,改变表面的润湿性。     

<Emphasis Type="Bold">Accurate Machining of Freeform Surfaces by Restraining Cutter Contouring Errors</Emphasis>

Machined parts having sculptured surfaces pose challenges in the field of CAD/CAM. Sculptured surfaces are essential in the manufacture of components with curved geometry, which are demanded mostly in the aerospace and die and mould industries. This paper presents an adaptive cutter path restraining method for freeform surface machining and its implementation in milling. The ultimate goal is to achieve high contouring accuracy for sculptured parts machining which is a principal index for the performance evaluation of CNC machines. The proposed method is robust in achieving the desired surface cutting with the capability of satisfying pre-specified tolerance requirements using certain adaptive laws. The given tolerance is measured as the angular deviation by which the generated cutter path differs from the desired path. Since the feedrate is considered to be the most significant cutting parameter, only feedrate variations from 5 mm s^-1 to 30 mm s ^-1 are applied in this system. The tool paths generated with and without the adaptive mechanism are compared. The proposed methodology has been tested on a CNC milling system with an open-architecture controller. The experimental results demonstrate that the proposed tolerance feedback mechanism is very effective for producing parts with sculptured surfaces.     

SPH method applied to high speed cutting modelling

The purpose of this study is to introduce a new approach of high speed cutting numerical modelling. A Lagrangian smoothed particle hydrodynamics (SPH)-based model is carried out using the Ls-Dyna software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control permits a “natural” workpiece/chip separation. The developed approach is compared to machining dedicated code results and experimental data. The SPH cutting model has proved is ability to account for continuous to shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Thus, comparable results to machining dedicated codes are obtained without introducing any adjusting numerical parameters (friction coefficient, fracture control parameter).     

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.     

Cusp error reduction under high speed micro/meso- scale milling with ultrasonic vibration assistance

In the conventional use of vibration assisted machining, vibratory motion is mostly applied to the continuous machining processes such as turning where the cutting speed is much lower than the vibration speed. Even the recent articles on vibration assisted milling processes are also quite limited to low spindle speed less than 3k RPM. This study investigates vibration assistance that is applied to the workpiece in a high speed micro/meso-scale intermittent milling system where the cutting speed is much higher than the vibration speed. In addition to this, the vibration effect is analyzed considering feed and cross-feed directional application separately, which gives an idea of a right vibration assistance direction for surface quality improvement. To validate this, a one-directional ultrasonic vibration assisted milling system with ultrasonic frequency at 40 kHz and with amplitudes of a few microns is designed and its effect on the machined surface quality is investigated at high spindle RPMs over 15k. As a result, cusp heights are found to be reduced with ultrasonic vibratory motion of cutting edge in high cutting speed. Furthermore, the machined surface quality clearly tells that feed directional vibration assistance is able to generate better surface quality with reduced wavy burrs than cross-feed directional vibration assistance.     

Micromechanisms of deformation and fracture in shearing aluminum alloy sheet

A systematic experimental investigation is presented on trimming of aluminum alloy autobody sheets. The variations of cut surface quality and burr height are related to the cutting parameters of clearance, blade sharpness and cutting angle. It was discovered that, contrary to conventional wisdom requiring the blade to travel perpendicularly to the sheet (0°-“cutting angle”), at appropriate cutting angles the surface quality becomes insensitive to the blade sharpness, and almost zero burrs are produced for large clearances and extremely dull blades. The findings suggest that the robustness of current shearing practices for aluminum sheets can potentially be greatly improved, requiring much less frequent tool-sharpening and less restrictions on clearance control. A counter-intuitive phenomenon was revealed. At certain cutting angles and intermediate clearances, instead of burr heights and cut surface roughnesses monotonically increasing with decreases in the blade sharpness as expected, they first increased and then surprisingly decreased. Instability conditions exist at which cut surface quality and burr height are extremely sensitive to the cutting parameters.     

基于铣削力精确建模的工件表面让刀误差预测分析

航空航天制造业结构件的高速铣削加工中,在切削力作用下由整体铣削刀具挠度变形所引起的工件表面让刀误差,严重制约零件的加工精度和效率。针对这一问题,通过建立铣削力精确预测模型,结合刀具刚度特点,对工件让刀误差进行预测分析。将切削速度和刀具前角对切削力的影响规律引入二维直角单位切削力预测模型,并通过试验进行相关系数标定。借助等效前角将直角切削力预测系数应用到斜角切削力的预测,通过矢量叠加构建整体刀具三维切削力模型。分析刀具挠度变形对铣削层厚度及铣削接触中心角范围影响规律。基于离散化的刀具模型和切削力模型,建立铣削载荷条件下刀具等效直径悬臂梁模型弯曲变形计算方法。构建以刀具变形对铣削过程影响作用规律为反馈的刚性工件表面让刀误差及切削力柔性预测模型,通过整体铣刀铣削试验验证所建立理论模型的预测精度。