Tool deflection compensation in peripheral milling of curved geometries

This paper presents compensation of surface error due to cutting force-induced tool deflections in a peripheral milling process. Previous research attempts on this topic deal with error compensation in machining of straight geometries only. This paper is concerned with peripheral milling of variable curvature geometries where the workpiece curvature changes continuously along the path of cut. In the case of curved geometries, both process geometry and the cutting forces have shown to have strong dependence on workpiece curvature and hence variation of surface error along the path of cut. This calls for a different error compensation strategy than the one which is normally used for machining straight geometries. The present work is an attempt to improve accuracy in machining of curved geometries by use of CNC tool path compensation. Mechanistic model for cutting force estimation and cantilever beam model for cutter deflection estimation are used. The results based on machining experiments performed on a variety of geometries show that the dimensional accuracy can be improved significantly in peripheral milling of curved geometries.     

Effect of direction of parameterization on cutting forces and surface error in machining curved geometries

The present paper investigates the effect of two variables, namely direction of parameterization and cutter diameter on process geometry, cutting forces, and surface error in peripheral milling of curved geometries. In machining of curved geometries where the curvature varies continuously along tool path, the process geometry variables, namely feed per tooth, engagement angle, and maximum undeformed chip thickness too vary along tool path. These variations will be different when a given geometry is machined from different parametric directions and with different cutter diameters. This difference in process geometry variations result in changed cutting forces and surface error along machined path. This aspect has been studied for variable curvature geometries by machining from both parametric directions and using cutters of different diameter. The computer simulation studies carried out show considerable amount of shift in the location of peak cutting forces with the change in cutting direction and cutter diameter, particularly in concave regions of workpiece geometry. A new parameter γ that relates the instantaneous curvature of workpiece with cutter radius is defined. The larger value of γ is an indicator of greater shift in the location of peak forces from the point of maximum curvature on the workpiece. The simulation results are validated by carrying out machining experiments with curved workpiece geometry and are found to be in good agreement.     

Process geometry modeling with cutter runout for milling of curved surfaces

Prediction of cutting forces and machined surface error in peripheral milling of curved geometries is non-trivial due to varying workpiece curvature along tool path. The complexity in this case, arises due to continuously changing process geometry as workpiece curvature varies along tool path. In the presence of cutter runout, the situation is further complicated owing to changing radii of cutting points. The present work attempts to model process geometry in machining of curved geometries and in the presence of cutter runout. A mathematical model computing process geometry parameters which include cutter/workpiece engagements and instantaneous uncut chip thickness in the presence of cutter runout is presented. The developed model is more realistic as it accounts for interaction of cutting tooth trajectory with that of preceding teeth trajectories in computing process geometry. Computer simulation studies carried for this purpose has shown that it is essential to account for teeth trajectory interactions for accurate prediction of process geometry parameters. This aspect is further confirmed with machining experiments, which were conducted to validate this aspect. From the outcomes of present work, it is clearly seen that the computation of process geometry during machining of curved geometries and in presence of cutter runout is not straightforward and requires a systematic approach as presented in this paper.     

Modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces

The paper presents modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces. The paper differs from previous work in this area, in two respects. Firstly it deals with milling of variable curvature geometries unlike zero and constant curvature geometries dealt in the past. Secondly true tooth trajectories are considered for modelling process geometry in milling of curved surfaces instead of simpler circular tooth trajectories. Mathematical expressions for, feed per tooth along cutter contact path, entry and exits angles of tooth, undeformed chip thickness and surface error are derived and effect of workpiece curvature on these variables is studied. As cutting forces depend on these process variables, physical experiments were also performed to study the effect of workpiece curvature on cutting forces. Process simulation experiments carried out show the need for modelling true tooth trajectories instead of circular tooth trajectories particularly for curved geometries. Results also show that using simpler constant curvature models to variable curvature geometries for the purpose of estimation of process geometry variables could be erroneous.     

Prediction of cutting forces in milling of circular corner profiles

This paper proposes an approach to predict the cutting forces in peripheral milling of circular corner profiles in which varying radial depth of cut is encountered. The geometric relationship between an end mill and the corner profile is investigated and a mathematical model is presented to describe the different phases of the cutter/workpiece contact. The milling process for circular corner 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. A time domain analytical model of cutting forces for the steady-state machining conditions is introduced to each segmented process for the cutting force prediction. The predicted cutting forces can be calculated in terms of tool/workpiece geometry, cutting parameters and workpirece material property, as well as the relative position of the tool to workpiece. Experiments are conducted and the measured forces are compared to the predictions for the verification of the proposed method.     

Sculpture surface machining: a generalized model of ball-end milling force system

A new mechanistic model is presented for the prediction of a cutting force system in ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter location (CL) file, cutter and workpiece geometries. Furthermore, an analytical approach is used to determine the instantaneous chip load (with and without runout) and cutting forces. In addition to predicting the cutting forces, the model also employs a Boolean approach for a given cutter, workpiece geometries, and CL file to determine the surface topography and scallop height variations along the workpiece surface which can be visualized in 3-D. The results of model validation experiments on machining Ti-6A1-4V are also reported. Comparisons of the predicted and measured forces as well as surface topography show good agreement.     

Analytical modeling of acoustic emission for monitoring of peripheral milling process

This paper presents the development of an analytical model relating the acoustic emission (AE) energy content to the cutting process parameters in peripheral milling and the experimental verification of the effects of the cutting parameters on the AE energy measurement to assess the applicability of AE sensing to the monitoring of peripheral milling. The model consists of an oblique cutting component and a rubbing component. It includes the contribution from both the AE attributed to plastic deformation in the primary shear zone and the AE resulting from interfaces between chips and the rake faces of the cutting teeth, between the workpiece and the cutter periphery as well as between the cutter flank and the machined workpiece surface. The adoption of an effective shear angle and a mean fraction angle in the model formulation provides insight into the fundamental mechanism of the cutting process responsible for the generation of the acoustic emission. A numerical example following the model development and a series of peripheral milling tests show that the true mean square voltage of the AE signal from peripheral milling increases with the primary cutting parameters (cutter rotating speed, feedrate, axial and radial depths of cut). The result of this work suggests that the energy measurement of the AE signal can be effectively used for the monitoring of peripheral milling processes.     

碳纤维/树脂基复合材料铣削表面粗糙度及表面形貌研究

目的研究了CFRP材料铣削加工过程中,部分主要工艺对CFRP材料加工表面质量的影响规律,为工艺参数优化,提高此类零件的表面质量提供依据。方法设计了CFRP材料铣削中的切削参数、刀具结构、加工方法与加工表面粗糙度及表面形貌之间的单因素试验。通过单调改变一个切削参数而其余切削参数不变,得到了工件表面粗糙度和表面形貌随切削参数、刀具结构、加工方法的变化规律。结果当铣削速度增大时,工件的表面粗糙度变化不大,表面微坑缺陷的数量却有所增加,但变小、变浅。当进给速度增大时,工件表面粗糙度呈上升趋势,表面缺陷也随之增加。无涂层多齿刀具铣削后的工件表面粗糙度最大,其次是金刚石涂层多齿刀具铣削的工件,最小的是金刚石涂层交错齿刀具铣削的工件。多齿刀具加工后的表面有较多的微坑缺陷,但普遍深度较浅且面积较小。交错齿刀具对分层缺陷的抑制作用最明显,但在左旋和右旋刀齿交错处容易出现较严重的加工缺陷。与普通机械加工方法相比,超声振动加工方法得到的工件表面质量较好,可以有效减少表面微坑缺陷,改善CFRP铣削加工表面质量。结论 CFRP材料铣削加工时,为了获得较好的加工表面质量,切削参数应选用较高的切削速度和较低的进给速度,切削刀具宜选用多齿带涂层刀具。和普通机械加工方法相比,超声振动铣削加工方法更为有利于获得好的表面质量。     

Efficient algorithms for calculations of static form errors in peripheral milling

This paper aims at developing numerical algorithms to predict the form errors in peripheral milling of thin-walled workpieces using finite element method. Some crucial algorithms associated with the judgment of contacts between the cutter and the workpiece, iterative corrections of radial and axial cutting depths as well as the workpiece's rigidity without remeshing are developed and presented in detail. By means of numerical tests, it is shown that the proposed approach is efficient and flexible. 3D irregular volume elements such as tetrahedral elements, prismatic elements, hexahedral elements or a combination of them can be freely used to predict form errors of machining workpieces.     

Geometric adaptive straightness control system for the peripheral end milling process with large error sources

An off-line Geometric Adaptive Control (GAC) scheme is proposed to compensate for machining straightness errors due to the machine tool's inaccuracy and those arising as a result of the metal cutting process during the finish peripheral end milling process. In the milling process, the workpiece travels along the guideway while the spindle system remains fixed. The scheme is based on the exponential smoothing of post-process measurements of relative machining errors due to the tool and bed deflections. Without a priori knowledge of the variations of the cutting parameters, the time-varying parameters are estimated by an Exponentially Weighted Recursive Least Squares (EWRLS) method. This method is able to incorporate a straightedge which is not necessarily accurate to identify the guideway errors. To reduce the drift of the cutting parameters, a single parameter adaptation method is introduced. Experimental results show that the location error is controlled within the range of the fixing error of the milling bed on the guideway. Further, the waviness error is reduced to less than 10 μm in the machining of a 508-mm long prismatic workpiece regardless of the machining conditions.     

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

Experimental investigation and simulation of machining thin-walled workpieces

An enhanced simulation model is presented in this paper to predict form deviations in end milling processes of thin-walled structures. The calculation of tool engagement is based on level curves representing surface geometry of the workpiece and the NC code driven sweep volume. To consider influences of force-induced deflections resulting in static form errors on machined surface of the workpiece, a model for superposed stresses is enclosed. Derived from the tool engagement, the cutting force is predicted using a parametric force model. The experimental investigations within the measuring of static and dynamic form errors during processing and afterwards are shown and measurement results are compared with results of the cutting simulation to verify the proposed method. The presented achievements are deduced from research activities aiming at an increased understanding of shape deviation induced by interactions between tool, workpiece and clamping device during machining.     

Modelling the machining dynamics of peripheral milling

The machining dynamics involves the dynamic cutting forces, the structural modal analysis of a cutting system, the vibrations of the cutter and workpiece, and their correlation. This paper presents a new approach modelling and predicting the machining dynamics for peripheral milling. First, a machining dynamics model is developed based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces, which are mathematically modelled and experimentally verified by the authors [Liu, X., Cheng, K., Webb, D., Luo, X.-C. Improved dynamic cutting force model in peripheral milling—Part 1: Theoretical model and simulation. Int. J. Adv Manufact Tech, 2002, 20, 631–638; Liu, X., Cheng, K., Webb, D., Longstaff, A. P., Widiyarto, H. M., Jiang, X.-Q., Blunt, L., Ford, D. Improved dynamic cutting force model in peripheral milling—Part 2: Experimental verification and prediction. Int. J. Adv Manufact Tech, 2004, 24, 794–805]. Then, the mechanism of surface generation is analysed and formulated based on the geometry and kinematics of the cutter. Thereafter a simulation model of the machining dynamics is implemented using Simulink. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machine centre were measured in both normal and feed directions by an instrumented hammer and accelerometers. Then a set of well-designed cutting trials was carried out to record and analyse the dynamic cutting forces, the vibrations of the spindle head and workpiece, and the surface roughness and waviness. Corresponding simulations of the machining processes of these cutting trials based on the machining dynamics model are investigated and the simulation results are analysed and compared to the measurements. It is shown that the proposed machining dynamics model can well predict the dynamic cutting forces, the vibrations of the cutter and workpiece. There is a reasonable agreement between the measured and predicted roughness/waviness of the machined surface. Therefore the proposed approach is proven to be a feasible and practical approach analysing machining dynamics and surface roughness/waviness for shop floor applications.     

Milling force prediction using a dynamic shear length model

Modelling of cutting forces in milling is often needed in machining automation. In this paper, a new method for the determination of the cutting forces in face milling is presented, which applies a predictive machining theory originally developed for orthogonal cutting to milling operations, with a dynamic shear length model developed and incorporated. The proposed dynamic shear length model is developed based on the analysis for the true tooth trajectories of a milling cutter, taking into account of the characteristic wavy surface effects in milling. The prediction for the cutting forces is carried out at each step of the angular increment of cutter rotation from input data of fundamental workpiece material properties, tool geometry and cutting conditions. Cutting forces at a cutter tooth can be predicted once the shear angle, shear length, shear plane area, and the shear flow stress along the shear length have been determined. The milling force prediction using the dynamic shear length model is verified through milling experimental tests. The sensitivity of the difference between the static and dynamic shear length models with respect to the feed per tooth and the cutter diameter is discussed.     

车铣加工UG-CAM制造技术研究与应用

应用TCL（Tool Command Language）开发了车铣加工中心BUNMOTECS192FT后处理模块,实现了该机床刀具中心点B轴随动的高级功能,利用UG～CAM数控编程技术,使用平头立铣刀,在车铣加工中心进行C、X、y轴联动,完成了零件曲面加工刀轨设计,解决了T型铣刀加工曲面环槽干涉问题,通过将平头立铣刀轴与曲面法线倾斜一定角度,避开平头立铣刀底齿中心切削,达到零件精度要求。     

Cutting force prediction in ball end milling of sculptured surface with Z-level contouring tool path

This paper presents an approach to predict cutting force in 3-axis ball end milling of sculptured surface with Z-level contouring tool path. The variable feed turning angle is proposed to denote the angular position of feed direction within tool axis perpendicular plane. In order to precisely describe the variation of feed turning angle and cutter engagement, the whole process of sculptured surface milling is discretized at intervals of feed per tooth along tool path. Each segmented process is considered as a small steady-state cutting. For each segmented cutting, the feed turning angle is determined according to the position of its start/end points, and the cutter engagement is obtained using a new efficient Z-map method. Both the chip thickness model and cutting force model for steady-state machining are improved for involving the effect of varying feed turning angle and cutter engagement in sculptured surface machining. In validation experiment, a practical 3-axis ball end milling of sculptured surface with Z-level contouring tool path is operated. Comparisons of the predicted cutting forces and the measurements show the reliability of the proposed approach.     

Error compensation in flexible end milling of tubular geometries

There are many machining situations where slender tools are used to machine thin walled tubular workpieces. Such instances are more common in machining of aircraft structural parts. In these cases, cutting force induced tool as well as workpiece deflections are quite common which result into surface error on machined components. This paper presents a methodology to compensate such tool and workpiece induced surface errors in machining of thin walled geometries by modifying tool paths. The accuracy with which deflections can be predicted strongly depends on correctness of the cutting force model used. Traditionally employed mechanistic cutting force models overestimate tool and workpiece deflections in this case as the change of process geometry due to deflections is not accounted in modeling. Therefore, a cutting force model accounting for change in process geometry due to static deflections of tool and workpiece is adopted in this work. Such a force model is used in predicting tool and workpiece deflection induced surface errors on machined components and then compensating the same by modifying tool path. The paper also studies effectiveness of error compensation scheme for both synclastic and anti-clastic configurations of tubular geometries.     

Modeling of process geometry in peripheral milling of curved surfaces

This paper presents an approach for modeling of the process geometry in peripheral milling of curved surfaces. The modeled process geometry involves feed direction, equivalent feedrate and cutter entry/exit angle. The equivalent feedrate, which is defined at the centroid of cutting cross-section, is proposed to measure the actual machining feedrate. The milling process of curved surface is discretized at intervals of feed per tooth for describing the variation of process geometry. The mathematical models for calculating the process geometry of each segmented cutting process are presented. Two same curved surfaces are machined. The tool paths are carried out with NURBS interpolation and traditional consecutive small line segments interpolation, respectively. The simulated and measured results are presented for the verification of the proposed method.     

Simulation of flank milling processes

The paper presents prediction of cutting forces when flank milling ruled surfaces with tapered, helical, ball end mills. The geometric model of the workpiece is imported from standard CAD systems, and the tapered helical ball end mill is modeled as the combination of sphere and cone primitives in ACIS^© solid modeling environment. The intersection of cutter and part with a ruled surface is evaluated, and the cutter entry into and exit angles from the work material are modeled, and stored as a function of tool center coordinates along the path. The cutter entry and exit angles, the immersion angles, are used as boundary conditions in predicting the cutting forces along the path. The methodology allows prediction of cutting load distribution on the tool and part, as well optimization of machining cycle times by scheduling the feedrate in such a way that torque, power and static deflections can be maintained at safe levels.     

Runout effects in milling: Surface finish, surface location error, and stability

This paper investigates the effect of milling cutter teeth runout on surface topography, surface location error, and stability in end milling. Runout remains an important issue in machining because commercially-available cutter bodies often exhibit significant variation in the teeth/insert radial locations; therefore, the chip load on the individual cutting teeth varies periodically. This varying chip load influences the machining process and can lead to premature failure of the cutting edges. The effect of runout on cutting force and surface finish for proportional and non-proportional tooth spacing is isolated here by completing experiments on a precision milling machine with 0.1 μm positioning repeatability and 0.02 μm spindle error motion. Experimental tests are completed with different amounts of radial runout and the results are compared with a comprehensive time-domain simulation. After verification, the simulation is used to explore the relationships between runout, surface finish, stability, and surface location error. A new instability that occurs when harmonics of the runout frequency coincide with the dominant system natural frequency is identified.