The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 2: Surface generation model and experimental verification

This paper presents a surface generation model for sculptured surface productions using the ball-end milling process. In this model, machining errors caused by tool deflections are studied. As shown in Part 1 of this paper, instantaneous horizontal cutting forces can be evaluated from the cutting geometries using mechanistic force models. In this paper, a tool deflection model is developed to calculate the corresponding horizontal tool deflection at the surface generation points on the cutter. The sensitivity of the machining errors to tool deflections, both in magnitude and direction, has been analyzed via the deflection sensitivity of the surface geometry. Machining errors are then determined from the tool deflection and the deflection sensitivity of the designed surface. The ability of this model in predicting dimensional errors for sculptured surfaces produced by the ball-end milling process has been verified by a machining experiment. In addition to providing a means to predict dimensional accuracy prior to actual cutting, this surface generation model can also be used as a tool for quality control and machining planning.     

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.     

Cutting force prediction of sculptured surface ball-end milling using Z-map

The cutting force in ball-end milling of sculptured surfaces is calculated. In sculptured surface machining, a simple method to determine the cutter contact area is necessary since cutting geometry is complicated and cutter contact area changes continuously. In this study, the cutter contact area is determined from the Z-map of the surface geometry and current cutter location. To determine cutting edge element engagement, the cutting edge elements are projected onto the cutter plane normal to the Z-axis and compared with the cutter contact area obtained from the Z-map. Cutting forces acting on the engaged cutting edge elements are calculated using an empirical method. Empirical cutting mechanism parameters are set as functions of cutting edge element position angle in order to consider the cutting action variation along the cutting edge. The relationship between undeformed chip geometry and the cutter feed inclination angle is also analyzed. The resultant cutting force is calculated by numerical integration of cutting forces acting on the engaged cutting edge elements. A series of experiments were performed to verify the proposed cutting force estimation model. It is shown that the proposed method predicts cutting force effectively for any geometry including sculptured surfaces with cusp marks and a hole.     

Improving Cycle Time in Sculptured Surface Machining Through Force Modeling

In this paper, an enhanced mathematical model is presented for the prediction of cutting force system in ball end milling of sculptured surfaces. This force model is also used as the basis for off-line feed rate scheduling along the tool path in order to decrease the cycle time in sculptured surface machining. As an alternative for setting a constant feed rate all along the tool path in rough machining of sculptured surfaces, resultant cutting forces are aimed to be kept under a pre-set threshold value along the tool path by off-line scheduled piecewise variable feed rates. In this paper, it is shown that machining time, depending on complexity of sculptured surfaces, can be decreased significantly by scheduling feed rate along the tool path. The model is tested under various cutting conditions and some of the results are also presented and discussed in the paper.     

基于开放式系统的曲面加工误差动态补偿控制

将基于传感器信息的智能型开放加工系统应用于曲面的高精度加工,提出了曲面加工误差的动态补偿方法。为预测加工误差的补偿量,建立了刀具弯曲模型,分析了刀具弯曲对加工误差的影响。实验结果表明,本系统可有效地提高加工精度,使加工误差降低1／3－1／4。     

The prediction of cutting force in ball-end milling

Due to the development of CNC machining centers and automatic programming software, the ball-end milling have become the most widely used machining process for sculptured surfaces. In this study, the ball-end milling process has been analysed, and its cutting force model has been developed to predict the instantaneous cutting force on given machining conditions. The development of the model is based on the analysis of cutting geometry of the ball-end mill with plane rake faces. A cutting edge of the ball-end mill was considered as a series of infinitesimal elements, and the geometry of a cutting edge element was analysed to calculate the necessary parameters for its oblique cutting process assuming that each cutting edge was straight. The oblique cutting process in the small cutting edge element has been analysed as an orthogonal cutting process in the plane containing the cutting velocity and chip flow vectors. And with the orthogonal cutting data obtained from end turning tests on thin-walled tubes over wide range of cutting and tooling conditions, the cutting forces of ball-end milling could be predicted using the model. The predicted cutting forces have shown a fairly good agreement with test results in various machining modes.     

Increasing productivity in sculpture surface machining via off-line piecewise variable feedrate scheduling based on the force system model

Sculpture surface machining is a critical process commonly used in various industries such as the automobile, aerospace, die/mold industries. Since there is a lack of scientific tools in practical process planning stages, feedrates for CNC machining are selected based on the trial errors and previous experiences. In the selections of the process parameters, production-planning engineers are conservative in order to avoid undesirable results such as chipping, cutter breakage or over-cut due to excessive cutter deflection. Currently, commonly used CAD/CAM programs use only the geometric and volumetric analysis, but not the physics of the processes, and rely on experience based cutting tool database and users’ inputs for selection of the process parameters such as feed and speed. Usually, the feeds and cutting speeds are set individual constant values all along the roughing, semi-finishing, and finishing processes. Being too conservative and setting feedrate constant all along the tool path in machining of sculpture surfaces can be quite costly for the manufacturers. However, a force model based on the physics of the cutting process will be greatly beneficial for varying the feedrate piecewise along the tool path.The model presented here is the first stage in order to integrate the physics of the ball-end milling process into the selection of the feeds during the sculpture surface machining. Therefore, in this paper, an enhanced mathematical model is presented for the prediction of cutting force system in ball end milling of sculpture surfaces. This physical force model is used for selecting varying and ‘appropriate’ feed values along the tool path in order to decrease the cycle time in sculpture surface machining. The model is tested under various machining conditions, and some of the results are also presented in the paper.     

Milling error prediction and compensation in machining of low-rigidity parts

The paper reports on a new integrated methodology for modelling and prediction of surface errors caused by deflection during machining of low-rigidity components. The proposed approach is based on identifying and modelling key processing characteristics that influence part deflection, predicting the workpiece deflection through an adaptive flexible theoretical force-FEA deflection model and providing an input for downstream decision making on error compensation. A new analytical flexible force model suitable for static machining error prediction of low-rigidity components is proposed. The model is based on an extended perfect plastic layer model integrated with a FE model for prediction of part deflection. At each computational step, the flexible force is calculated by taking into account the changes of the immersion angles of the engaged teeth. The material removal process at any infinitesimal segment of the milling cutter teeth is considered as oblique cutting, for which the cutting force is calculated using an orthogonal–oblique transformation. This study aims to increase the understanding of the causes of poor geometric accuracy by considering the impact of the machining forces on the deflection of thin-wall structures. The reported work is a part of an ongoing research for developing an adaptive machining planning environment for surface error modelling and prediction and selection of process and tool path parameters for rapid machining of complex low-rigidity high-accuracy parts.     

Predictive force model for ball-end milling and experimental validation with a wavelike form machining test

This paper presents a predictive force model for ball-end milling based on thermomechanical modelling of oblique cutting. The tool geometry is decomposed into a series of axial elementary cutting edges. At any active tooth element, the chip formation is obtained from an oblique cutting process characterised by local undeformed chip section and local cutting angles. This method predicts accurately the cutting force distribution on the helical ball-end mill flutes from the tool geometry, the pre-form surface, the tool path, the cutting conditions, the material behaviour and the friction at the tool-chip interface. The model is applied for a complex surface which is a wavelike form used as a validation machining test. The results are compared with experimental data obtained from ball-end milling tests performed on a 3-axis CNC equipped with a Kistler dynamometer.     

Cutting force estimation in sculptured surface milling

Cutting force milling models developed up to now are mostly used for planar milling using end-mills. Only a reduced number of models applying ball-end mills have been developed. Furthermore these models usually only consider horizontal surface machining, even though the main application of ball-end mills is sculptured surface machining. This article proposes a model that is able to estimate the cutting forces in inclined surfaces machined both up-milling and down-milling. For this purpose a semi-mechanistic model has been developed that calculates the cutting forces based on a set of coefficients which depend on the material, the tool, the cutting conditions, the machining direction and the slope of the surface.A coordinate transformation has been included in order to consider the slope milling case with different cutting directions.The model has been tested on two materials, an aluminum alloy Al7075-T6 and a 52 HRC tool steel AISI H13. Validation tests have been carried out on inclined planes using different slopes and different machining directions.The results provide errors below 10% in most of the cases and both the value and shape of the predicted forces adjust the measured cutting force.     

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.     

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

Sculptured surface machining is a time-consuming and costly process. It requires simultaneously controlled motion of the machine axes. However, positioning inaccuracies or errors exist in machine tools. The combination of error motions of the machine axes will result in a complicated pattern of part geometry errors. In order to quantitatively predict these part geometry errors, a new application framework ‘enhanced virtual machining’ is developed. It integrates machine tool error models into NC machining simulation. The ideal cutter path in the NC program for surface machining is discretized into sub-paths. For each interpolated cutter location, the machine geometric errors are predicted from the machine tool error model. Both the solid modeling approach and the surface modeling approach are used to translate machine geometric errors into part geometry errors for sculptured surface machining. The solid modeling approach obtains the final part geometry by subtracting the tool swept volume from the stock geometric model. The surface modeling approach approximates the actual cutter contact points by calculating the cutting tool motion and geometry. The simulation results show that the machine tool error model can be effectively integrated into sculptured surface machining to predict part geometry errors before the real cutting begins.     

Integrated tool path and feed rate optimization for the finishing machining of 3D plane surfaces

An integrated approach for the concurrent optimization of tool path and feed rate for the finishing machining of 3D plane surfaces using ball-end milling is presented in this paper. This work is important, as the developed optimization approach is readily applicable to the finishing machining of sculptured surfaces. The concurrently optimized tool path and feed rate correspond to the maximum machining efficiency and satisfy the scallop height and machining error requirements. The cutter feed direction is employed as the optimization variable. For each cutter feed direction, tool path is determined according to the scallop height requirement and feed rate is maximized with the tolerance requirement by using a mechanistic cutting force model for three-dimensional ball-end milling. Optimization results have indicated that the shortest total tool path length, favored by most existing optimization approaches, does not result in maximum efficiency because the corresponding feed rate is often constrained by the specified tolerance. The optimum cutter feed direction is in general not unique but falls within an optimum range in the finishing machining of 3D plane surfaces.     

Feed rate scheduling model considering transverse rupture strength of a tool for 3D ball-end milling

This paper presents an analytical model of off-line feed rate scheduling to determine desired feed rates for 3D ball-end milling. Off-line feed rate scheduling is presented as the advanced technology to regulate cutting forces through change of feed per tooth, which directly affects variation of uncut chip thickness. In this paper, the uncut chip thickness is calculated by following the movement of the position of the cutter center, which is determined by runout and cutter deflection. Also, since the developed cutting force model uses the cutting-condition-independent coefficients, off-line feed rate scheduling can be effectively performed regardless of continuous change of cutting conditions. Transverse rupture strength of the tool is used to determine the reference cutting force at which resultant cutting forces are regulated through feed rate scheduling. Experiments validated that the presented feed rate scheduling model reduced machining time drastically and regulated cutting forces at the reference cutting force.     

Precise prediction of forces in milling circular corners

Pocket corner is the most typical characters of aerospace structure components. To achieve high-quality product and stable machining operation, manufacturer constantly seek to control the cutting forces in pocket corner milling process. This paper presents the cutting force in corner milling considering the precision instantaneous achievements of tool engagement angle and undeformed chip thickness. To achieve the actual milling tool engagement angle in corner milling process, the details of tool–corner engagement relationship are analyzed considering the elements of tool trajectory, tool radius, and corner radius. The actual undeformed chip thicknesses in up and down milling operations are approached on account of the trochoid paths of adjacent teeth by a presented iteration algorithm. Error analysis shows that the presented models of tool engagement angle and undeformed chip thickness have higher precision comparing with the traditional models. Combined with the cutting force coefficients fitted by a series of slot milling tests, the predicted cutting force in milling titanium pocket with different corner structure and milling parameters are achieved, and the prediction accuracy of the model was validated experimentally and the obtained predict and the experiment results were found in good agreement.     

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.     

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.     

The form error prediction in side wall machining considering tool deflection

In this research, an effective method for the form error prediction in side wall machining with a flat end mill is suggested. The form error is predicted directly from the tool deflection without surface generation by cutting edge locus with time simulation. The developed model can predict the surface form error accurately about 300 times faster than the previous method. Cutting forces and tool deflection are calculated considering tool geometry, tool setting error and machine tool stiffness. The characteristics and the difference of generated surface shape in up milling and down milling are discussed. The usefulness of the presented method is verified from a set of experiments under various cutting conditions generally used in die and mold manufacturing. This study contributes to real time surface shape estimation and cutting process planning for the improvement of form accuracy.     

复杂型面数控加工中的切削力预测

球头铣刀加工水平面的切削力的预测模型已经非常成熟,而对于球头铣刀加工复杂型面切削力预测的研究却很少。文章提出一种模型来预测复杂型面加工过程中的切削力。此模型通过坐标转换．使零件坐标系统与刀具坐标系统一致,并根据具体的材料,刀具,切削条件,加工方向以及表面斜率的一套参数来预测切削力。这个模型将为复杂型面加工条件的选择提供参考,并提高加工效率。