Ball-end Milling Process Research Articles

An Enhanced Force Model for Sculptured Surface Machining

Abstract The ball-end milling process is used extensively in machining of sculpture surfaces in automotive, die/mold, and aerospace industries. In planning machining operations, the process planner has to be conservative when selecting machining conditions with respect to metal removal rate in order to avoid cutter chipping and breakage, or over-cut due to excessive cutter deflection. These problems are particularly important for machining of sculptured surfaces where axial and radial depths of cut are abruptly changing. This article presents a mathematical model that is developed to predict the cutting forces during ball-end milling of sculpture surfaces. The model has the ability to calculate the workpiece/cutter intersection domain automatically for a given cutter path, cutter, and workpiece geometries. In addition to predicting the cutting forces, the model determines the surface topography that can be visualized in solid form. Extensive experiments are performed to validate the theoretical model with measured forces. For complex part geometries, the mathematical model predictions were compared with experimental measurements.

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.

A solid modeler based ball-end milling process simulation

A system for geometric and physical simulation of the ball-end milling process using solid modeling is presented in this paper. A commercially available geometric engine is used to represent the cutting edge, cutter and updated part. The ball-end mill cutter modeled in this study is an insert type ball-end mill and the cutting edge is generated by intersecting an inclined plane with the cutter ball nose. The contact face between cutter and updated part is determined from the solid model of the updated part and cutter solid model. To determine cutting edge engagement for each tool rotational step, the intersections between the cutting edge with boundary of the contact face are determined. The engaged portion of the cutting edge for each tool rotational step is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting data base available in the open literature. For each tool rotational position, the cutting force components are calculated by summing up the differential cutting forces. The instantaneous dynamic chip thickness is computed by summing up the rigid chip thickness, the tool deflection and the undulations left from the previous tooth, and then the dynamic cutting forces are obtained. For calculating the ploughing forces, Wu's model is extended to the ball-end milling process [21]. The total forces, including the cutting and ploughing forces, are applied to the structural vibratory model of the system and the dynamic deflections at the tool tip are predicted. The developed system is verified experimentally for various up-hill and down-hill angles.

Estimation of cutter deflection and form error in ball-end milling processes

This paper presents a method to analyze the 3-dimensional form error of a ball-end milled surface due to the elastic compliance of the cutting tool. In order to estimate the form error in various cutting modes, the cutting force and the cutter deflection models including the effect of the surface inclination were established. The cutting forces were calculated by using the cutter contact area determined from the Z-map of the surface geometry and the current cutter location. The tool deflection responding to the cutting force was then calculated by considering the cutter and the holder stiffness. The cutter was modeled as a cantilever beam consisting of the shank and the flute. The stiffness of the holder was measured experimentally. Various experimental works have been performed to verify the validity of the proposed model. It is shown that the proposed method is capable of accurate prediction of cutting forces and the surface form error.

Simulation of cutting forces in ball-end milling

The paper presents a simulation system (SCP) that determines the cutting forces in the ball-end milling process. The system is based on numerical methods, computer programme, theoretical knowledge of technological processes, machining and tests performed. The system for simulation of the cutting process combines the technological data base, the analytical and experimental model and the data base SCP. The experimental model contains a collection of variables of the cutting process by means of sensors and transformation of those data into numerical values, which are a starting point for data calculation of characteristic coefficients of materials. The analytical model is used to estimate the tangential, radial and axial cutting forces, along with a material data base obtained from cutting experiments. Ball-end milling test has been conducted to verify simulation results. The simulation results, are the basis for the development of the tool-designing model and for the model of optimization of the machining process cutting parameters.

Prediction of Cutting Process with Curved-Edge End Mill (1st Report, Application of Ball End Milling Process in Energy Approach)

An approach is presented to predict the chip formation and the three components of cutting force in the machining with the curved-edge end mill, which has the tool geometries changing with the cutter height. Those geometrical parameters are defined as the functions of the cutter height. The chip formation in the milling process is modeled as a pilling up of orthogonal cuttings along the cutting edge. The orthogonal cuttings are made in the planes containing the cutting velocities and the chip flow velocities so that chip flows up to a certain direction as a rigid body. The chip flow direction can be given to minimize the cutting energy, which can be given as the sum of the shear energy on shear plane and the friction energy on rake face. The cutting force, then, can be predicted with the chip formation having the minimum cutting energy. The presented approach is applied to the prediction of cutting process in the machining with the insert-ball end mill. The predicted results are verified to be accurate enough in a variety of depth of cut. The change of the chip flow angle and that of the orthogonal cutting model during a rotation of the cutter can be shown in the presented approach.

Chip load prediction in ball-end milling

In the modern manufacturing of sophisticated parts with 3D sculptured surfaces such as dies and molds, ball-end milling is one of the most widely used machining processes to remove unwanted material. However, the machining processes are accompanied by cutting forces that cause tool chattering and dimensional errors. In this paper, a calculation algorithm for the chip load along the cutting edge is proposed, so that it is can be used for predicting cutting forces and the region with excessive dimensional error in the ball-end milling process. For this purpose, an exact chip engagement surface (ECES) from cutting edge geometry is suggested to be a mathematical model with the feed rate effect of cutter, instead of a semi-spherical surface. With the calculated chip load distribution, a simplified method for calculating cutting force at a cutter location is also proposed.

Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces

A mechanistic modeling approach to predicting cutting forces is developed for multi-axis ball end milling of free-form surfaces. The workpiece surface is represented by discretized point vectors. The modeling approach employs the cutting edge profile in either analytical or measured form. The engaged cut geometry is determined by classification of the elemental cutting point positions with respect to the workpiece surface. The chip load model determines the undeformed chip thickness distribution along the cutting edges with consideration of various process faults. Given a 5-axis tool path in a cutter location file, shape driving profiles are generated and piecewise ruled surfaces are used to construct the tool swept envelope. The tool swept envelope is then used to update the workpiece surface geometry employing the Z-map method. A series of 3-axis and 5-axis surface machining tests on Ti6A14V were conducted to validate the model. The model shows good computational efficiency, and the force predictions are found in good agreement with the measured data.

A Mechanistic Cutting Force Model for 3D Ball-end Milling

This paper presents an improved mechanistic cutting force model for the ball-end milling process. The objective is to accurately model the cutting forces for nonhorizontal and cross-feed cutter movements in 3D finishing ball-end milling. Main features of the model include: (1) a robust cut geometry identification method to establish the complicated engaged area on the cutter; (2) a generalized algorithm to determine the undeformed chip thickness for each engaged cutting edge element; and (3) a comprehensive empirical chip-force relationship to characterize nonhorizontal cutting mechanics. Experimental results have shown that the present model gives excellent predictions of cutting forces in 3D ball-end milling.

Integrated planning for precision machining of complex surfaces—III. Compensation of dimensionai errors

This paper presents an approach that compensates machining errors in ball-end milling processes using the control-surface strategy. In the proposed approach, machining errors induced by cutter deflections are predicted from a surface generation model so that actual machining experiments and dimensional inspections are not required. Therefore, the proposed approach can be integrated into an integrated framework for machining planning in which prediction and compensation of dimensional errors take place in the process development phase rather than in the manufacturing phase of the production cycle. Based on the predictive capability of the surface generation model, a sensitivity function is defined so as to characterize the variations of the machining errors when perturbing the control surface. Using the defined sensitivity function, a compensated control surface can be constructed, based on which new cutting paths can be planned and “near-zero” surface dimensional errors can be accomplished. In order to verify the proposed strategy, actual production of a turbine blade die using a CNC machining center was conducted. By using the control-surface strategy with the sensitivity function approach, the maximum surface dimensional error is reduced from ± 340 to ± 10 μm.

A Flexible Ball-End Milling System Model for Cutting Force and Machining Error Prediction

This paper presents a flexible system model for the prediction of cutting forces and the resulting machining errors in the ball-end milling process. Unlike the previously developed rigid system model, the present model takes into account the instantaneous and regenerative feedback of cutting system deflections to establish the chip geometry in the cutting force calculation algorithm. The deflection-dependent chip geometry is identified by using an iterative procedure to balance the cutting forces and the associated cutting system deflections. A series of steady state 3D cross-feed ball-end milling cuts were performed to validate the capability of the present model in predicting the cutting forces and the resulting machining errors. It is shown that the flexible system model gives significantly better predictions of the cutting forces than the rigid system model. Good agreement between the predicted and measured machining errors is demonstrated for the simple surfaces generated by horizontal cuts.

The prediction of cutting forces in the ball-end milling process

This paper presents the development and verification of a predictive model for the force system in ball-end milling. The force model is essentially derived from metal cutting theory and for the geometric relations of the ball-end milling process. A concise method for characterizing the complex geometry of a ball-end mill is first determined. This method of generation not only simplifies the description of the geometry of the cutting edge, but also provides the basis for the determination of all geometric parameters to an accuracy commensurate with that needed for the oblique cutting process. The force model developed in able to deal with many of the process variables, including changes in the axial and radial depths of cut and in the feed-rate, as well as the eccentricity (run-out) inevitably found in practice. As a result, the predicted cutting forces show a fairly good agreement with the values from the verification experiments.

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.

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.

Model for cutting forces prediction in ball-end milling

This paper presents the development and verification of a predictive model for the force system in ball-end milling. The force model is essentially derived from metal cutting theory and for the geometric relations of the ball-end milling process. A concise method for characterizing the complex geometry of a ball-end mill is first determined. This method of generation not only simplifies the description of the geometry of the cutting edge, but also provides the basis for the determination of all geometric parameters to an accuracy commensurate with that needed for the oblique cutting process. The force model developed is able to deal with many of the process variables, including changes in the axial and radial depths of cut and in the feedrate, as well as the eccentricity (runout) inevitably found in practice. As a result, the predicted cutting forces show a fairly good agreement with the values from the verification experiments.

A predictive force model in ball-end milling including eccentricity effects

In this study, a new predictive force model in ball-end milling has been derived from a metal cutting theory and for the geometric relations of the ball-end milling process. It was necessary initially to define the cutting edge shape and then to determine the tool geometry of each cutting edge element by simple geometric procedures. The cutting edge on a ball-end mill can be considered as the curve of an intersection of a spherical surface with a skew plane. The advantage of this method is that the effects of the various parameters concerning the oblique cutting process can be readily calculated. The force model developed considers many of the process variables as well as the eccentricity (run-out) inevitably found in practice. The predicted and experimental results show good correlation and highlight the importance of the eccentricity on the forces and their fluctuations.

The prediction of cutting forces in the ball-end milling process—I. Model formulation and model building procedure

This paper presents a model for the prediction of cutting forces in the ball-end milling process. The steps used in developing the force model are based on the mechanistic principles of metal cutting. The cutting forces are calculated on the basis of the engaged cut geometry, the underformed chip thickness distribution along the cutting edges, and the empirical relationships that relate the cutting forces to the undeformed chip geometry. A simplified cutter runout model, which characterizes the effect of cutter axis offset and tilt on the undeformed chip geometry, has been formulated. A model building procedure based on experimentally measured average forces and the associated runout data is developed to identify the numerical values of the empirical model parameters for the particular workpiece/cutter combination.

The prediction of cutting forces in the ball-end milling process—II. Cut geometry analysis and model verification

In Part 1 of this work, a model for the prediction of cutting forces in the ball-end milling process has been presented. The model has the capability of estimating the cutting forces at any cutting conditions. In Part 2, 3-axis ball-end milling cut geometry is analyzed and combined with the force model so as to predict the cutting forces in the machining of a 3-D sculptured surface. A set of steady state model verification experiments has been performed to experimentally validate the predictive power of the model by comparing the predicted results of various cutting conditions frequently encountered in practice with force measurements. It is shown that, because of the inevitable deflections of the cutting system, the measured force signal is generally close to the prediction without runout and falls in the envelope created by the predictions with and without runout.

Reduction of machining errors by adjustment of feedrates in the ball-end milling process

In the ball-end milling process, cutter deflection is one of the main causes of machining errors on free-form surfaces. A methodology which adjusts feedrates to avoid these machining errors has been developed. A model, which is represented by the cutter feed vector and the normal vector at the surface, is derived to predict these machining errors. This model is applied to the determination of the rational feedrates, which satisfy the machining tolerance to the full, and simultaneously prevent unwanted results. A series of down ball-end milling experiments are run in order to examine this surface error prediction model and to verify the ability of the rational feedrates. In these tests, it is shown that the predicted surface errors by the suggested model are in fairly good agreement with the measured data along the cutter path, and the rational feedrates effectively keep the surface errors on the surface in the range of the machining tolerance.

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.