Ball-end Milling Of Sculptured Surfaces Research Articles

CWE identification and cutting force prediction in ball-end milling process

Ball-end milling of sculptured surfaces is an efficient and cost effective manufacturing technique when compared with other methods. However, an accurate cutting force prediction is still challenging when the Cutter Workpiece Engagement (CWE) and Instantaneous Undeformed Chip Thickness (IUCT) vary simultaneously. In order to predict the milling force accurately, an algorithm is designed to obtain the CWE boundaries with the variable tool orientations. Inspired by the main idea of analytical CWE model, an improved Z-map method is developed, which is based on the classic Z-map method. The point cloud of tool envelope surface method is generated based on the classic Z-map and the points of the CWE are screened according to the chosen criteria. Afterwards, the IUCT is calculated numerically by the accurate cutting thickness model. In order to overcome the drawbacks of the IUCT method, a simplified IUCT model is proposed to eliminate the iterative calculation. Related milling experiments were carried out on Al7075 workpiece to validate the proposed models showing a good agreement with errors smaller than 12.5%. It can be concluded from simulation results that tool postures have a significant effect on the machining process. This contributes to in-depth understanding the material removal process and optimizing the process parameters of multi-axis machining processes.

Smart tool path generation for 5-axis ball-end milling of sculptured surfaces using process models

Abstract Efficient 5-axis milling of free form surfaces required smart parameter selection and tool path generation approaches. Current computer-aided manufacturing (CAM) technology offers limited flexibility and assistance for such purposes, where purely geometrical issues are considered. Consequently, the generated tool path may be off the high-performance milling parameters. In 5-axis milling, the efficient process parameter set usually vary along the tool path due to varying engagement conditions because of inherent reasons. In this paper, a novel approach is proposed for identification of efficient surface milling parameters according to the variation of cutting forces and stability along the tool path, and then continuously implementation of these parameters for smart tool path generation, obeying the geometrical requirements. The proposed approach is applied on representative cases relevant to industrial applications to demonstrate the benefits. It is shown that, use of process simulations in tool path planning and generation offers significant benefits in decreasing the total cycle time in 5-axis milling.

Tool deflection error compensation in five-axis ball-end milling of sculptured surface

During the machining of sculptured surface, the tool deflection induced by cutting force has a great influence on the shape and dimensional accuracy of the machined components. Previous research attempts on this topic deal with error compensation in three-axis milling process. The purpose of this paper is to provide a novel methodology to compensate these deflections in five-axis ball-end milling of sculptured surface by modifying tool paths. The approach can be implemented in three steps. First, the representation of the five-axis machine configuration and kinematic transformations is given as the basis of the geometry analysis of five-axis milling operations. Second, through the analysis of tool deflection during the five-axis ball-end milling process, the mirror method can be applied to calculate the tool position and orientation. Meanwhile, the compensation reference can be modeled to optimize the tool paths. Finally, all experiments are carried out under the same cutting parameters to prove its effectiveness. The experimental results show effective improvement in the accuracy of the sculptured surface.

Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map

This paper presents an approach for prediction of cutting forces in three-axis ball-end milling of a sculptured surface along an arbitrary tool path. The idea of differentiation is adopted to deal with the problems of varying feed direction, varying cutter engagement, and the consequent varying cutting forces in sculptured surface machining. Based on the differential idea, the whole process of sculptured surface milling is discretized at intervals of feed per tooth, and each segmented process is considered as a small steady-state cutting. For the discrete cuttings, mathematical models of feed turning angle and feed inclination angle are proposed according to the position of start/end points. By using an improved Z-map method, the detailed algorithms of determining the cutter–workpiece interface and the instantaneous in-cut edge segment for sculptured surface machining are suggested. A new integrative chip thickness model which involves the effects of feed turning angle, feed inclination angle, and cutter engagement is also presented. In validation experiment, two practical examples of a sculptured surface three-axis ball-end milling with arbitrary tool path are operated. Comparisons of the predicted cutting forces with the measurements show the effectiveness of the proposed approach.

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

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

Tool Deflection Modeling in Ball-End Milling of Sculptured Surface

The error due to tool deflection is detrimental to machining precision. In order to predict tool deflection more accurately, this paper presents a special three segments cantilever beam model for ball-end tool deflection in sculptured surface milling. Different from the traditional two segments cantilever beam method, the ball-end tool is divided into the shank, the flute and the ball-end parts in this new model. Then the ball-end tool deflection is simulated also by utilizing the finite element software ANSYS 12.0 Workbench to calibrate the accuracy of the tool deflection models. The three segments cantilever beam model for ball-end tool deflection matches better the finite element method (FEM). In the last part of the paper, the sculptured surface machining experimental results show that, the surface precision after tool deflection compensation based on the new three segments cantilever beam model is higer than that based on the two segments cantilever beam model.

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.

Estimation and experimental validation of cutting forces in ball-end milling of sculptured surfaces

Chip thickness calculation has a key important effect on the prediction accuracy of accompanied cutting forces in milling process. This paper presents a mechanistic method for estimating cutting force in ball-end milling of sculptured surfaces for any cases of toolpaths and varying feedrate by incorporation into a new chip thickness model. Based on the given cutter location path and feedrate scheduling strategy, the trace modeling of the cutting edge used to determine the undeformed chip area is resulted from the relative part-tool motion in milling. Issues, such as the selection of the tooth tip and the computation of the preceding cutting path for the tooth tip, are also discussed in detail to ensure the accuracy of chip thickness calculation. Under different chip thicknesses cutting coefficients are regressed with good agreements to calibrated values. Validation tests are carried out on a sculptured surface with curved toolpaths under practical cutting conditions. Comparisons of simulated and experimental results show the effectiveness of the proposed method.

Two-dimensional representation of machining geometry and tool path generation for ball-end milling of sculptured surfaces

This article applies a two-dimensional representation of the machining geometry relevant to tool path generation for the three-axis ball-end milling of sculptured surfaces. A two-dimensional geometric model detecting the machined strip is suggested as the concept for the ‘effective cutting profile’ which fits well into the three-dimensional machining geometry. The model is the same as the intersection of the cutter with the plane perpendicular to the tangent direction of the cutter location curve and incident with the cutter location point. In order to achieve the specified machining accuracy, an iterative approach is needed. The paper also presents a new iterative method to generate tool paths with a constant scallop height. It is based on the proposed model which resorts to a two-dimensional representation of the three-dimensional machining geometry. The proposed method reduces significantly the computing time to generate tool paths. Implementations and illustrated examples are discussed.

Feed rate optimization for 3-axis ball-end milling of sculptured surfaces

The aim of this research is to improve the productivity of CNC machine tools by optimizing feed rate. To optimize feed rate two programs were used: “ACIS” (with scheme language) and “Visual Basic”. The scheme program for modeling the work piece, tool, cutting edge, and calculating maximum cutting force and the Visual Basic program to control all the activities linked to the ACIS program for estimating optimized feed values. Laboratory tests were conducted to verify the results from the modeling, using an insert-type one-flute ball-end cutter on a CK45 carbon steel work piece. No coolant was used throughout the experimental works. Comparisons were made between the maximum cutting forces, in the “fix” feed rate tests. The results indicate significant increases in productivity, which can be achieved, by using the optimized feed rate method.

Static rigid force model for 3-axis ball-end milling of sculptured surfaces

Static rigid force model is used to estimate cutting forces of sculptured surface in a straightforward way, without considering tool deflection, machine tool dynamic behavior and any vibration effects. Two programs were used for calculations, “ACIS” the 3-D geometric modeler and “VISUAL BASIC”. Two programs were edited and used to perform the calculations, the scheme program to model the work piece, tool and cutting edge and to obtain the geometric data and the VISUAL BASIC program design to use ACIS geometric data to calculate the cutting forces. The engaged part of the cutting edge and work piece is divided into small differential oblique cutting edge segments. Friction, shear angles and shear stresses are identified from orthogonal cutting database available in literature. The cutting force components, for each tool rotational position, are calculated by summing up the differential cutting forces. Laboratory tests were conducted to verify the predictions of the model. The work pieces were prepared from CK45 steel using an insert-type ball-end cutter. No coolant was used in any of the experimental works. The cutting forces predicted have shown good agreement with experimental results.

Fast tool path generation by the iso-scallop height method for ball-end milling of sculptured surfaces

This article reports on tool path generation by the iso-scallop height method for the three-axis ball-end milling of sculptured surfaces. In order to achieve the specified machining accuracy, constant scallop height machining requires an understanding of the three-dimensional machining geometry and the use of iterative approaches. Feng and Li have accomplished such work using the bisection method to search the scallop curves and the tool centre curves. This paper presents an analytic and geometric study of the machining aspects. Analysing the local properties of the distance functions, which indicate where the scallop point and the tool are centred, the bisection method can be replaced by the Newton iterative algorithm which converges faster. The derivatives of the functions are formulated by their Taylor approximations with a small error. The initial guesses are obtained by considering the local machining geometry. The proposed method significantly reduces the total computing time necessary to generate tool paths.

Mean cutting force prediction in ball-end milling using force map method

In this paper, a new method is proposed to predict mean cutting force in ball-end milling of sculptured surfaces. The cutter contact area, which is obtained from Z-map of the hemispherical part of the cutter, is expressed as a set of grids on the cutter plane orthogonal to the cutter axis. Before calculation of cutting force, cutting force density in each grid is calculated using empirical cutting parameters. The calculated force density corresponding to the grid position on the cutter plane is defined as a force map. The mean cutting force in an arbitrary cutter contact area is easily calculated by summing up the cutting force densities of the engaged grids in the force map. The proposed method was verified through the slotting and slanted surface machining by varying the surface inclination angle. From the experimental results, it was shown that mean cutting force can be calculated accurately and fast.

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.

An improved process simulation system for ball-end milling of sculptured surfaces

A simulation system is developed in this paper, which deals with the geometry and mechanics of machining with ball-end milling cutters. The geometry of the workpiece, the cutter, and the cutter/workpiece engagement is modeled using a geometric simulation system. This module uses a commercial solid modeler (ACIS) as a geometric engine and automatically extracts the critical geometric information required for the physical simulation system. To calculate the instantaneous cutting forces, a new mechanistic force model is developed. This force model takes into account the variations of the cutting coefficients along the cutting edge, and considers the variations of the rake angle and the chip flow direction on the rake face. The calibration of the developed model is performed for half-immersion ball-end milling operation. The applicability of the developed system is verified experimentally for various up-hill angles. It is shown that as the up-hill angle increases, the ball-nose tip engagement decreases which in turn significantly affects the magnitude of the resultant forces. Also, lower cutting forces and powers are experienced if cutting with the vicinity of the tool tip is avoided.