5-axis Ball-end Milling Research Articles

A real-time intelligent method to identify mechanistic cutting force coefficients in 3-axis ball-end milling process using stochastic gradient decent: the mechanistic network

A real-time intelligent method to identify mechanistic cutting force coefficients in 3-axis ball-end milling process using stochastic gradient decent: the mechanistic network

A new geometric approach for real-time cutting force simulation in 3-axis ball-end milling compatible with graphical game engines

A new geometric approach for real-time cutting force simulation in 3-axis ball-end milling compatible with graphical game engines

Geometric modeling of the rubbing zone limits in 3-axis ball-end milling

Geometric modeling of the rubbing zone limits in 3-axis ball-end milling

The influence of CAD model continuity on accuracy and productivity of CNC machining

Efficient and productive manufacturing of freeform shapes requires a suitable three-dimensional CAD model at the entrance to the CAM system. The paper deals with the impact of NURBS or B-spline CAD model geometric continuity on the accuracy and productivity of 5-axis ball-end milling of freeform surfaces. The relationship between a different order of CAD model geometric continuity and the quality of the toolpath generated in CAM system is analysed and demonstrated on an example of a Blisk blade profile. In order to reveal the effect of CAD geometry on the quality of the machined surface, linear interpolation of cutter location points, i.e. piecewise linear discrete toolpath, is considered. Also, no further smoothing of the toolpath is applied. The distance of the cutter location points is commonly used as the indicator of toolpath quality. In addition, the discrete curvature of a linear discrete toolpath is introduced here, and its dependence on the curvature and continuity of the underlying CAD model is demonstrated. In this paper, it is shown that increasing the order of CAD model geometric continuity significantly eliminates sharp changes in the distance of cutter location points, and smoothes the discrete curvature of the toolpath. Finally, it is experimentally verified that increasing the continuity of the CAD model from G0 to G3, while maintaining the same cutting conditions, leads to an increase in workpiece accuracy and a reduction in machining time, without the need to smooth the toolpath generated in the CAM system.

An analytical formulation of ZOA-based machining stability for complex tool geometries: application to 5-axis ball-end milling

The paper describes a computationally convenient analytical formulation of the stability of the cutting process with respect to self-excited vibrations in the case of five-axis milling based on the commonly used zero-order approximation. In the case of five-axis milling with general milling cutters, it is difficult to calculate stable machining process conditions for two main reasons. The first reason is the difficulty of calculating the mean value of the cutting force Jacobian with respect to the regenerative displacement (closely related to a milling directional matrix) for a generally inclined tool, and the second reason is the nonlinearity of this Jacobian with respect to the process parameters, which means that the problem cannot be reduced to a linear eigenvalue problem as is usual for linear cases (e.g. cylindrical milling with respect to the axial depth of cut). In the first part, this paper presents a modification of the calculation of the machining stability limits for a nonlinearly dependent cutting force Jacobian. A new formulation of this Jacobian for a general tool based on the surface integral over the tool and workpiece engagement region is presented which leads directly to the mean value of the Jacobian of the cutting force (direction matrix) without the need to calculate it as a function of time and then calculate the mean value over one revolution. The advantage is that if we can analytically describe the engagement area, we also obtain an analytical relation for the cutting force Jacobian. This is presented with the practical example of a generally inclined ball-end mill. This analytical formulation of the force Jacobian allows the calculation of its derivatives with respect to the technological parameters (depth of cut, step over, tilt and lead angles), which is useful both for the calculation of stability diagrams and for solving optimization problems related to machining stability.

Towards understanding and controlling of the surface texture pattern in 5-axis ball-end milling using fast texture simulation

Surface texture is critical for the functionality of industrial parts. This work aims to effectively control the surface texture by applying the phase difference angle between adjacent cutting passes using 5-axis ball-end milling. Because the texture pattern is complicated and is formed by combining feed-interval and step-interval scallops, we propose a level-contour-based fast simulation method to effectively generate the surface texture by inputting the phase difference angle with tilt and lead angles of the cutter. After clarifying the influence of these three parameters on the texture pattern, the desired texture was controlled by modifying the tool path according to the simulated phase difference angle. As a result, the milled surface texture corresponded well with the simulation. The details of the cutting features were efficiently and comprehensively simulated. The mechanism underlying the sudden change in the texture ridge direction was clarified as the major-minor ridge transition when the phase difference angle increased to a certain level, wherein the surface roughness could be decreased because the rearrangement of the cutting region reduced the scallop height. The proposed fast simulation method was also applied to the optimization process with a case study to demonstrate the benefits it can bring to the surface texture design and control.

Prediction of plastic surface defects for 5-axis ball end milling of Ti-6Al-4 V with rounded cutting edges using a material removal simulation

The resulting surface quality after 5-axis ball end milling is of superior importance because finish milling is often the last process step determining the functional performance of a component. However, the prediction of surface topography is still a challenging task. Especially in ball end milling with the characteristic sickle shaped chip cross section, ploughing effects in the area of low chip thickness result in plastic deformation and surface defects (also known as burr). This paper provides a new approach to predict those surface defects by considering the minimum chip thickness for complex milling engagement conditions within a virtual process design. This allows the choice of suitable process parameters without extensive experimental efforts.

Process design for 5-axis ball end milling using a real-time capable dynamic material removal simulation

For repairing turbine blades or die and mold forms, additive manufacturing processes are commonly used to build-up new material to damaged sections. Afterwards, a subsequent re-contouring process such as 5-axis ball end milling is required to remove the excess material restoring the often complex original geometries. The process design of the re-contouring operation has to be done virtually, because the individuality of the repair cases prevents actual running-in processes. Hard-to-cut materials e.g. titanium or nickel alloys, parts prone to vibration and long tool holders complicate the repair even further. Thus, a fast and flexible material removal simulation is needed. The simulation has to predict suitable processes focusing shape deviations under consideration of process stability for arbitrary complex engagement conditions. In this paper, a dynamic multi-dexel based material removal simulation is presented, which is able to predict high-resolution surface topography and stable parameters for arbitrary processes such as 5-axis ball end milling. In contrast to other works, the simulation is able to simulate an unstable process using discrete cutting edges in real-time.

Self-optimizing compensation of surface deviations in 5-axis ball-end milling based on an enhanced description of cutting conditions

This article presents an approach for a self-optimizing compensation of tool load induced surface deviations in 5-axis ball-end milling. In order to predict the surface deviation independently from the workpiece geometry, the tool deflection is modelled as a function of the tool engagement using a machine learning approach. For that purpose, a novel description of the cutting conditions in ball-end milling is introduced. The selected features are derived from a process-parallel simulation. Subsequently, the learning behavior, the transferability of process knowledge to other shapes and the feasible compensation are investigated experimentally. It is shown that the developed approach can reduce the shape error by over 70%.

3D surface topography simulation and experiments for ball-end NC milling considering dynamic feedrate

Dynamic change of feedrate is almost inevitable in high speed milling along a curved path due to the drive limits of the machine tools. The surface topography caused by the change of feedrate, which has a significant influence on mechanical prosperities and performances of the machined part, cannot be predicted using the existing methods that only consider constant feedrate. To better understand the surface topography formation process in high speed milling and also to more effectively control the machining parameters, in this paper we present a surface topography model for a ball-end cutter, which takes varying feedrate into full consideration. Our model considers the affecting elements including the surface's local geometry, the cutting edge shape, the path interval, as well as the relative motion of tool-workpiece (especially the changes of the tool orientation and feedrate). 3- and 5-axis ball-end milling experiments, in computer simulation and physical cutting, are performed to validate the developed model. The simulation results exhibit good agreement with that of the actual cutting, thereby showing the potential of the developed model for controlling the surface topography and roughness in real NC ball-end milling.

A method for the prediction of cutting force for 5-axis ball-end milling of workpieces with curved surfaces

In existing researches, only the milling tests in the state of single-tooth engagement can be used to identify cutting force coefficients. So, when the average cutting force–based calibration is performed for a 4-fluted cutter, several slots must be machined and the cutting parameters must be properly selected to ensure single-tooth engagement. To reduce the consumed time of calibration tests, we present the new identification expressions of the cutting force coefficient for the 4-fluted ball-end mill based on the average cutting force obtained by the slotting tests with double-tooth engagement. Meanwhile, a three-orthogonal dexel–based model is presented to calculate the cutter-workpiece engagement. Also, the researches show that cutting element position and spindle speed have significant effects on cutting force coefficients; however, there is no research that has built a fitting model of cutting force coefficients simultaneously related to this two factors. To accurately predict cutting forces for different cutting conditions, the influences of these two factors on cutting force coefficients are studied. Then, a fitting model of the cutting force coefficient related to this two factors is presented. After, to verify the accuracy of the proposed method, milling tests are performed on both the rectangular workpiece and curved surface. The results show that the proposed model can predict the cutting force for different cutting parameters with the relative error less than 15%.

A geometric approach of working tool diameter in 3-axis ball-end milling

When machining free-form surfaces with a ball-end milling tool, the working tool diameter is constantly changing even if the tool path is constant. The reason is that the surface normal of the milled surface is continuously changing along the milling path. When the working diameter is changing, the cutting parameters also change. This variation effects the roughness homogeneity of the smoothed surface. Simultaneous five-axis milling solves this problem; however, the price and complexity of this technology can be a problem for some industrial sectors. In the paper, the geometrical background of a solution to this problem is presented for a 3-axis ball-end milling process for machining a free form surface. The paper provides the deduction of the theory by the use of homogeneous transformations. The geometrical problem of the cutting process is treated locally where the general machined surface is substituted at every point by its tangent plane. From the result of the presented method, a milling strategy can be formulated for ball-end milling that minimises the change in the momentary working diameter thus providing a more constant cutting parameter.

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.

An approach to modeling the chip thickness and cutter workpiece engagement region in 3 and 5 axis ball end milling

The determination of the chip thickness in 5-axis ball end milling is most fundamental to calculate the cutting force which affects the machining stability and surface quality. In the 5-axis ball end milling, adding to the parameters of the 3-axis milling we have two important parameters which are the tilt and the lead angles. They affect the engagement region and the chip thickness and modify the cutting forces. Based on the true tooth trajectory and the machining surface geometries, this paper presents a new analytical model of the cutter workpiece engagement (CWE) region and the instantaneous undeformed chip thickness in three and five axis ball end milling. To validate the model a mechanistic force model was used, the simulation was compared to the measured one and a good agreement between them was proved.

The Effects of Milling Strategies on Forces, Material Removal Rate, Tool Deflection, and Surface Errors for the Rough Machining of Complex Surfaces

The high-performance machining of curved surfaces is a highly critical process that is crucial in modern engineering applications. Different methodologies and CAM tools have been developed by manufacturers to improve the efficiency of the sculptured surface milling. The determination of appropriate tool path strategies and milling conditions is crucial in ensuring a high productivity rate, meeting the bettersurface texture values, and lower cutting forces, tool deflection, and surface errors. The objective of this research is to analyse the effect oftool path strategies on dynamic tool deflection, cutting forces, machining time, effective cutter diameter (ECD), cutter/workpiece engagement (CWE) area, instantaneous material removal rate (IMRR), and machining errors in rough machining of a sculptured surface. The B-rep solid modeling-based simulation and the optimization system were developed and integrated with the commercial CAD/CAM software for 3-axis ball-end milling. The experimental results clearly show the influence of the cutter path strategies on machining times and their importance for reducing time needed and, consequently, costs. It was observed that the profiles of deflection, IMRR values, cutting forces, machining errors and ECD values match very well for cutting strategies. Machining strategies employed include various degrees of zig-zag, profiling, and spiral. The conclusion is that the 90° zig-zag strategy provokes the lowest cutting forces, tool deflection, and surface error values. The in-house NC simulation system performed well in determining values and the location of milling form errors on the surface.

Tool orientation optimization of 5-axis ball-end milling based on an accurate cutter/workpiece engagement model

Tool orientation in 5-axis ball-end milling plays a significant role in machining efficiency and accuracy. The cutter/workpiece engagement varies with tool orientation continuously including lead and tilt angles during machining, which results in the obvious time-varying characteristic for consecutive cutting forces. Considering tool orientation, actual cutter runout and cutter motion process, an accurate calculation model for instantaneous cutter/workpiece engaging process in 5-axis ball-end milling is proposed based on an improved analytical method with high order Taylor formula, which can reach an excellent accuracy. Then base on the cutting force model, the tool orientation optimization strategies with a flexible cutter and rigid workpiece for roughing and finishing milling operation are further presented. For the three kinds of geometrical characteristic (plane, cylindrical and spherical surface), this study analyzes the influence of tool lead and tilt angles, and step over on the maximum cutting force and form error, and finally obtains an optimal tool orientation to realize a high efficiency and accuracy machining.

3D surface topography analysis in 5-axis ball-end milling

This article presents a new analytical model to predict the topography and roughness of the machined surface in 5-axis ball-end milling operation for the first time. The model is able to predict the surface topography and profile roughness parameters such as 3D average roughness (Sa) and 3D root mean square roughness (Sq) by considering the process parameters such as the feedrate, number of flutes, step-over and depth of cut as well as the effects of eccentricity and tool runout in 5-axis ball-end milling. This model allows to simulate the effects of the lead and tilt angles on the machined surface quality in the virtual environment prior to the costly 5-axis machining operations. The effectiveness of the introduced surface topography prediction model is validated experimentally by conducting 5-axis ball-end milling tests in various cutting conditions.

A tool path patching strategy around singular point in 5-axis ball-end milling

In 5-axis high-speed milling, large incoherent movements of rotary axes around the singular point are known to be a problem. Correction methods found in the literature deal mostly with the collision that may happen between the tool and the part but not with the feedrate slowdowns which affect surface quality and machining productivity. The method proposed in this paper addresses both geometrical and productivity issues by modifying the tool axes orientation while respecting maximum velocity, acceleration and jerk of the machine tool axes. The aim is to detect these behaviours and replace the considered portion of the tool path by a patch curve respecting kinematical constraints of the machine tool. Compared to previous works, the inserted patch curve is not constrained to pass through the singularity but respect tangential constraints to ensure the monotony of the tool path and is also connected with the rest of the tool path to ensure a continuity up to the third derivative in order to fulfil jerk limitations. For that purpose, the initial articular positions of the rotary axes around the singular point are fitted with B-spline curves, modified and finally discretised for linear interpolation. Experimental investigations on a test part are carried out to show the efficiency of the method in terms of feedrate and surface quality.

Chatter free tool orientations in 5-axis ball-end milling

Dies, molds and parts with complex free form surfaces are usually machined with ball end mills on 5-axis CNC machining centers. This paper presents automatic adjustment of tool axis orientations to avoid chatter along the tool path. The process mechanics and dynamics of ball end milling are modeled in cutter-workpiece engagement coordinate system. The structural dynamics of tool and workpiece are transformed to cutter-workpiece engagement coordinates by considering the tool path and the kinematics of the machine tool. The stability of the 5-axis ball end milling is modeled at each tool path location, and the chatter free tool axis orientations are searched iteratively using Nyquist criterion while avoiding gouging limits. The tool path, i.e. cutter location (CL) file, is updated to generate chatter free, 5-axis ball end milling of the parts. The proposed algorithm has been experimentally proven in 5-axis ball end milling tests.

Prediction of the Principal Stress Direction for 5-axis Ball End Milling

While regenerating damaged components, e.g. compressor blades, the removal of excess weld material called re-contouring often determines the surface integrity including the residual stress state. A load-specific residual stress state is beneficial for lifetime. This leads to the necessity to predict the resulting residual stress state after machining. The paper describes two models, which predict the principal stress direction as a residual stress characteristic for 5-axis ball nose end milling of Ti-6Al-4V. One model uses process force components, the other is based on the microtopography of the workpiece, which is influenced by the kinematics of the process.