Chatter stability prediction for five-axis ball end milling with precise integration method

By studying the workpiece-edge-coupling (WEC) in five-axis ball-end milling, the contact characteristics between the workpiece and edge curve are analyzed, and the chip model is extracted and simplified. The edge curve involved in the cutting process of each edge are calculated at each time and a new instantaneous numerical chip thickness model is established. Then the milling forces and stability lobe diagram (SLD) are calculated in following cut process with lead and tilt angle. The milling forces and SLD of lead angle at 15° and tilt angle at −15° are verified by comparing with Otzurk model as references, and it is found the SLD of WEC model can reflect the unstable points more properly than that of Otzurk model. Also the vibration in x and y directions show a divergence trend, which proves the high precision for the new algorithm adapted to the stability prediction of five-axis ball-end milling process. In addition, the surface topography is acquired considering lead and tilt angle as well as forced vibration, and the result is consistent with the experiment in the existing literature. It is found that the milling forces, SLD and surface topography show the same variation trend with the increase of lead and tilt angle. Besides, the stability region significantly expands and the surface topography improves by applying positive tilt angle other than the negative. Then, under the conditions of positive lead and tilt angle, increasing lead angle and decreasing tilt angle reduces the milling force, expands the stability region of SLD and improve the surface topography. The optimized tool posture is acquired by the coincident analysis of milling force, SLD and surface topography under different lead and tilt angle.

Prediction of chatter stability for milling process using precise integration method

Primary manufacturing processes like casting, forming, and shaping (forging, rolling, drawing, extrusion, sheet forming, and molding) further need any of the secondary manufacturing processes like turning, drilling, boring, planing, milling, grinding, etc. In order to produce superior quality products, and to enhance productivity, the selection of desirable process parameters is significant. The selection of suitable process parameters is essential for accomplishing the desired component. Based on the existing literature, this study examines the causes, effects, and variances regarding chip formation, tool geometry, thrust force, torque, surface roughness, drilling time, and other drilling quality characteristics in the most typical machining operations such as drilling. Developing a repository on these process parameters will guide the process planning engineer for ready reckon. Therefore, this work aims at the development of a detailed repository with the study of characteristics. Further, this literature review comprehends the characteristics of a behavior with its reasoning, which was detailed in the past decade. It reveals the beneficial process parameters for achieving better production rate and superior quality.

Friction welding is one of the efficient metal joining processes used in mechanical industries for the last several years due to difficulties prevailed in fusion welding techniques. Mechanical characteristics of friction welded joint entirely depends upon a selection of suitable process parameters and their intensity. In this paper, the artificial intelligence tool fuzzy logic is used for the forecast of welding input parameters to get reliable output parameters. The proposed fuzzy model covers four key parameters such as forging pressure, friction pressure, upset time, and speed while tensile strength, impact toughness, and axial shortening as the output parameters. Three-dimensional surface models developed which are establishing a relationship between input parameters and output parameters at an instant which helps monitor and control the quality of a friction welded joint. The fuzzy predicted output compared with the experimental result and found that fuzzy-based mathematical model is highly accurate.

Face milling is a process predominantly affected by dynamic variation of cutting forces, thermo-mechanical shocks and vibration leading to catastrophic tool failure along with gradual wear of the inserts. Keeping in view the industrial importance of this process, it is necessary to devise suitable methods to predict in advance the onset of tool failure without grossly impairing the machining set-up and the job. Hence, the applicability of back propagation neural network with delta bar delta learning rule for faster convergence has been studied with the above objective. The multi sensor based tool condition monitoring strategy shows that the learning rate adaptation scheme combined with the selection of suitable process parameters drastically reduces the training time of the artificial neural network without dispensing with the prediction accuracy.

The stability lobe diagram (SLD) is commonly used to determine the suitable cutting parameters of the machining system in order to achieve a chatter-free machining process. An improved full-discretization method (FDM) is proposed to predict the SLD based on the hybrid interpolation scheme of the Newton and Lagrange polynomials. In order to solve the SLD, a third-order Newton polynomial is employed to interpolate the state term of the physical space equation of the system. Meanwhile, to investigate the influence of the interpolation order on predicting the SLD, the delayed term is estimated using the Lagrange polynomials of orders one to four successively. Subsequently, after constructing the transition matrix, a series of calculation for the stability prediction are carried out by applying Floquet theory. The calculated results from these constructed methods demonstrate that the FDM with a second-order Lagrange polynomial is optimal, and further has better computational performance compared with some existing discretization methods. Lastly, the influences of the dynamic parameters on chatter stability are analyzed based on the proposed FDM. When the stiffness and damping ratio increase, the limit cutting depth will be enhanced. The increasing natural frequency not only causes an obvious shift of the lobes to the right, but also raises the limit cutting depth to some extent. These theoretical analyses can guide the prediction and improvement of the chatter stability of a machining system.

The present article focuses on side milling of wooden workpieces on a five-axis NC machine tool. Firstly, a path comprising points and axes is sensed on a manually produced prototype. To control the machine continuously, the path on the machine has to be programmed using a polynomial curve. The influence of parameterisation associated with a scatter pattern of points over the continuity of feed rates is studied. In order to avoid sudden variations in speeds that can lead to burning on the wooden workpieces, the relation to be respected between parameterisation and the tangents associated with interpolation points is demonstrated.

Quantification of uncertainty in machining operations based on probabilistic and robust approaches

With the rapid development of aerospace technology, Al7075 has been widely used for structural components. High-speed milling is one of the most effective ways to improve machining efficiency of Al7075. During the milling process, regenerative chatter which restricts the milling quality and productivity often occurs. With the aim of avoiding regenerative chatter, stability lobe diagram (SLD) is widely used to obtain chatter-free parameters. This work presents a stability prediction method by using shifted Chebyshev polynomials. The milling dynamics with consideration of the regenerative effect is described by time periodic delay-differential equations (DDEs). The transition matrix of the milling system is constructed with the help of Chebyshev–Gauss–Lobatto (CGL) points. In order to demonstrate the accuracy of the proposed method, the rate of convergence of the proposed method is compared with that of the classical benchmark methods. On the other hand, in the process of thin-walled workpiece milling, the dynamic behavior of the workpiece depends on the tool position. To study the influence of the tool position dependent dynamics on the chatter stability of the thin-walled workpiece, a three-dimensional SLD is obtained. The verification experiments are conducted to verify the reliability of the proposed method. The results show that the experimental results are consistent with the predicted results.

In milling process, chatter is one of the most unfavorable factors, which will reduce surface quality, limit tool life, accelerate tool wear, and decrease machining efficiency. To solve this problem, a great deal of research has been done in milling dynamic modeling and chatter suppression. In this paper, a new milling force calculation method considering helix angle and bending is presented, in which the instantaneous cutting area is calculated in an improved way. The milling dynamic equations are established based on the proposed model, and the stability limit is obtained with semi discretization method (SDM). Results show that tool bending and helix play important roles in stability lobe diagram (SLD). Subsequently, the stability prediction is verified in the milling experiment. Stability analysis can just provide the guidance for selection of milling parameters. In order to get higher efficiency and larger stable region, the time-domain least mean square (LMS) adaptive algorithm is constructed and implemented for chatter suppression in this article. For the sake of applying the method to experiments, the smart toolholder equipped with piezoelectric stack actuators is designed and mounted to a three-axis milling machine. The experimental results show that this method can suppress chatter effectively.

This dissertation outlines research on studying the effects of machining parameters such that cutting speed, feed rate, axial depth of cut, radial depth of cut and helix angle on system dynamic stability and the surface quality of high-speed milling. With the use of structural tool modal parameters, the material cutting force coefficients and the axial depth of cut, the system can avoid the chatter phenomenon of the tool at high cutting speeds. The surface roughness finish in the milling process is determined by the machining parameters and tool structure dynamics. To perform high-speed milling, the chance of tool vibration (chatter phenomenon) which affects the cutting tool, must be minimized or eliminated. In this research, the linear and nonlinear mathematical force models including the effect of the helix angle are presented for an end-milling process. The linear force model includes cutting-edge coefficients. The cutting force coefficients are determined for an end-milling process using two methods, the average force method and the optimization technique method. The second method is developed to identify the cutting force coefficients in the milling process by forming the objective functions using the optimization technique to minimize the error between the experimental and the analytical forces. Moreover, this method produced a good force model that approximates the experimental force results, which compared with the average force method. The stability lobe diagrams are created using the analytical method to determine whether the cut is stable or unstable. In addition, simulations are performed to predict stability of the milling process. By comparing simulated and experimental results, the dynamics and stability of the milling operation can be easily identified before performing any cutting operation. The slot milling experiments show that while the system in the chatter region close to the stability limits and the axial depth of cut increased, the system changes from stable chatter to chaotic chatter. Furthermore, the nature of bifurcation in milling is investigated by performing experiments and simulations. The linear and nonlinear mathematical force models are used for simulating end-milling process. Simulated bifurcation diagrams are generated using both models and compared to experimental results. In addition, the effect of the feed rate on the location of the bifurcation point (start and end of bifurcation) is studied. By comparing simulated and experimental results, the simulation using a nonlinear force model is found more accurate in predicting the dynamics and stability of the milling operation. The applications of Taguchi and response surface methodologies (RSM) are used to minimize the surface roughness in the end milling process. Taguchi’s method for optimum selection of the milling process parameters is applied based on the signal to noise ratio and ANOVA analysis of the surface finish. A second-order model contains quadratic terms that have been created between the cutting parameters and surface roughness using response surface methodology (RSM). Surface roughness of the machined surfaces are measured and used to identify the optimum levels of the milling parameters. Based on Taguchi, ANOVA, and RSM analyses, the end milling process can be optimized to improve surface finish quality and machining productivity.

Despite recent advances and improvements in modeling and prediction of the dynamics of the machining process, an efficient machining process is limited due to chatter and instability of machining system. In fact, the machining system contains various kinds of joints, which cause difficulties in dynamics modeling, simulation and prediction. Moreover, the flexible support system results in large deformation and violent vibration of the workpiece when machining, and the thin-walled workpiece easily gives rise to the chatter of the machining system. Therefore, the dynamics of the flexible support system was considered to calculate stability lobe diagram in the modeling of milling process. The whole machining system was regarded as a closed loop composed by the machine tool structures, support, workpiece and machining process. In this paper, the receptance coupling (RC) method was introduced to predict the dynamics of the closed machining system. A milling process was taken for example to predict the chatter limitations using the dynamics of closed model. The mathematical model of the machining system (machine tool structures, spindle, holder and tool), together with the details of joint contacts, was given based on the RC method. The RC model was used to obtain the dynamics of the system, while receptance of the tool point was coupled. Based on the coupling model of the machining system, the depth limitations under different speeds were estimated for the technology parameter optimization in milling process. The response was considered to be the sum of the cutting point and the support system. The flexibility of the support system was considered to be the feedback of the cutting stiffness. By this means, the traditional model was modified to calculate the stability lobe diagram based on the dynamics of the spindle and support system. Furthermore, the milling experiment was carried out to verify the prediction results, and the dominant natural frequencies of receptance at tool point were obtained by modal testing to define the stability lobe diagram. It was found that the chatter results matched well with the stability lobes. It was concluded that the support system with poor stiffness might cause violent chatter especially when the workpiece was thin-walled. The cutting depth limitations of the flexible support system were lower than that of the rigid one. Moreover, this closed model of the machining system is appropriate for the chatter prediction of the flexible support system or thin-walled workpiece, so it is helpful for a better parameter optimization.

Prediction of time-varying dynamics and chatter stability analysis for surface milling of thin-walled curved CFRP workpiece

Five-axis milling vibration attenuation of freeform thin-walled part by eddy current damping

We have established the geometric theory of cutting stock with flat end mills in five-axis CNC machining and an accurate and efficient approach to 3D geometric modeling of un-deformed chips in this machining (Chang et al. Comput Aided Des 88:42–59, 2017). The work has laid a theoretical foundation for geometrical and physical simulation for five-axis milling. However, fillet and ball end mills are more popular than flat end mills. The equations of the instantaneous cutting edges of a fillet end mill are more complicated in the geometric theory, and the boundary of the area covered by the cutting edges is more difficult to determine. Therefore, this article is to formulate the instantaneous cutting edges and their critical points in five-axis milling and to illustrate how to use the boundary construction diagram to determine the boundary with two examples of the geometric and the physical simulations. This work is verified with the valid results of the examples, and the results indicate that this model can take into account the errors of cutter and machine tool. Therefore, the geometric theory is viable, and its application on the five-axis milling simulation is feasible for high-performance machining.