Dynamic Milling Process Research Articles

A novel model reduction technique for time-varying dynamic milling process of thin-walled components

A novel model reduction technique for time-varying dynamic milling process of thin-walled components

Difference Discretization Method for Milling Stability Prediction

This paper proposes a difference discretization method (DDM) under a difference frame for the prediction of milling stability. In this method, the dynamic milling process is described by a delay differential equation (DDE) with two degrees of freedom rather than the traditional state-space form with a single discrete time delay. After discretization, only the velocity and acceleration in the DDE are approximated by the first- and second-order central difference for each smaller time interval, while the other items are kept unchanged. Then, the criterion for the optimal discretization interval number is put forward and derived based on the largest effective time interval (also called the critical time interval). The use of the critical time interval cannot only obtain sufficient accuracy, but also promotes as much efficiency as possible. Subsequently, a new DDM (NDDM) with varied discretization interval numbers as the milling rotating speeds is developed. Finally, the effectiveness of the proposed algorithm is demonstrated by using a benchmark example for a two-degrees-of- freedom milling model compared to the full discretization method (FDM) and the Hermite-interpolation full discretization method (HFDM). The results show that the proposed method has satisfactory stability charts and is able to increase the efficiency by 100% or more.

An unformed chip thickness approach to study the influence of process vibration on machining performance in milling

The vibration in the milling process plays a key role in machining, which can significantly affect the machining quality of the workpiece. Some vibrations have negative influences on the workpiece surface, while other vibrations can improve machining stability. Therefore, it is critical to distinguish the influence of different types of vibration on machining quality. A simulation method of undeformed chip thickness considering process vibration is presented in this article, in which a finite element model is established to analyze the dynamic milling process of 7075-T651 aluminum alloy from the aspects of cutting force and temperature. A series of experiments are carried out to verify the effectiveness of the simulation model, and the results show that the proposed model is accurate in predicting both milling force and temperature. Furthermore, the effect of milling vibration on machining performance is studied with the proposed method, in which the relationship between the amplitude-frequency characteristics of vibration and milling force-temperature fluctuation is revealed. The results show that the proposed method can determine the influence of milling vibration and provide a basis for distinguishing favorable and unfavorable vibration parameters of machining quality in milling.

A short review on milling dynamics in low-stiffness cutting conditions: Modeling and analysis

The dynamic responses of milling system change the ideal trajectories of cutting teeth and therefore plays a critical role in determining the machining accuracy. The amplitude of cutting vibrations could reach tens of or even hundreds of micrometers in low-stiffness cutting conditions, for example, when milling thin-walled parts and/or using slender tools. Usually, moderate cutting parameters are utilized to avoid excessive cutting loads, strong milling chatter or large dynamic deflections, which however, significantly lowers the productivity. In spite of decades of study, it is still a challenge to accurately model, efficiently analyze, reliably monitor and precisely control the dynamic milling process in low-stiffness cutting conditions. In this paper, the recent advances and research challenges on dynamics modeling and response analysis are briefly reviewed.

Dynamic simulation of robot milling process based on ADAMS

In this paper, a stability model for milling chatter based on instantaneous cutting thickness was established, and the flap diagram of the stability region was drawn accordingly. The finite element simulation of dynamic milling process was carried out by using AdvantEdge, and the dynamic simulation was carried out by using ADAMS, and the torque of each joint was obtained. The conclusions show that: 1) The torque on all joints of the robot reaches the maximum value and fluctuates greatly at the initial cutting, and then tends to be stable; 2) the linear velocity jitter of the end-effector is less than 2.5·10−5m/s, and the angular velocity jitter is less than 3.3·10−5s−1, meeting the processing requirements.

Two novel prediction methods for milling stability analysis based on piecewise polynomial interpolations

Chatter has been one of the major limiting factors leading to poor productivity and surface finish. The prediction of the stable cutting zones of cutting parameters is thus vital in machining. On the basis of piecewise polynomial interpolations, two efficient and accurate methods are developed in this paper for calculating the stability lobes. Firstly, the dynamic milling process with regenerative effect is modeled by delay differential equations (DDEs) with time-periodic coefficients. The principal period of system is easily separated based on the existence of any non-zero elements of coefficient matrix, and the forced vibration phase is equally discretized into a series of subintervals. Piecewise polynomial interpolations are adopted in two contiguous subintervals to estimate all parts of the DDEs. Secondly, the state transition matrix is formed to search for the borderline of stable cutting region based on Floquet theory. Thirdly, the convergence rates of the two proposed methods are analyzed through comparison with four existing algorithms. The results validate that the two proposed approaches achieve higher convergence rate, accuracy, and efficiency than the others within the same time intervals. Finally, the operability of the two proposed methods is verified by cutting tests, which indicate that the two proposed methods are of effectiveness and practicability.

The reconstruction of a semi-discretization method for milling stability prediction based on Shannon standard orthogonal basis

In order to increase the calculation speed of the semi-discretization method (SDM) without accuracy loss, this paper reconstructs the SDM for predicting the stability lobes of the dynamic milling process, mainly considering the regenerative effect. The model of the dynamic milling process is expressed as the linear delay-differential equations (DDE). The fast calculation method is established by reconstructing the SDM based on the Shannon standard orthogonal basis (SSOB). First, the delay term of DDE is constructed without information loss based on Shannon interpolation functions, and SSOB is derived. Secondly, the closed form expression for the transition matrix of the system is constructed based on the SSOB, and the stability limit is predicted based on the Floquet theory. The transition matrix-based SDM and SSOB are theoretically compared, and it shows that the SDM is a special case of the method based on SSOB when the SSOB is regarded as the average in the sampling interval. The fast calculation method is established by using the variable sampling numbers during the period of the delay time in which the variable sampling numbers are determined by the condition which is used to construct the SSOB. Finally, this proposed fast method is used to the one and two degrees of freedom milling model, and the results show that the calculation accuracy is not reduced, and the calculation speed based on the proposed method can be improved nearly five times on the one degree of freedom model and 2.6 times on the two degrees of freedom model, compared to the semi-discretization method.

Study on the construction mechanism of stability lobes in milling process with multiple modes

The stability of milling process dominated by multiple modes was traditionally predicted in the time domain by only selecting the most flexible mode. This paper theoretically studies the construction mechanism of stability lobes by simultaneously considering all dominant modes and provides an efficient method to predict stability lobes of milling systems with multiple modes in the time domain. It is theoretically proved that the effective stability lobes of milling system with multiple modes is made up of the lowest envelop of the stability lobes achieved with each single mode; hence, lowest envelop method (LEM) is established to predict the ultimate stability lobe by taking the lowest envelop of a group of stability lobes, which are calculated by separately considering different dominant modes composing the overall dynamic compliance. Typical advantage of LEM lies in that the computation time and the memory usage required in stability prediction can be greatly reduced for time domain solution. Moreover, the accuracy of prediction can be increased, when the effects of multiple modes are taken into account instead of considering only the most flexible mode. Formulation of the dynamic milling process with multiple modes is derived in semi-discrete time domain by including the effects of multiple delays. A series of simulations and experiments demonstrate the high efficiency and validity of LEM.

Research on Stability of High Speed Milling System

Machining instability is often the limiting factor on metal removal rate. So the stability of cutting system is an important research in high-speed machining area. It is widely used in engineering practice. In this paper, the stability of high-speed milling was studied by the numbers aiming at the dynamic milling process model of ball-end mill. The dynamic model of high-speed milling process was established. On the basis of Altintas’s theory, the formula about the limit axial depth of cut was derived. Besides, the model parameters of the system were obtained and the accuracy of the stability lobes diagram was verified through the experiments. From this research, it was learned that structure parameters of machine tool-cutting tool system, cutting force coefficients, spindle speed and axial depth of cut were factors affecting the stability in high-speed cutting. And the obtained stability lobes diagram provided a reliable basis in selecting cutting parameters during tool path planning.

Response sensitivity analysis of the dynamic milling process based on the numerical integration method

As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.

An efficient full-discretization method for prediction of milling stability

This paper presents an efficient full-discretization method for the prediction of milling stability. The dynamic milling process is represented in state-space form with a single discrete time delay. After discretizing the time period equally into a finite set of intervals, in each small time discretization step, the time-delayed item is first approximated with three neighboring discrete state values, and the time-periodic item is represented by the linear interpolation method. Meanwhile, by utilizing the derivability of the state item and considering the unique structure of the state-space equation, the derivatives of the state items at the start and end of each interval could be obtained, with which the state item could then be more precisely and compactly approximated by using Hermite interpolation. Finally, the transition matrix over a single period is determined to predict the milling stability via the Floquet theory. The rate of convergence of the proposed method is estimated and compared with other methods. Two benchmark examples are utilized to verify the effectiveness of the proposed method for the prediction of milling stability both in low and high spindle speed domains. The results show that the proposed method has high computational efficiency.

An improved dynamic milling force coefficients identification method considering edge force

The identification of the dynamic coefficients is the key to realize accurate simulation of dynamic milling process. To enlarge the scope of dynamic simulation without ignoring edge force, an improved method is presented to calculate milling force coefficients. In this method, linear approximation of average milling force is integrated with multiple linear regressions by supposing that milling force coefficients are time invariant for small variation of feed rate. Therefore, both the shear coefficients and the edge coefficients can be calculated simultaneously. A comparison of simulated milling force with and without the edge force is illustrated and the result shows that the accuracy is higher if the edge force coefficients are considered. This method casts new light on fast and accurate simulation of the dynamic milling force in real industrial environment.

Effects of cutting conditions on dynamic cutting factor and process damping in milling

This paper investigates how cutting conditions affect dynamic cutting factor and system process damping in a dynamic milling process. By considering variation of edge plowing force, a frequency domain method is presented to identify the dynamic cutting factor through measured vibration in a milling process, and cutting conditions most suitable for the identification experiments are also discussed. A series of experiments are carried out to investigate the effects of cutting conditions on the dynamic cutting factor. This factor is shown to be significantly affected by the cutting speed, but relatively independent of the feed per tooth and the radial depth of cut. An average process damping model is further constructed and shown to be effective in representing the time-varying damping function. The average process damping is shown to increase rapidly at lower cutting speed, but remain constant as the cutting speed beyond a critical value.

A full-discretization method for prediction of milling stability

This paper presents a full-discretization method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-discretization method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.

The effect of runout on the milling tool vibration and surface quality

When milling with tools of a high length to diameter ratio, there is often a non negligible runout. Since those tools tend towards chatter because of their low stiffness, the effect of runout on the dynamic behavior of the tool must be considered. Runout adds an additional dynamic component to the tool vibration and thus to the dynamicly changing cutting forces. Furthermore runout affects the surface quality even in stable machining. This paper analyzes the effect of runout by simulation of the dynamic milling process and compares the results to experimental data. One aspect is the difference of the vibration patterns with and without runout. Furthermore, a method for the analysis of timeseries is presented in order to distinguish between chatter and runout. Another topic is the expected surface quality resulting from stable processes with runout. This surface is modeled, examined and compared to the one produced by a process without runout.

Simulation of machined surface topography in end-milling processes using a shear-plane-based cutting force model

The purpose of this paper is to extend the theoretical understanding of the dynamic milling process and to derive a computational model to predict machined surface topography using, as the foundation, a newly developed shear-plane-based rather than the customary chip-thickness-based cutting force model. The machined surface is synthesized by concatenating two-parameter bicubic surface patches generated by discretized cutting edge segments as they follow their respective trajectories. To maintain positional and tangential continuity, both the coordinates of nodal points on the cutting edges and the associated instantaneous velocities are used to construct the surface patches. A computer simulation program that incorporates the shear-plane-based cutting force model and geometric, kinematic and surface topography prediction models is developed. Computer simulations and cutting tests confirm the validity of the computational models.

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.