Stability Analysis Of Milling Processes Research Articles

An Updated Method for Stability Analysis of Milling Process with Multiple and Distributed Time Delays and Its Application

Predicting and avoiding the onset of milling chatter are desirable to reduce its harm to machine tools, workpieces, and cutters. This paper presents an updated method to complete the stability prediction for the milling process with multiple and distributed time delays. After the dynamic of the combination milling process with variable helix cutter (VHC) and variable spindle speed (VSS) is modeled as linear delay differential equations with multiple and distributed time delays, the presented method is applied to carrying out its stability prediction for the first time. By comparing with the existing researches and time-domain simulations, the effectiveness of the presented method has been validated. The influence and feasibility of the combination process on chatter suppression are explored and investigated for the associated one- and two-degree-of-freedom systems. Results show that the application of the combination process can realize a further suppression of milling chatter in practice. It can result in nearly 2-fold as high as the minimum depth of cut for the traditional milling or VSS milling and about 1.3-fold for VHC milling for some special domain, and can respectively lead to the average increase of stable area by 30.4%, 23.5%, and 1.5% for the adopted simulations. However, consider the contribution, the combination process is actually one process in which VHC plays an absolutely leading role but VSS plays an auxiliary role, in terms of milling stability.

Stability Analysis of Milling Process with Variable Spindle Speed and Pitch Angle considering Helix Angle and Process Phase Difference

Suppression of milling chatter by disrupting regenerative effect is a well-known method to obtain higher cutting stability domain. In this paper, a dynamic model of the milling process with variable spindle speed and pitch angle considering helix angle and process phase difference is presented. Then, an updated semidiscretization method is applied to obtain the stability chart. After the effectiveness of the proposed method is confirmed by comparisons with the previously published works and the time-domain simulations, lots of analyses are conducted to deeply evaluate the influence of the helix angle, the process phase difference, and feed per tooth on milling stability. Results show that the change of helix angle can result in significant stability discrepancies for both high-speed and low-speed regions. Though the process phase difference has the randomness and immeasurability in the practical application, it has an important influence on the stability and will result in a periodic evolution of the stability with a period π. Also, its recommended values are given for the practical milling process.

Stability Analysis of Milling Process with Multiple Delays

Cutting chatter is extremely harmful to the machining process, and it is of great significance to eliminate chatter through analyzing the stability of the machining process. In this work, the stability of the milling process with multiple delays is investigated. Considering the regeneration effect, the dynamics of the milling process with variable pitch cutter is modeled as periodic coefficients delayed differential equations (DDEs) with multiple delays. An adaptive variable-step numerical integration method (AVSNIM) considering the effect of the helix angle is developed firstly, which can discretize the cutting period accurately, thereby improving the calculation accuracy of the stability limit of the milling process. The accuracy and efficiency of the AVSNIM are verified through a benchmark milling model. Subsequently, a novel spindle speed-dependent discretization algorithm is proposed, which is combined with the AVSNIM to further reduce the calculation time of the stability lobes diagram (SLD). The simulation experiment results demonstrate that the proposed algorithm can effectively reduce the calculation time.

Reducing computational requirement of stability analysis of milling by partial averaging

The trapezoidal rule and Taylor theorem are used to establish a novel reformulation technique called Partial Averaging (PA). PA is seen to reduce computational time (CT) of computer central processing unit (CPU) with- out lose of accuracy. Two types of PA are proposed, one involves use of trapezoidal rule to give a map called Full Trapezoidal Rule Map with Partial Averaging (FTRMPA) while the other is achieved through exact analysis to give a map called Partial Trapezoidal Rule Map with Partial Averaging (PTRMPA). The latter is demonstrated to be more accurate and more time conserving in stability analysis of milling process (both one and two degree of freedom systems were considered) and delayed damped Mathieu equation. With all other things being equal the results of stability analysis of fully-immersed milling process using FTRMPA and PTRMPA are seen to be identical with those of full-discretization by Ding et al. (1) further validating the presented reformulation. PA is applied on the Second Order Least Squares Approximated Full-discretization method of (18) to illustrate its usefulness for reducing the cumbersome analysis and CT of the full-discretization method when analysis gets more complicated by higher order interpolation/ approximation theory.