scholarly journals Stability Analysis for Milling Process with Variable Pitch and Variable Helix Tools by High-Order Full-Discretization Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yang Zhang ◽  
Kenan Liu ◽  
Wuyun Zhao ◽  
Wei Zhang ◽  
Fei Dai
Keyword(s):  
Milling Process ◽  
Small Time ◽  
High Order ◽  
The State ◽  
Multiple Delays ◽  
Variable Pitch ◽  
Discretization Methods ◽  
Variable Helix ◽  
The Stability ◽  
Space Equation

Chatter is one of the significant limitations in the milling process, which may cause poor surface quality, reduced productivity, and accelerated tool wear. Variable pitch and variable helix tools can be used to suppress regenerative chatter. This study extends the high-order full-discretization methods (FDMs) to predict the stability of milling with variable pitch and variable helix tools. The time-periodic delay-differential equation (DDE) with multiple delays is used to model the milling process using variable pitch and variable helix tools. Then, the DDE with multiple delays is reexpressed by the state-space equation. Meanwhile, the spindle rotational period is divided into many small-time intervals, and the state space equation is integrated on the small-time interval. Then, the high-order interpolation polynomials are used to approximate the state term, and the weights related to the time delay are employed to approximate the time-delay term. The second-order, third-order, and fourth-order extended FDMs (2nd EFDM, 3rd EFDM, and 4th EFDM) are compared with the benchmark in terms of the rate of convergence. It is found that the 2nd EFDM, 3rd EFDM, and 4th EFDM converge faster than the benchmark method. The difference between the curves obtained by different EFDMs and the reference curve is very small. There is no need to extend hypersecond FDMs to analyze the stability of milling with variable pitch and variable helix tools.

Stability prediction of milling process with variable pitch and variable helix cutters

2013 ◽  
Vol 228 (2) ◽  
pp. 281-293 ◽  
Author(s):  
Gang Jin ◽  
Qichang Zhang ◽  
Shuying Hao ◽  
Qizhi Xie
Keyword(s):  
Helix Angle ◽  
Milling Process ◽  
Force Model ◽  
Stability Prediction ◽  
Chatter Vibration ◽  
Variable Pitch ◽  
Tool Geometries ◽  
Variable Helix ◽  
Piecewise Continuous ◽  
The Stability

The use of variable pitch or helix cutters is a known means to prevent chatter vibration during milling. In this article, an alternative method based on an improved semi-discretization method is proposed to predict the stability of variable pitch or variable helix milling. In order to consider the effect of distributed system delays attributed to helix variation, the average delays were calculated for each flute after the engaged cutting flutes were divided into a finite number of axial elements. Meanwhile, a straightforward integral force model, which can consider the piecewise continuous regions of the cutting that describe the helix angle is used to determine the cutting force. Through comparisons with prior works, time-domain simulations, and cutting tests, the proposed approach was verified. In addition, the method was applied to examine the effect of tool geometries on stability trends. Several phenomena for certain combinations of pitch and helix angles are shown and explained.

scholarly journals An updated Simpson-Based Method for Chatter Stability Prediction in Milling

2021 ◽  
Author(s):  
Zhenghu Yan ◽  
Changfu Zhang ◽  
Jianli Jia ◽  
Baoji Ma ◽  
Xinguang Jiang ◽  
...  
Keyword(s):  
Forced Vibration ◽  
Degrees Of Freedom ◽  
Computation Time ◽  
Milling Process ◽  
Small Time ◽  
The State ◽  
Stability Lobe ◽  
The Stability ◽  
The One ◽  
Delay Differential

Abstract An updated Simpson-based method (USBM) is presented for milling stability analysis. Firstly, the delay differential equation (DDE) is employed to describe the milling process mathematically. Then, the tooth passing period is divided into two subintervals, i.e., the free and forced vibration intervals. Only the forced vibration interval is divided into many equal small-time intervals. Subsequently, the DDE in the state space is solved based on direct integration. By combining the two-step Simpson method and the semi-discretization method, the state transition matrix of the milling system is constructed. The comparison of convergence rate is conducted to validate the accuracy of the proposed method. The results show that the proposed method converges faster than the benchmark methods. The stability lobe diagrams for the one degree of freedom (one-DOF) and two degrees of freedom (two-DOF) milling systems are also obtained by different methods for further evaluation. Meanwhile, the computation time analysis is also carried out. It is revealed that the proposed USBM has advantages in both accuracy and efficiency. Besides, the proposed method can accurately and efficiently predict the stability of milling with both large and low immersion conditions.

scholarly journals Stability Analysis of Milling Process with Multiple Delays

2020 ◽  
Vol 10 (10) ◽  
pp. 3646 ◽  
Author(s):  
Yonggang Mei ◽  
Rong Mo ◽  
Huibin Sun ◽  
Bingbing He ◽  
Kun Bu
Keyword(s):  
Stability Limit ◽  
Helix Angle ◽  
Milling Process ◽  
Machining Process ◽  
Multiple Delays ◽  
Calculation Time ◽  
Discretization Algorithm ◽  
Cutting Chatter ◽  
Regeneration Effect ◽  
The Stability

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.

Effect of Cutting Conditions on the Stability Lobes for End Milling Process

2010 ◽  
Vol 139-141 ◽  
pp. 748-751
Author(s):  
Min Wan ◽  
Yi Ting Wang ◽  
Wei Hong Zhang ◽  
Jian Wei Dang
Keyword(s):  
End Milling ◽  
Cutting Parameters ◽  
Helix Angle ◽  
Milling Process ◽  
Cutting Condition ◽  
Multiple Delays ◽  
Cutter Runout ◽  
Stability Lobes ◽  
The Stability ◽  
New Phenomena

Milling process will be dominated by multiple delays due to the effect of the cutter runout or the pitch angles of the cutter. In this paper, research efforts are focused on the dynamic behavior of milling processes under different cutting condition parameters such as different radial immersions, feed directions, feeds per tooth and helix angles. To improve the prediction accuracy of stability lobe, the combined influences of feed rate and cutter runout on the stability lobes are also taken into account. The basic principle of the method presented in one existing work is applied to examine the asymptotic stability trends for both down milling and up milling. Some new phenomena for certain combinations of cutting parameters are shown and explained in detail. It is found that as cutter runout occurs, feed per tooth, feed direction and cutter helix angle have great effects on the stability lobes.

scholarly journals Milling Stability Prediction with Multiple Delays via the Extended Adams-Moulton-Based Method

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Jianfeng Tao ◽  
Chengjin Qin ◽  
Chengliang Liu
Keyword(s):  
Transition Matrix ◽  
Rotation Period ◽  
Small Time ◽  
Multiple Delays ◽  
Stability Prediction ◽  
Regenerative Chatter ◽  
Milling Stability ◽  
Milling Operations ◽  
The Stability ◽  
Delay Differential

The occurrence of machining chatter may undermine the workpiece surface quality, accelerate the tool wear, and even result in serious damage to the machine tools. Consequently, it is of great importance to predict and eliminate the presence of such unstable and detrimental vibration. In this paper, we present an extended Adams-Moulton-based method for the stability prediction of milling processes with multiple delays. Taking the nonuniform pitch cutters or the tool runout into account, the regenerative chatter for milling operations can be formulated as delay differential equations with multiple delays. The dynamics model for milling regenerative chatter is rewritten in the state-space form. Dividing the spindle rotation period equally into small time intervals, the delay terms are approximated by Lagrange interpolation polynomials, and the Adams-Moulton method is adopted to construct the Floquet transition matrix. On this basis, the milling stability can be derived from the spectral radius of the transition matrix based on Floquet theory. The calculation efficiency and accuracy of the proposed algorithm are verified through making comparisons with the semidiscretization method (SDM) and the enhanced multistage homotopy perturbation method (EMHPM). The results show that the proposed method has both high computational efficiency and accuracy.

A Generalized Runge-Kutta Method for Stability Prediction of Milling Operations With Variable Pitch Tools

2014 ◽  
Author(s):  
Jinbo Niu ◽  
Ye Ding ◽  
Limin Zhu ◽  
Han Ding
Keyword(s):  
Helix Angle ◽  
Depth Of Cut ◽  
Multiple Delays ◽  
Machining Parameters ◽  
Kutta Method ◽  
Computational Accuracy ◽  
Variable Pitch ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

This paper extends the generalized Runge-Kutta method (GRKM) to predict the machining stability of milling systems with variable-pitch tools. Different from the uniform cutters with fixed pitch angles, the variation of tooth distribution angles of variable pitch cutters significantly affects the stability diagrams of the milling systems. From the viewpoint of the regenerative chatter, the milling system with non-uniform tools is governed by a delayed differential equation (DDE) with multiple delays. Afterwards, the GRKM, an approach verified with high computational accuracy and efficiency for DDEs with a single delay, is extended to tackle the milling systems with multiple delays based on Floquet theory. Besides the pitch angles, other geometry parameters of the cutter are also taken into consideration, such as the helix angle, which is proved with limited influence on the stability lobes. With the objective of maximizing productivity, the resultant stability charts provide valuable reference for the geometry design of variable-pitch cutters and for the choice of machining parameters, i.e. the spindle speed and the depth of cut.

A frequency-domain solution for efficient stability prediction of variable helix cutters milling

2014 ◽  
Vol 228 (15) ◽  
pp. 2702-2710 ◽  
Author(s):  
Gang Jin ◽  
Qichang Zhang ◽  
Houjun Qi ◽  
Bing Yan
Keyword(s):  
Frequency Domain ◽  
Order Approximation ◽  
Effective Means ◽  
Taylor Series Expansion ◽  
Depth Of Cut ◽  
Time Varying ◽  
Variable Pitch ◽  
Variable Helix ◽  
The Stability ◽  
Axial Depth

The utilization of variable pitch or helix cutters is an effective means to prevent chatter vibration during milling. In this paper, a frequency-domain solution to efficiently predict the stability for variable helix cutters milling is presented. This method is based on the principles of variable pitch model developed by Altintas and only considers the zero-order approximation of time-varying directional cutting constants. After discretizing the axial depth of cut into finite elements and modeling each element as a variable pitch cutter, time-varying regenerative delays in the case of variable helix cutters are transformed into multiple constant regenerative times. The chatter free axial depth of cut is solved from a stability expression in which the regenerative delay terms are approximated by the Taylor series expansion, whereas the spindle speed is identified from regenerative phase delays. Compared with time-averaged semidiscretization method, the accuracy and efficiency of the proposed technique has been verified. The results show that the proposed method has high computational efficiency. It is suited to calculate optimal geometries of milling tools and beneficial for application.

scholarly journals Stability Prediction of Milling Process with Variable Pitch Cutter

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Gang Jin ◽  
Qichang Zhang ◽  
Shuying Hao ◽  
Qizhi Xie
Keyword(s):  
Helix Angle ◽  
Milling Process ◽  
Depth Of Cut ◽  
Force Model ◽  
Stable Limit ◽  
Variable Pitch ◽  
Tool Geometries ◽  
Piecewise Continuous ◽  
The Stability ◽  
New Phenomena

The use of variable pitch cutter is a known means to increase the stable limit depth of cut by disrupting the regenerative effect. In this paper, an improved semidiscretization algorithm is presented to predict the stability lobes for variable pitch cutters. Modeling efforts develop a straightforward analytical integral force model that can cover any case of piecewise continuous cutting regions regarding the helix angle. The proposed approach has been verified with the comparisons with prior works, time domain simulations, and cutting tests. In addition, the method is also applied to examine the effect of the tool geometries on the stability trends for variable pitch milling. Some new phenomena for certain combinations of parameters are shown and explained.

Dynamics of Drill Bits With Cutting Edges of Varying Parameters

2013 ◽  
Author(s):  
Zoltan Dombovari ◽  
Gabor Stepan
Keyword(s):  
Metal Cutting ◽  
Helix Angle ◽  
Milling Process ◽  
Drilling Process ◽  
Deep Drilling ◽  
Stability Properties ◽  
Stability Diagrams ◽  
Drill Bits ◽  
Variable Helix ◽  
The Stability

In the metal cutting industry it is well known that milling processes can be stabilized by applying different strategies in order to destroy the pure single delay regeneration that arise in case of conventional milling tools when high material removal rates are used either at low or at high cutting speeds. To achieve this goal, variable pitch angle, variable helix angle and serrated tools are already available in the market and serve alternative solutions for process designers to enhance milling process stability. Regeneration can occur and can cause instability on the tip of the deep drilling equipment when the drill bit is driven across hard earth crust materials. This work shows that theories introduced for milling processes can be implemented to improve the stability properties of deep drilling processes, too. Unlike in case of most milling processes, however, the stability properties of deep drilling are affected by the longitudinal and the torsional vibration modes. In this paper, the geometrical and mechanical models are derived for drill bits with general shapes of cutting edges and it is shown that the two DOF dynamics can be described by distributed state dependent delay differential equations. The stability properties are characterized in stability diagrams that can help to select the optimal drilling process parameters.

Stability in Variable-Pitch Milling Regarding Regenerative Chatter

2006 ◽  
Author(s):  
Nejat Olgac ◽  
Rifat Sipahi
Keyword(s):  
Cutting Tool ◽  
Milling Process ◽  
Depth Of Cut ◽  
Multiple Delays ◽  
Regenerative Chatter ◽  
Variable Pitch ◽  
Characteristic Roots ◽  
Analysis Methodology ◽  
Delay Differential ◽  
Critical Aspects

The regenerative chatter in milling process is studied for two different variable-pitch cutters one with (a) four flutes and the other with (b) six flutes. The cutting dynamics of the process is evaluated from stability perspective. Mathematically, the problem is recognized in a general class of delay differential equations (DDE) with multiple delays, whose stability can be analyzed by a recent stability analysis methodology called the Cluster Treatment of Characteristic Roots, CTCR. This method proves to be very beneficial to surface two critical aspects of the process, which maintain chatter-free cutting: (i) the pitch angle geometry of the cutting tool and (ii) admissible cutting conditions to determine the depth-of-cut and the spindle speeds. Case studies are provided to demonstrate the capabilities.

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