scholarly journals Stability of Milling Process with Variable Spindle Speed Using Runge–Kutta-Based Complete Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Shujie Lv ◽  
Yang Zhao
Keyword(s):  
Removal Rate ◽  
Modulation Frequency ◽  
Milling Process ◽  
Spindle Speed ◽  
Calculation Time ◽  
Time Varying Delay ◽  
Speed Modulation ◽  
Runge Kutta ◽  
The Stability ◽  
Delay Differential

The variable-spindle-speed (VSS) technique is effective in preventing regenerative chatter in milling processes. However, spindle-speed-modulation parameters should be deliberately selected to augment the material removal rate. Stability-prediction algorithms of stability predicting play an important role in this respect, as they allow the prediction of stability for all ranges of a given spindle speed. The increase in calculation time in variable-spindle-speed milling, which is caused by the modulation frequency, hinders its practical use in the workshop. In this paper, a Runge–Kutta-based complete discretization method (RKCDM) is presented to predict the stability of milling with variable spindle speeds, which is described by a set of delay differential equations (DDEs) with time-periodic coefficients and time-varying delay. The convergence and calculation efficiency are compared with those of the semidiscretization method (SDM) under different testing configurations and milling conditions. Results show that RKCDM is more accurate and saves at least 50% of the calculation time of SDM. The effects of modulation parameters on the stability of VSS milling are explored through stability lobe diagrams produced from RKCDM.

Stability Analysis of Turning With Periodic Spindle Speed Modulation Via Semidiscretization

2004 ◽  
Vol 10 (12) ◽  
pp. 1835-1855 ◽  
Author(s):  
Tamas Insperger ◽  
Gabor Stepan
Keyword(s):  
Modulation Frequency ◽  
Spindle Speed ◽  
Hopf Bifurcations ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Time Varying Delay ◽  
High Modulation ◽  
Speed Modulation ◽  
Delay Differential ◽  
Varying Delay

We investigate a single-degree-of-freedom model of turning with sinusoidal spindle speed modulation and the corresponding delay-differential equation with time-varying delay. The equation is analyzed by the numerical semidiscretization method. Stability charts and chatter frequencies are constructed. Improvement in the efficiency of machining is found for high modulation frequency and for low spindle speed domain. Period-one, period-two (flip), and secondary Hopf bifurcations were detected by eigenvalue analysis.

Spindle Speed Variation for Regenerative Chatter Suppression in Turning Process With Tool Wear Effect

2010 ◽  
Author(s):  
Kambiz Haji Hajikolaei ◽  
Masoud Rahaeifard ◽  
Gholamreza Vossoughi ◽  
Mohammadreza Movahhedy
Keyword(s):  
Tool Wear ◽  
Removal Rate ◽  
Spindle Speed ◽  
Turning Process ◽  
Machining Processes ◽  
Chatter Suppression ◽  
Spindle Speed Variation ◽  
Set Up ◽  
The Stability ◽  
Delay Differential

Chatter suppression in machining processes results in more material removal rate, high precision and surface quality. In this paper, a single degree of freedom model of orthogonal turning process is used to set up the delay differential equation of motion with considering the tool wear effect as a contact force between the workpiece and tool flank surfaces. Sinusoidal spindle speed variations with different frequencies around the mean speed are modulated to disturb the regenerative mechanism. The optimal amplitudes of the speed modulations are found based on a genetic algorithm such that the input energy to the turning process is minimized. Results of the stability analysis and the controller effect for two distinct cases of one and three sinusoidal speed are presented and compared.

Stability Analysis of a Variable Spindle Speed Milling Process

2005 ◽  
Author(s):  
X.-H. Long ◽  
B. Balachandran
Keyword(s):  
Milling Process ◽  
Spindle Speed ◽  
Depth Of Cut ◽  
Infinite Dimensional ◽  
Dimensional Matrix ◽  
Finite Dimensional ◽  
Milling Operations ◽  
Milling Operation ◽  
The Stability ◽  
Delay Differential

In this effort, a stability treatment is presented for a milling process with a variable spindle speed (VSS). This variation is caused by superimposing a sinusoidal modulation on a nominal spindle speed. The dynamics of the VSS milling process is described by a set of delay differential equations (DDEs) with time varying periodic coefficients and a time delay. A semi-discretization scheme is used to discretize the system over one period, and the infinite dimensional transition matrix is converted to a finite dimensional matrix over this period. The eigenvalues of this finite dimensional matrix are used to determine the stability of the VSS milling operation with respect to selected control parameters, such as the axis depth of cut and the nominal spindle speed. The benefits of VSS milling operations are discussed by comparing the stability charts obtained for VSS milling operations with those obtained for constant spindle speed (CSS) milling operations.

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.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Gang Jin ◽  
Haotian Jiang ◽  
Jianxin Han ◽  
Zhanjie Li ◽  
Hua Li ◽  
...  
Keyword(s):  
Phase Difference ◽  
Pitch Angle ◽  
High Speed ◽  
Helix Angle ◽  
Stability Domain ◽  
Milling Process ◽  
Spindle Speed ◽  
The Stability ◽  
The Time Domain ◽  
Milling Chatter

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.

scholarly journals A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Gang Jin ◽  
Houjun Qi ◽  
Zhanjie Li ◽  
Jianxin Han ◽  
Hua Li
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Spindle Speed ◽  
Multiple Time ◽  
Variable Pitch ◽  
Periodic Delay ◽  
The Stability ◽  
Delay Differential ◽  
Time Periodic ◽  
Periodic Delays

Delay differential equations (DDEs) are widely utilized as the mathematical models in engineering fields. In this paper, a method is proposed to analyze the stability characteristics of periodic DDEs with multiple time-periodic delays. Stability charts are produced for two typical examples of time-periodic DDEs about milling chatter, including the variable-spindle speed milling system with one-time-periodic delay and variable pitch cutter milling system with multiple delays. The simulations show that the results gained by the proposed method are in close agreement with those existing in the past literature. This indicates the effectiveness of our method in terms of time-periodic DDEs with multiple time-periodic delays. Moreover, for milling processes, the proposed method further provides a generalized algorithm, which possesses a good capability to predict the stability lobes for milling operations with variable pitch cutter or variable-spindle speed.

On the Investigation of Machine Tool Chatter in the Milling Process

2007 ◽  
Author(s):  
Mahsa Moghaddas ◽  
Mohammad H. Ghaffari Saadat
Keyword(s):  
Milling Process ◽  
Depth Of Cut ◽  
Non Linear Equation ◽  
Stability And Instability ◽  
Machine Tool Chatter ◽  
Stability Chart ◽  
Periodic Delay ◽  
The Stability ◽  
Two Parameters ◽  
Delay Differential

In this paper, the chatter phenomenon is investigated through a single degree of freedom model of the milling process. In this regard, the non-linear equation of motion obtained from modeling of the milling process, which is a time-periodic delay differential equation, is simulated, and by changing the parameters: spindle speed and depth of cut, and assuming constant quantities for other parameters of the system the stable and instable points for the system are gained according to these two parameters by numerical method. In the end, the stability chart for this system is plotted and the approximate boundaries between the stability and instability regions are obtained numerically.

scholarly journals Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Neutral Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Haiyan Yuan ◽  
Cheng Song ◽  
Peichen Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Stability ◽  
Delay Differential Equations ◽  
Stability And Convergence ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Restricted Type ◽  
Runge Kutta ◽  
The Stability ◽  
Delay Differential

This paper is devoted to the stability and convergence analysis of the two-step Runge-Kutta (TSRK) methods with the Lagrange interpolation of the numerical solution for nonlinear neutral delay differential equations. Nonlinear stability and D-convergence are introduced and proved. We discuss theGR(l)-stability,GAR(l)-stability, and the weakGAR(l)-stability on the basis of(k,l)-algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure.

Sign in / Sign up

Export Citation Format

Share Document