Stability Analysis of Milling Processes With Periodic Spindle Speed Variation Via the Variable-Step Numerical Integration Method

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Jinbo Niu ◽  
Ye Ding ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Spindle Speed ◽  
Numerical Integration Method ◽  
Speed Variation ◽  
Spindle Speed Variation ◽  
Variable Step ◽  
Modulation Schemes ◽  
The Stability

This paper proposes a general method for the stability analysis and parameter optimization of milling processes with periodic spindle speed variation (SSV). With the aid of Fourier series, the time-variant spindle speeds of different periodic modulation schemes are unified into one framework. Then the time-varying delay is derived implicitly and calculated efficiently using an accurate ordinary differential equation (ODE) based algorithm. After incorporating the unified spindle speed and time delay into the dynamic model, a Floquet theory based variable-step numerical integration method (VNIM) is presented for the stability analysis of variable spindle speed milling processes. By comparison with other methods, such as the semi-discretization method and the constant-step numerical integration method, the proposed method has the advantages of high computational accuracy and efficiency. Finally, different spindle speed modulation schemes are compared and the modulation parameters are optimized with the aid of three-dimensional stability charts obtained using the proposed VNIM.

Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ye Ding ◽  
Jinbo Niu ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Numerical Integration ◽  
Integration Method ◽  
Transcendental Equation ◽  
Spindle Speed ◽  
Machining Parameters ◽  
Numerical Integration Method ◽  
Stability Diagrams ◽  
Time Period

A semi-analytical method is presented in this paper for stability analysis of milling with a variable spindle speed (VSS), periodically modulated around a nominal spindle speed. Taking the regenerative effect into account, the dynamics of the VSS milling is governed by a delay-differential equation (DDE) with time-periodic coefficients and a time-varying delay. By reformulating the original DDE in an integral-equation form, one time period is divided into a series of subintervals. With the aid of numerical integrations, the transition matrix over one time period is then obtained to determine the milling stability by using Floquet theory. On this basis, the stability lobes consisting of critical machining parameters can be calculated. Unlike the constant spindle speed (CSS) milling, the time delay for the VSS is determined by an integral transcendental equation which is accurately calculated with an ordinary differential equation (ODE) based method instead of the formerly adopted approximation expressions. The proposed numerical integration method is verified with high computational efficiency and accuracy by comparing with other methods via a two-degree-of-freedom milling example. With the proposed method, this paper details the influence of modulation parameters on stability diagrams for the VSS milling.

Effiziente Ermittlung von Stabilitätsgrenzen*/Detection of stability boundaries during milling

2017 ◽  
Vol 107 (05) ◽  
pp. 313-317
Author(s):  
C. Prof. Brecher ◽  
P. Chavan ◽  
A. Epple
Keyword(s):  
Stability Boundary ◽  
Spindle Speed ◽  
Wird Eine ◽  
Chatter Detection ◽  
Speed Variation ◽  
Spindle Speed Variation ◽  
Detection Software ◽  
The Stability ◽  
Stability Limits

Um Stabilitätskarten für Fräsprozesse effizient zu erstellen, bietet sich eine kontinuierliche Variation der Drehzahl an. Jedoch kann die permanente Änderung der Drehzahl zu einer Verfälschung der tatsächlichen Stabilitätsgrenzen führen. Dieser Fachbeitrag analysiert den Einfluss der Spindeldrehzahlvariation auf die Stabilitätsgrenzen bei Fräsversuchen mit verschiedenen Drehzahlbeschleunigungen. Für das Erkennen der Stabilitätsübergänge wird eine Rattererkennungssoftware eingesetzt.   Milling with varying spindle speed allows an efficient determination of instabilities. However, spindle speed variation may also influence the actual stability boundary with constant spindle speed. This paper analyzes the influence of spindle speed variation on the stability limits by evaluating milling trials at different spindle accelerations. For the detection of instability and stability during cutting trials, a time-domain chatter detection software was enhanced, validated and implemented.

Machine-Tool Chatter Suppression by Multi-Level Random Spindle Speed Variation

1999 ◽  
Author(s):  
Alpay Yilmaz ◽  
Emad AL-Regib ◽  
Jun Ni
Keyword(s):  
Spindle Speed ◽  
New Method ◽  
Spindle System ◽  
Speed Variation ◽  
Chatter Suppression ◽  
Random Fashion ◽  
Spindle Speed Variation ◽  
Machine Tool Chatter ◽  
Multi Level ◽  
The Stability

Abstract This paper presents a new method for varying the spindle speed to suppress chatter in machining. The spindle speed is varied in pseudo-random fashion within the bandwidth of the spindle system. Both implementation issues and spindle system responses to such signals are investigated. A new method to analyze the stability of machining systems with varying spindle speed is also introduced. The effectiveness and advantages of the random spindle speed variation in chatter suppression is verified using numerical simulations and experiments.

Machine Tool Chatter Suppression by Multi-Level Random Spindle Speed Variation

2002 ◽  
Vol 124 (2) ◽  
pp. 208-216 ◽  
Author(s):  
Alpay Yilmaz ◽  
Emad AL-Regib ◽  
Jun Ni
Keyword(s):  
Spindle Speed ◽  
New Method ◽  
Spindle System ◽  
Speed Variation ◽  
Chatter Suppression ◽  
Random Fashion ◽  
Spindle Speed Variation ◽  
Machine Tool Chatter ◽  
Multi Level ◽  
The Stability

This paper presents a new method for varying the spindle speed to suppress chatter in machining. The spindle speed is varied in a pseudo-random fashion within the bandwidth of the spindle system. Both implementation issues and spindle system responses to such signals are investigated. A new method to analyze the stability of machining systems with varying spindle speed is also introduced. The effectiveness and advantages of the random spindle speed variation in chatter suppression is verified using numerical simulations and experiments.

Stability Analysis of Machining with Spindle Speed Variation

2011 ◽  
Vol 223 ◽  
pp. 600-609 ◽  
Author(s):  
Andreas Otto ◽  
Gerhard Kehl ◽  
Michael Mayer ◽  
Günter Radons
Keyword(s):  
Spindle Speed ◽  
Time Varying ◽  
Exact Methods ◽  
Speed Variation ◽  
Time Varying Delay ◽  
Stability Lobes ◽  
Milling Operations ◽  
Spindle Speed Variation ◽  
The Stability ◽  
Varying Delay

In this paper the chatter stability of turning and full-immersion milling operations with spindle speed variation is studied. We present a method to calculate the stability lobes in the limit of very low and very high frequencies of the delay modulation. These approximations help to classify the results of numerically exact methods, as for example semi-discretization or multi-frequency approaches. For slowly time-varying delay, the position of the stability lobes is understandable from a simple connection between the lobes for constant and time-varying delay. Furthermore, this method can be used to estimate the efficiency of an application of spindle speed variation and helps to find optimal parameters for it.

scholarly journals On the stability of high-speed milling with spindle speed variation

2009 ◽  
Vol 48 (9-12) ◽  
pp. 883-895 ◽  
Author(s):  
Sébastien Seguy ◽  
Tamás Insperger ◽  
Lionel Arnaud ◽  
Gilles Dessein ◽  
Grégoire Peigné
Keyword(s):  
High Speed ◽  
Spindle Speed ◽  
High Speed Milling ◽  
Speed Variation ◽  
Spindle Speed Variation ◽  
The Stability

scholarly journals Control of Chatter by Spindle Speed Variation in High-Speed Milling

2010 ◽  
Vol 112 ◽  
pp. 179-186 ◽  
Author(s):  
Sébastien Seguy ◽  
Gilles Dessein ◽  
Lionel Arnaud ◽  
Tamás Insperger
Keyword(s):  
High Speed ◽  
Spindle Speed ◽  
High Speed Milling ◽  
Speed Variation ◽  
Milling Operations ◽  
Spindle Speed Variation ◽  
Machine Tool Chatter ◽  
Parametric Studies ◽  
Sinusoidal Shape ◽  
The Stability

High-speed milling operations are often limited by regenerative vibrations. The aim of this paper is to analyze the effect of spindle speed variation on machine tool chatter in high-speed milling. The stability analysis of triangular and sinusoidal shape variations is made numerically with the semi-discretization method. Parametric studies show also the influence of the frequency and amplitude variation parameters. This modeling is validated experimentally by variable spindle speed cutting tests with a triangular shape. Stable and unstable tests are analyzed in term of amplitude vibration and surface roughness degradation. This work reveals that stability must be considered at period variation scale. It is also shown that spindle speed variation can be efficiently used to suppress chatter in the flip lobe area.

The Effect of Spindle Speed Variation on Chatter Suppression in Rotating-Tool Machining

2006 ◽  
Vol 505-507 ◽  
pp. 859-864 ◽  
Author(s):  
Chen Jung Li ◽  
A.G. Ulsoy ◽  
W.J. Endres
Keyword(s):  
Spindle Speed ◽  
System Stability ◽  
Constant Delay ◽  
Machining Processes ◽  
Speed Variation ◽  
Chatter Suppression ◽  
Spindle Speed Variation ◽  
Common Process ◽  
The Stability ◽  
Stability Limits

Spindle speed variation (SSV) is one of a number of promising strategies to suppress chatter. Most previous research on SSV stability analysis for nonintermittent machining processes has focused on stationary-bar boring or turning. However, nonintermittent rotating-tool machining is also a common process. This paper investigates the effect of SSV in nonintermittent rotating-tool machining, using rotating-bar boring as an example. This paper takes advantage of the rotating-frame approach and the resulting constant delay in the angle domain to investigate the SSV effect on system stability for rotating-bar boring. The results show that the SSV effect on rotating-bar boring flattens the stability lobes and lifts the tangential stability limits.

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