Floquet Theory Based Approach for Stability Analysis of the Variable Speed Face-Milling Process

2001 ◽  
Vol 124 (1) ◽  
pp. 10-17 ◽  
Author(s):  
Sridhar Sastry ◽  
Shiv G. Kapoor ◽  
Richard E. DeVor

This paper presents a new method for stability analysis of the variable spindle speed face milling process whose dynamics are described by a set of differential-difference equations with periodic coefficients and time varying time delay. Fourier analysis and Floquet theory applied to the system equations result in a characteristic equation of infinite order with constant coefficients. Its truncated version is used to determine the limit of stability by employing standard techniques of control theory. Analytically predicted stability boundaries are compared with lobes generated by time domain simulations. Experimental results are also presented that validate the proposed analytical method for chatter stability analysis. Finally, an example is presented that demonstrates the advantage of using spindle speed variation when machining a workpiece having multiple modes of vibration.

2018 ◽  
Vol 780 ◽  
pp. 105-110
Author(s):  
Ukrit Thanasuptawee ◽  
Chamrat Thakhamwang ◽  
Somsak Siwadamrongpong

In this study, there are three machining parameters consist of spindle speed, feed rate and depth of cut which were conducted through full factorial with four center points to determine the effect of machining parameters on the surface roughness and verify whether there is curvature in the model for CNC face milling process in an automotive components manufacturer in Thailand. The workpieces used semi-solid die casted ADC12 aluminum alloy crankcase housing which they were performed by the ARES SEIKI model R5630 3-axis CNC vertical machining center and face milling cutter with diameter of 63 millimeters. The surface roughness of face-milled was measured by the surface roughness tester. It was found that the greatest main effect influence to surface roughness was spindle speed, followed by feed rate and depth of cut at significance level of 0.05.


Author(s):  
Jinbo Niu ◽  
Ye Ding ◽  
LiMin Zhu ◽  
Han Ding

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.


Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6562
Author(s):  
Krzysztof J. Kaliński ◽  
Marek A. Galewski ◽  
Michał R. Mazur ◽  
Natalia Stawicka-Morawska

The paper presents an original method concerning the problem of vibration reduction in the general case while milling large-size and geometrically complex details with the use of an innovative approach to the selection of spindle speed. A computational model is obtained by applying the so-called operational approach to identify the parameters of the workpiece modal model. Thanks to the experimental modal analysis results, modal subsystem identification was performed and reliable process data for simulation studies were obtained. Next, simulations of the milling process, for successive values of the spindle speed, are repeated until the best vibration state of the workpiece is obtained. For this purpose, the root mean square values of the time plots of vibration displacements are examined. The effectiveness of the approach proposed for reducing vibrations in the process of face milling is verified on the basis of the results of appropriate experimental investigations. The economic profitability of the implementation of the operational technique in the production practice of enterprises dealing with mechanical processing is demonstrated as well.


2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Gang Jin ◽  
Xinyu Zhang ◽  
Kaifei Zhang ◽  
Hua Li ◽  
Zhanjie Li ◽  
...  

Dynamic stability problems leading to delay differential equations (DDEs) are found in many different fields of science and engineering. In this paper, a method for stability analysis of periodic DDEs with multiple distributed and time-varying delays is proposed, based on the well-known semidiscretization method. In order to verify the correctness of the proposed method, two typical application examples, i.e., milling process with a variable helix cutter and milling process with variable spindle speed, which can be, respectively, described by DDEs with the multidistributed and time-varying delays are considered. Then, comparisons with prior methods for stability prediction are made to verify the accuracy and efficiency of the proposed approach. As far as the milling process is concerned, the proposed method supplies a generalized algorithm to analyze the stability of the single milling systems associated with variable pith cutter, variable helix cutter, or variable spindle speed; it also can be utilized to analyze the combined systems of the aforementioned cases.


2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Ye Ding ◽  
Jinbo Niu ◽  
LiMin Zhu ◽  
Han Ding

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.


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