scholarly journals Stability of High-Speed Milling

2000 ◽  
Author(s):  
Tamás Insperger ◽  
Gábor Stépán
Keyword(s):  
Parametric Excitation ◽  
Stability Criterion ◽  
High Speed ◽  
Period Doubling ◽  
Flip Bifurcation ◽  
Vibration Frequencies ◽  
High Speed Milling ◽  
Low Speed ◽  
The Stability ◽  
Excitation Model

Abstract The stability charts of high-speed milling are constructed. Non-conventional unstable regions and vibration frequencies are identified. These are related to flip bifurcation, i.e. period doubling vibrations occur apart of the conventional self-excited vibrations typical for turning or low-speed milling with multiple active teeth. A new stability criterion is proposed and applied for the delayed parametric excitation model of milling.

Vibration Frequencies in High-Speed Milling Processes or a Positive Answer to Davies, Pratt, Dutterer and Burns

2004 ◽  
Vol 126 (3) ◽  
pp. 481-487 ◽  
Author(s):  
T. Insperger ◽  
G. Ste´pa´n
Keyword(s):  
High Speed ◽  
Period Doubling ◽  
Flip Bifurcation ◽  
Vibration Frequencies ◽  
High Speed Milling ◽  
Machine Tool Chatter ◽  
Special Cases ◽  
Universal Approach ◽  
The Stability ◽  
Excitation Model

The stability charts of high-speed milling are constructed. New unstable regions and vibration frequencies are identified. These are related to flip bifurcation, i.e. period doubling vibrations occur apart of the conventional self-excited vibrations well-known for turning or low-speed milling with multiple active teeth. The Semi-Discretization method is applied for the delayed parametric excitation model of milling providing the connection of the two existing and experimentally verified results of machine tool chatter research. The two extreme models in question, that is, the traditional autonomous delayed model of time-independent turning, and the recently introduced discrete map model of time-dependent highly interrupted machining, are both involved as special cases in the universal approach presented in this study.

Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments

2004 ◽  
Vol 127 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Gabor Stepan ◽  
Robert Szalai ◽  
Brian P. Mann ◽  
Philip V. Bayly ◽  
Tamas Insperger ◽  
...  
Keyword(s):  
Small Parameter ◽  
High Speed ◽  
Period Doubling ◽  
Hopf Bifurcations ◽  
Cutting Condition ◽  
Flip Bifurcation ◽  
Machining Parameters ◽  
High Speed Milling ◽  
The Stability ◽  
Discrete Mathematical Model

High-speed milling is often modeled as a kind of highly interrupted machining, when the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model, playing an essential role in machine tool vibrations, breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe-doubling is related to the appearance of period doubling vibrations originated in a flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the Neimark-Sacker bifurcations related to the classical self-excited vibrations or Hopf bifurcations. The present work investigates the nonlinear vibrations in the case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. The identification of the global attractor in the case of unstable cutting leads to contradiction between experiments and theory. This contradiction draws the attention to the limitations of the small parameter approach related to the highly interrupted cutting condition.

Global Attractors of High-Speed Milling: Analyses, Numerics and Experiments

2003 ◽  
Author(s):  
Gabor Stepan ◽  
Robert Szalai ◽  
Brian P. Mann ◽  
Philip V. Bayly ◽  
Tamas Insperger ◽  
...  
Keyword(s):  
Small Parameter ◽  
High Speed ◽  
Period Doubling ◽  
Global Attractors ◽  
Hopf Bifurcations ◽  
Cutting Condition ◽  
Flip Bifurcation ◽  
Machining Parameters ◽  
High Speed Milling ◽  
Discrete Mathematical Model

High-speed milling is often modeled as a kind of highly interrupted machining, when the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model, playing an essential role in machine tool vibrations, breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe-doubling is related to the appearance of period doubling vibrations originated in a flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the Neimark-Sacker bifurcations related to the classical self-excited vibrations or Hopf bifurcations. The present work investigates the nonlinear vibrations in case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. The identification of the global attractor in case of unstable cutting leads to contradiction between experiments and theory. This contradiction draws the attention to the limitations of the small parameter approach related to the highly interrupted cutting condition.

Stability Boundaries of High-Speed Milling Corresponding to Period Doubling Are Essentially Closed Curves

Manufacturing ◽  
2003 ◽  
Author(s):  
Ro´bert Szalai ◽  
Ga´bor Ste´pa´n
Keyword(s):  
Characteristic Function ◽  
High Speed ◽  
Period Doubling ◽  
Stability Boundaries ◽  
Closed Curves ◽  
High Speed Milling ◽  
Complex Roots ◽  
Stability Chart ◽  
The Stability ◽  
Special Case

In this paper a new method for the stability analysis of high-speed milling processes is introduced. The approach is based on the construction of a characteristic function whose complex roots determine the stability of the system. By using the argument principle, the number of roots causing instability can be counted, and thus, an exact stability chart can be drawn. In the special case of period doubling bifurcation, the corresponding multiplier −1 is substituted into the characteristic function leading to an implicit formula of the stability boundaries. Further investigations show that all the period doubling boundaries are closed curves, except the first lobe at the highest cutting speeds. Together with the stability boundaries of Neimark-Sacker (or secondary Hopf) bifurcations, the unstable parameter domains are formed from the union of lobes and lenses.

An adaptive sliding mode controller for the lateral control of articulated long vehicles

2018 ◽  
Vol 233 (3) ◽  
pp. 487-515 ◽  
Author(s):  
Naser Esmaeili ◽  
Reza Kazemi ◽  
S Hamed Tabatabaei Oreh
Keyword(s):  
High Speed ◽  
Sliding Mode ◽  
Sliding Mode Controller ◽  
Lane Change ◽  
Lateral Velocity ◽  
Low Speed ◽  
Adaptive Sliding Mode ◽  
Adaptive Sliding Mode Controller ◽  
Articulated Vehicle ◽  
The Stability

Today, use of articulated long vehicles is surging. The advantages of using large articulated vehicles are that fewer drivers are used and fuel consumption decreases significantly. The major problem of these vehicles is inappropriate lateral performance at high speed. The articulated long vehicle discussed in this article consists of tractor and two semi-trailer units that widely used to carry goods. The main purpose of this article is to design an adaptive sliding mode controller that is resistant to changing the load of trailers and measuring the noise of the sensors. Control variables are considered as yaw rate and lateral velocity of tractor and also first and second articulation angles. These four variables are regulated by steering the axles of the articulated vehicle. In this article after developing and verifying the dynamic model, a new adaptive sliding mode controller is designed on the basis of a nonlinear model. This new adaptive sliding mode controller steers the axles of the tractor and trailers through estimation of mass and moment of inertia of the trailers to maintain the stability of the vehicle. An articulated vehicle has been exposed to a lane change maneuver based on the trailer load in three different modes (low, medium and high load) and on a dry and wet road. Simulation results demonstrate the efficiency of this controller to maintain the stability of this articulated vehicle in a low-speed steep steer and high-speed lane change maneuvers. Finally, the robustness of this controller has been shown in the presence of measurement noise of the sensors. In fact, the main innovation of this article is in the designing of an adaptive sliding mode controller, which by changing the load of the trailers, in high-speed and low-speed maneuvers and in dry and wet roads, has the best performance compared to conventional sliding mode and linear controllers.

1997 Best Paper Award—Turbomachinery Committee: A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1998 ◽  
Vol 120 (3) ◽  
pp. 393-401 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Short Length ◽  
Operating Conditions ◽  
Length Scale ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms in a low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short length-scale disturbance known as a “spike,” and the second with a longer length-scale disturbance known as a “modal oscillation.” In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented that relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: Long length-scale disturbances are related to a two-dimensional instability of the whole compression system, while short length-scale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed that explains the type of stall inception pattern observed in a particular compressor. Measurements from a single-stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

Study on the Stability of High-Speed Milling of Thin-Walled Workpiece

2010 ◽  
Vol 97-101 ◽  
pp. 1849-1852
Author(s):  
Tong Yue Wang ◽  
Ning He ◽  
Liang Li
Keyword(s):  
Aluminum Alloy ◽  
Machine Tool ◽  
High Speed ◽  
Modal Parameters ◽  
Inertia Effect ◽  
Cutting Force Coefficients ◽  
High Speed Milling ◽  
Machining System ◽  
Thin Walled ◽  
The Stability

Thin-walled structure is easy to vibrate in machining. The dynamic milling model of thin-walled workpiece is analyzed based on the analysis of degrees in two perpendicular directions of machine tool-workpiece system. In high speed milling of 2A12 aluminum alloy, the compensation method based on the modification of inertia effect is proposed and accurate cutting force coefficients are obtained. The machining system is divided into “spindle-cutter” and “workpiece-fixture” two sub-systems and the modal parameters of two sub-systems are acquired via modal analysis experiments. Finally, the stability lobes for high speed milling of 2A12 thin-walled workpiece are obtained by the use of these parameters. The results are verified against cutting tests.

A Study of Spike and Modal Stall Phenomena in a Low-Speed Axial Compressor

1997 ◽  
Author(s):  
T. R. Camp ◽  
I. J. Day
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Stability Criteria ◽  
Stall Inception ◽  
Low Speed ◽  
The Stability ◽  
Dimensional Instability

This paper presents a study of stall inception mechanisms a in low-speed axial compressor. Previous work has identified two common flow breakdown sequences, the first associated with a short lengthscale disturbance known as a ‘spike’, and the second with a longer lengthscale disturbance known as a ‘modal oscillation’. In this paper the physical differences between these two mechanisms are illustrated with detailed measurements. Experimental results are also presented which relate the occurrence of the two stalling mechanisms to the operating conditions of the compressor. It is shown that the stability criteria for the two disturbances are different: long lengthscale disturbances are related to a two-dimensional instability of the whole compression system, while short lengthscale disturbances indicate a three-dimensional breakdown of the flow-field associated with high rotor incidence angles. Based on the experimental measurements, a simple model is proposed which explains the type of stall inception pattern observed in a particular compressor. Measurements from a single stage low-speed compressor and from a multistage high-speed compressor are presented in support of the model.

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