Numerical Research on Machining Stability Subject to Delayed PID Control

Author(s):  
Mingjie Li ◽  
Xiaojian Zhang ◽  
Yakun Xie

Machining stability analysis is important for chatter avoiding and production efficiency improvement. This paper conducts the numerical research on machining stability subject to delayed PID active control which is used to avoid chatter in machine milling. This control strategy is introduced into a two-degree-of-freedom milling system for illustration, the resulting hybrid system with both regenerative and feedback delays is represented as a delay-differential equation with time-periodic coefficients. From the comparison of stability region, it is found that the delayed PID control with proper parameters can lift the stability boundary largely compared with the case without control. To evaluate the stabilizability of the controlled system in cutting, the sensitivity of the stability boundary with respect to the PID parameters is analyzed. The numerical simulation of critical axial depth to PID parameters indicate that the milling stability critical boundary varies drastically with the derivative parameter. It also demonstrates that the stability critical boundary is strongly influenced by the proportional parameter, but it is less effected by the integral parameter. Hence, the stability domain can be expanded drastically with appropriate PID parameters based on the analysis above.

Author(s):  
Jirˇi´ Na´prstek

Slender structures exposed to a cross air flow are prone to vibrations of several types resulting from aeroelastic interaction of a flowing medium and a moving structure. Aeroelastic forces are the origin of nonconservative and gyroscopic forces influencing the stability of a system response. Conditions of a dynamic stability loss and a detailed analysis of a stability domain has been done using a linear mathematical model. Response properties of a system located on a stability boundary together with tendencies in its neighborhood are presented and interpreted from physical point of view. Results can be used for an explanation of several effects observed experimentally but remaining without theoretical explanation until now.


2013 ◽  
Vol 785-786 ◽  
pp. 1418-1422
Author(s):  
Ai Gao

In this paper, we provide a partition of the roots of a class of transcendental equation by using τ-D decomposition ,where τ>0,a>0,b<0 and the coefficient b is fixed.According to the partition, one can determine the stability domain of the equilibrium and get a Hopf bifurcation diagram that can provide the Hopf bifurcation curves in the-parameter space, for one dimension delay differential equation .


2013 ◽  
Vol 644 ◽  
pp. 123-128
Author(s):  
Ling Yu Sun ◽  
Jian Hua Zhang ◽  
Xiao Jun Zhang

The wheel-legged mobile robot in a complex three-dimensional environment has strong through capacity .Study is very critical for the stability of the control of their body systems. In this paper , based on analysis of the structure of wheel-legged mobile robot designed, the stability is evaluated by the use of (Effective Mass Center) EMC , and the stability domain is established accordingly. A fuzzy adaptive PID control method is created , and verified by ADAMS and MATLAB co-simulation . Simulation results show that the robot in different terrestrial environment, can maintain good stability.


10.14311/1400 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
O. N. Kirillov

Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.


2020 ◽  
Vol 62 (8) ◽  
pp. 484-492
Author(s):  
Kai Yang ◽  
Guofeng Wang ◽  
Kaile Ma

Chatter that occurs between a cutting tool and a workpiece greatly reduces the surface quality and production efficiency. Therefore, it is of great importance to predict and avoid chatter so as to guarantee the stability of the manufacturing process. To realise the accurate prediction of the stability boundary of machine tools, operational modal analysis (OMA) is increasingly receiving attention due to its adequate consideration of variations in working conditions in the industrial environment. However, because of the influence of harmonic components in the response signals, the accuracy in identifying the modal parameters is seriously compromised. In this paper, an adaptive complex Morlet filter (ACMF) is presented to remove the harmonic components by adaptively adjusting the centre frequency and bandwidth according to the local character of the ambient environment in a specific frequency range and filtering out harmonic components that are not strict integer multiples of the fundamental frequency owing to non-rigid periodic motion of the machine tool spindle. In order to show the effectiveness of the proposed method, milling experiments are carried out and experimental modal analysis (EMA) is utilised to make comparisons with the proposed method. Moreover, comparisons between the ACMF and two other typical filtering methods are made. The results indicate that the proposed method performs well in modal parameter recognition for machine tools.


2007 ◽  
Vol 2 (4) ◽  
pp. 360-365 ◽  
Author(s):  
Christoph Henninger ◽  
Peter Eberhard

Dynamic stability of cutting processes such as milling and turning is mainly restricted by the phenomenon of the regenerative effect, causing self-excited vibration, which is well known as machine-tool chatter. With the semidiscretization method for periodic delay-differential equations, there exists an appropriate method for determining the stability boundary curve in the domain of technological parameters. The stability boundary is implicitly defined as a level set of a function on the parameter domain, which makes the evaluation computationally expensive when using complete enumeration. In order to reduce computational cost, we first investigate two types of curve tracking algorithms finding them not appropriate for computing stability charts as they may get stuck at cusp points or near-branch zones. We then present a new curve tracking method, which overcomes these difficulties and makes it possible to compute stability boundary curves very efficiently.


Author(s):  
O. N. Kirillov

Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity–time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.


2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.


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