A predictor-corrector-based holistic-discretization method for accurate and efficient milling stability analysis

Currently, accurate and efficient determination of chatter-free cutting conditions is becoming increasingly important. This paper proposes a semi-analytical stability prediction method for milling processes using the holistic-interpolation scheme. The dynamics considering regeneration effect for milling operations is formulated as delay differential equations with time-periodic coefficients. The period of milling dynamic system is divided into two time periods according to the value of the coefficient matrix. On each small time interval for the forced vibration time period, the holistic-interpolation method is utilized by approximating the state term, the delay term, and the time-periodic parameter matrix as a whole unit with the second-order Lagrange interpolating polynomials. Then the Floquet transition matrix can be semi-analytically constructed for milling stability prediction according to Floquet theory. Finally, the benchmark examples of milling models are utilized to validate the effectiveness of the proposed method, which shows that the proposed algorithm achieves both high computational accuracy and efficiency.

Regenerative chatter easily occurs in milling and has become the common limitation to achieve good surface quality and high productivity. For the purpose of chatter avoidance, the structural effect of the thin-walled part should be considered for the milling chatter stability analysis for the optimization of axial cutting depth and spindle speed pairs. The main objective of this paper is to examine the link between the structural modes (i.e. modal shapes) and the chatter stability limits in the case of finish milling thin-walled workpieces. In this paper, the dynamic stability of the milling process of thin-walled workpieces is investigated through a two-degree-of-freedom mechanical model. The mathematical relationship between the critical axial depth and the thin-walled part modal shapes is deduced and an optimal calculation process of milling stability lobes is presented. Peripheral milling of aluminium alloy (2A70 Al) plates is carried out on a computer numerically controlled (CNC) five-axis super high-speed machining centre to validate the method. The experimental results agree with the prediction by the presented method. Additionally, the experimental results show that the cutting stability is also influenced by the modal frequencies of the thin-walled part, which have a great influence on the milling stability analysis when the tool passing frequency (i.e. the inverse of the tooth passing period) harmonics are close to the modal frequencies of the part. The presented method is effective in the prediction of milling chatter limits in the thin-walled case for the optimization of machining parameters.

Event-driven sorting algorithm-based Monte Carlo method with neighbour merging method for solving aerosol dynamics

Stability prediction with both high computational accuracy and speed is still a challenging issue and has been attracting significant attention from the academia and industry. This study presents a Legendre-Chebyshev-based stability analysis method (LCM) for milling operations. According to the cutting state, it divides the system period of milling model into the free and the forced vibration time periods. By introducing appropriate transformation, the latter time interval is further discretized nonuniformly into the Chebyshev-Gauss-Lobatto points, which has explicit expression. Then, the state term over the discrete time points is approximated with the Legendre expansion, and its corresponding derivative is acquired via a novel and efficient algorithm. Thereafter, Floquet matrix within the system period of milling model can be determined for predicting the system stability via the known Floquet theory. Finally, we validate the effectiveness of the LCM by employing the single and two degrees of freedom (DOF) milling operations and making detailed comparisons with the recent representative algorithms, which indicates that the presented Legendre-Chebyshev-based method has both high prediction accuracy and speed.

Chatter is the most obscuring phenomenon and significant amount of research has been documented regarding prediction, control and elimination of chatter. Chatter is still a main hindrance in achieving good surface finish and productivity. This paper presents the influence of helix angle of milling cutter in down-milling, up-milling and slotting operation. Altintas multi-frequency solution (MFS) is advanced by adding the impact of helix angle in milling forces. A comparison is made for stability lobes diagram based on the helix angle model for different helix angles against the Altintas multi-frequency solution model (MFS) and zero order approximation (ZOA) model. The comparison shows that for small helix angle the stability lobes follow the Altintas (MFS) model and for high helix angle the stability lobes follow the Altintas (ZOA) model. The experimental results prove the simulations. Introduction

Chapter 7 - Overview of stability analysis methods in power electronics

The influence of cryogenic cooling on milling stability

Due to the internal dynamics of the modular multilevel converter (MMC), the coupling between the positive and negative sequences in impedance, which is defined as frequency coupling, inherently exists in MMC. Ignoring the frequency coupling of the MMC impedance model may lead to inaccurate stability assessment, and thus the multi-input multi-output (MIMO) impedance model has been developed to consider the frequency coupling effect. However, the generalized Nyquist criterion (GNC), which is used for the stability analysis of an MIMO model, is more complicated than the stability analysis method applied on single-input-single-output (SISO) models. Meanwhile, it is not always the case that the SISO model fails in the stability assessment. Therefore, the conditions when the MIMO impedance model needs to be considered in the stability analysis of an MMC system should be analyzed. This paper quantitatively analyzes the effect of frequency coupling on the stability analysis of grid-connected MMC, and clarifies the frequency range and grid conditions that the coupling effect required to be considered in the stability analysis. Based on the quantitative relations between the frequency coupling and the stability analysis of the grid-connected MMC system, a simple and accurate stability analysis method for the grid-connected MMC system is proposed, where the MIMO impedance model is applied when the frequency coupling has a significant effect and the SISO impedance model is used if the frequency coupling is insignificant.

Earthquake is one of the primary factors that triggers the failure of slopes and the landslides in the mountainous area. In this study, an efficient method for the seismic slope stability analysis and seismic failure process simulation is proposed. The seismic slope stability and the failure process of a two-dimensional slope model are analyzed via the explicit finite element method with the influence of the dynamic mechanical behavior of soil and the frictional resistance characteristic of the slope rupture surface. A dynamic visco-elasto-plastic constituted model for soil is established and written in FORTRAN as a user subroutine of the finite element method code of ABAQUS. The validation of the visco-elasto-plastic constituted model and the explicit finite element method are compared with the experimental results and the implicit method. The seismic factor of safety and the sliding distance of the soil slopes under the natural earthquake conditions are calculated via the dynamic visco-elasto-plastic constituted model and the explicit finite element method. The influence of the ground motion characteristics on the seismic slope stability is analyzed in this study via the specified elastic response acceleration spectrum. The analysis results of this paper suggest that the seismic slope stability analysis and the progressive failure process of the slope under the seismic condition can be analyzed by the explicit finite element method efficiently. The results show that the dynamic mechanical behavior of soil and the ground motion characteristics are both critical influence factors for the seismic slope stability. The frictional resistance characteristic of the slope rupture surface is the principal influence factor for the sliding distance of the slope, and it also has more influence on the sliding distance of a high slope than that of the small slope.

The high penetration of power electronic converters with complex control systems is changing the power system dynamics, introducing new challenges such as converter-driven stability incidents. Traditional stability analysis methods, suitable for classical problems like voltage, frequency, and rotor angle stability in large systems, are insufficient for addressing the fast control dynamics of converters, which involve electromagnetic phenomena. These phenomena require detailed converter and network modeling, which can be performed in both the frequency and time domains, enabling the respective stability analyses to be carried out. However, frequency domain methods, based on small-signal impedances linearized at a single operating point, inherently ignore time domain phenomena like switching events and nonlinear behaviors. In contrast, time domain electromagnetic transient (EMT) simulations are effective for analyzing converter-driven stability but are computationally intensive when applied to large transmission systems with numerous use cases. Therefore, to reduce the simulation complexity in EMT tools, a complexity reduction procedure is proposed in this paper. Leveraging the advantages of the frequency domain, such as faster simulation times and information on wideband frequency characteristics of the system, this procedure utilizes the small-signal impedances and introduces a method for network reduction. The procedure also uses the frequency domain stability analysis method to screen for critical network use cases. Primarily, this procedure is a frequency domain toolchain encompassing frequency domain stability analysis and frequency domain network reduction. The result of the toolchain is a reduced network size and reduced network use cases that can be used for EMT simulations. The procedure is applied to an IEEE 39 bus system, where converter-driven stability is evaluated for two use cases. Furthermore, the network reduction method is tested on a critical use case, demonstrating reductions in network size and computation times without compromising the quality of stability analysis results.

According to the interaction between the inverter and the grid in the large-scale photovoltaic grid-connected system, an auxiliary system based on grid connection of a single inverter is introduced. Research shows that the stability of the inverter output current in large-scale photovoltaic grid-connected systems depends on the stability of the auxiliary system and the stability of the inverter itself. But the stability of the total grid-connected current depends only on the stability of the auxiliary system. Therefore, a method for stability analysis of large-scale photovoltaic grid-connected systems is proposed. For a large-scale photovoltaic grid-connected system that is connected to the ideal grid through the grid impedance Zg after the inverters of the same specification and model are connected in parallel, the stable determination conditions are: (1) The inverter itself is stable, that is, a single inverter is stable when it is directly connected to the ideal power grid; (2) A single inverter in a large-scale PV grid-connected system is stable through the grid impedance nZg to the ideal grid. The stability analysis method can transform the research on the stability of large-scale photovoltaic grid-connected systems into the stability of the grid-connected system of a single inverter. For the multi-inverter parallel grid-connected system with uniform specifications and models, the stability analysis method is applicable regardless of whether all inverter current loop input reference currents are identical. The simulation results verify the correctness of the theoretical analysis.

This paper extends small-signal stability analysis methods developed for balanced three-phase systems to the more general unbalanced three-phase system. The impedance-based stability analysis method in the phase-domain is generalized to unbalanced systems characterized by coupled positive-sequence and negative-sequence impedance networks. Compared to balanced three-phase systems, modeling of unbalanced converter systems is more complicated due to the negative-sequence trajectory that is impressed on the ac system by the unbalanced condition. Small-signal models are developed to determine whether or not a small unbalance voltage condition introduces any significant change to the inverter impedance models of the perfectly balanced case. Simulation and experimental measurements are used for verification of the small-signal models and the proposed stability analysis method.

The performance of the stability chart (SC), limit equilibrium (LE), and finite element (FE) methods for stability analysis of weathered volcanic rock slopes under static and earthquake loads is not fully understood. This research aimed to evaluate the performance of the SC, LE, and FE methods for slope stability analyses by studying a case of a weathered volcanic rock slope at the Leuwikeris Dam diversion tunnel in Indonesia. Site characterisations were carried out to obtain the input parameters for the static and pseudostatic slope stability analyses. The results showed that using various search methods of failure surface and the suggested optimum number of finite elements, multiple non-circular failure surfaces were predicted from the LE and FE methods that were not anticipated in the initial slope design based on the SC method. The location and shape of the failure surfaces from the LE method agreed with those from the FE method. The difference between the Fs values from the static LE analysis and those from the static FE analyses was less than 14%, but the discrepancy increased up to 78% in the pseudostatic analyses. This study highlights the importance of validating the results from one method with the other methods to prevent slope failures.

It is shown that the return difference matrix possesses the same functions and plays the same important role in stability analysis and design of a multivariable feedback network as it does in control theory. The generalized Nyquist criterion, characteristic loci and other methods of stability analysis and design for multivariable feedback systems in control theory are applicable directly to multivariable feedback networks. In particular, a general frequency stability criterion for a multivariable lumped and distributed-parameter feedback network is presented.

Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances.Important conclusions and decisions are made based on the results of stability studies.The conventional method of analyzing stability is to calculate the transient behaviour of generators due to a given disturbance.Direct methods of stability analysis identify whether or not the system will remain stable once the disturbance is removed by comparing it with a calculated threshold value.Direct methods not only avoid the time consuming solutions required in the conventional method, but also provide a quantitative measure of the degree of system stability.This additional information makes direct methods very attractive when the relative stability of different plans must be compared or when stability limits must be calculated quickly.Direct methods of transient stability analysis of a multi machine power system, using a function describing the system's transient energy, are discussed.By examining the trajectory of the disturbed system, the following fundamental questions are dealt with: the concept of a controlling unstable equilibrium point (U.E.P), the manner in which some generators tend to lose synchronism, and identifying the energy directly responsible for system separation.Resolving this issue will substantially improve transient stability analysis by direct method.